SM-11827: Preliminary Design of an Experimental World-Circling Spaceship. PAGES: , DATE: 1946 COST: $25.00 ISBN: 083302672 KEYS: Artificial satellites ABST: An engineering analysis of the possibilities of designing an earth-circling satellite vehicle. The analysis considers power plants, structural weights, multiple stages, optimum design values, trajectories, stability, and landing. RM-5-PR: Randomness. AUTH: O. Helmer PAGES: 4, DATE: 1947 COST: $ 4.00 ABST: No abstract available. 4 pp. RM-10-PR: An Experiment in Estimation. AUTH: O. Helmer PAGES: 3, DATE: 1947 COST: $ 4.00 ABST: No abstract available. 3 pp. RM-40-PR: A "Semi-Poisson" Distribution. AUTH: H.H. Germond PAGES: 7, DATE: 1948 COST: $ 4.00 ABST: No abstract available. 7 pp. RM-74-PR: A Differential Equation with Random Shocks. AUTH: T.E. Harris, E.W. Paxson PAGES: 8, DATE: 1948 COST: $ 4.00 ABST: No abstract available. 8 pp. RM-87-PR: Examination of Some Models of Failure of Equipment During Operation. AUTH: D.J. Davis, W.J. Howard PAGES: 30, DATE: 1948 COST: $ 4.00 ABST: No abstract available. 30 pp. RM-92-PR: Forecast of Production Time. AUTH: H.H. Germond PAGES: 8, DATE: 1949 COST: $ 4.00 ABST: No abstract available. 8 pp. RM-97-PR: Hermite Polynomials of Imaginary Argument. AUTH: H.H. Germond PAGES: 15, DATE: 1949 COST: $ 4.00 ABST: No abstract available. 15 pp. RM-100-PR: A General Problem in the Calculus of Variations with Applications to Paths of Least Time. AUTH: M.R. Hestenes PAGES: 46, DATE: 1950 COST: $ 4.00 ABST: No abstract available. 46 pp. RM-101-PR: A Hidden-Target Model. AUTH: L.S. Shapley PAGES: 12, DATE: 1949 COST: $ 4.00 KEYS: Game theory; Targets ABST: A description of a game between two players, which is a variant of "Button, button." One player has an object of great value which he may conceal in one of two containers. The other attempts to destroy the object by destroying the containers. 12 pp. RM-111-PR: An Asymptotic Distribution for a Mortality Problem. AUTH: A.M. Mood PAGES: 9, DATE: 1949 COST: $ 4.00 KEYS: Life cycle costing; Numerical methods and approximations; Reliability ABST: A study of the phase of the estimation problem which determines the average life and replacement rate for physical items or assemblies. 9 pp. Ref. RM-118-PR: Note on Duels with Continuous Firing. AUTH: L.S. Shapley PAGES: 5, DATE: 1949 COST: $ 4.00 KEYS: Duels; Game theory ABST: A proof that mixed strategies need not be considered in certain duel situations, provided there may be a continuously variable rate of fire. 5 pp. RM-131-PR: The Noisy Duel, One Bullet Each, Arbitrary Non-Monotone Accuracy. AUTH: D.H. Blackwell PAGES: 7, DATE: 1949 COST: $ 4.00 KEYS: Duels; Game theory ABST: Solution of a game which is the essential element of all duels with perfect information. 7 pp. RM-133-PR: Expected Overlap. AUTH: H.H. Germond PAGES: 10, DATE: 1949 COST: $ 4.00 ABST: No abstract available. 10 pp. RM-134-PR: An Approximate Solution for a Coverage Problem. AUTH: H.H. Germond PAGES: 8, DATE: 1949 COST: $ 4.00 ABST: No abstract available. 8 pp. RM-135-PR: Estimation of Mortality Parameters. AUTH: G.W. Brown PAGES: 4, DATE: 1949 COST: $ 4.00 ABST: No abstract available. 4 pp. RM-145-PR: Target Coverage. AUTH: H.H. Germond PAGES: 5, DATE: 1949 COST: $ 4.00 ABST: No abstract available. 5 pp. RM-148-PR: Some Comments on an Estimation Problem for Contaminated Populations. AUTH: J.E. Walsh PAGES: 5, DATE: 1949 COST: $ 4.00 KEYS: Numerical methods and approximations; Statistical analysis ABST: The title of this Memorandum describes its content. 5 pp. RM-163-PR: Area Coverage with Ordinary Bombs. AUTH: H.H. Germond PAGES: 6, DATE: 1949 COST: $ 4.00 ABST: No abstract available. 6 pp. RM-165-PR: A Bomber-Fighter Duel. AUTH: R.E. Bellman, D.H. Blackwell PAGES: 7, DATE: 1949 COST: $ 4.00 KEYS: Aerial combat; Duels; Game theory ABST: A study of a duel in which a fighter, capable of firing a single rocket burst, attacks a bomber, which defends itself by firing intermittently. (See supplement, RM-193.) 7 pp. RM-177-PR: On the Usefulness of Artificial Dispersion for a Certain Bombing Problem. AUTH: J.E. Walsh PAGES: 5, DATE: 1949 COST: $ 4.00 ABST: A derivation of criterion to ascertain the cases in which artificial dispersion is useful in maximizing expected target coverage. RM-181-PR: An Upper Limit to Cycle-Length in a Sequence of Digit Groups. AUTH: H.H. Germond PAGES: 5, DATE: 1949 COST: $ 4.00 ABST: No abstract available. 5 pp. RM-184-PR: An Apparent Ambiguity in the Interpretation of Minimum Risk. AUTH: L.J. Savage PAGES: 4, DATE: 1949 COST: $ 4.00 KEYS: Risk ABST: A proof that it is in a sense equivalent to work with a mixed risk in the doctrine of minimum risk. 4 pp. RM-191-PR: Expected Coverage When All Bombs Are Aimed at the Center of the Target. AUTH: H.H. Germond PAGES: 7, DATE: 1949 COST: $ 4.00 ABST: No abstract available. 7 pp. RM-193-PR: A Bomber-Fighter Duel: II. AUTH: D.H. Blackwell, M. Shiffman PAGES: 10, DATE: 1949 COST: $ 4.00 KEYS: Aerial combat; Duels; Game theory ABST: A supplement to RM-165. 10 pp. RM-195-PR: The Problem of Cunningham and Hynd. AUTH: D.A. Darling PAGES: 21, DATE: 1949 COST: $ 4.00 KEYS: Stochastic processes; Survivability; Survival; Targets ABST: An investigation to determine the mean survival time and survival probability of a target from a burst of shots. The aim of the gunner is assumed to be a stochastic wandering process around the center of a target. 21 pp. RM-197-PR: Application of Theory of Games to Identification of Friend and Foe. AUTH: R.E. Bellman, D.H. Blackwell, J.P. Lasalle PAGES: 16, DATE: 1949 COST: $ 4.00 KEYS: Game theory; Identification; Military strategy ABST: An identification of friend and foe by game-theory analysis for a player who must choose the best strategy from two courses of action. 16 pp. RM-202-PR: Total Reconnaissance with Total Countermeasures: Simplified Model. AUTH: S. Sherman PAGES: 19, DATE: 1949 COST: $ 4.00 KEYS: Game theory; Reconnaissance NOTE: See also: RM-203. ABST: A game-theory model which determines the effect of total reconnaissance and total countermeasures on the payoff and desirable strategies. Only a finite set of pure strategies is available to each player. (Also published as P-106.) (See also RM-203.) 19 pp. RM-203-PR: Solutions of a Special Reconnaissance Game. AUTH: R.L. Belzer PAGES: 24, DATE: 1949 COST: $ 4.00 KEYS: Game theory; Reconnaissance ABST: A presentation of solutions for a special case of a general reconnaissance model previously investigated in RM-202. 24 pp. RM-204-PR: Note on the Solution of Convex Games. AUTH: L.S. Shapley PAGES: 5, DATE: 1949 COST: $ 4.00 KEYS: Game theory ABST: A method of selecting a finite subset from an arbitrary set of linear functions for convex regions of arbitrary finite dimension. 5 pp. RM-205-PR: A Tactical Reconnaissance Model. AUTH: L.S. Shapley PAGES: 7, DATE: 1949 COST: $ 4.00 KEYS: Game theory; Reconnaissance ABST: A study of the advisability of reconnaissance before a single bombing mission on a single target of uncertain military worth. 7 pp. RM-206-PR: A Generalization of the Silent Duel, Two Opponents, One Bullet Each, Arbitrary Accuracy. AUTH: M.A. Girshick PAGES: 9, DATE: 1949 COST: $ 4.00 KEYS: Duels; Game theory ABST: A generalization of a duel, considering several cases in which the bullets may be duds and the hits not lethal. 9 pp. RM-208-PR: Reconnaissance in Game Theory. AUTH: H.F. Bohnenblust, L.S. Shapley, S. Sherman PAGES: 19, DATE: 1949 COST: $ 4.00 KEYS: Game theory; Reconnaissance ABST: A study of the influence of reconnaissance on the strategies of the players and on the value of the game. In the case studied, one player uses a fixed type of reconnaissance and the second player attempts neither reconnaissance on his own nor countermeasure. 19 pp. RM-212-PR: On Non-Zero Games and Stochastic Processes. AUTH: R.E. Bellman, J.P. Lasalle PAGES: 13, DATE: 1949 COST: $ 4.00 KEYS: Games ABST: An introduction to a class of stochastic games which arose in an attempt to find an approach to non-zero-sum games. 13 pp. RM-213-PR: The Duel with Time of Flight Not Zero. AUTH: E.S. Quade PAGES: 9, DATE: 1949 COST: $ 4.00 KEYS: Duels; Game theory ABST: An analysis of a duel in which the time of flight of the shots is not assumed to be zero. The survival chance of each contestant against the uninterrupted fire of the other is determined. 9 pp. RM-215-PR: Solutions of a Class of Continuous Games. AUTH: J.P. Lasalle PAGES: 12, DATE: 1949 COST: $ 4.00 KEYS: Game theory ABST: A report on a general class of games whose solutions are discrete probability functions. A special case is presented in which one player has a pure best strategy. 12 pp. RM-219-PR: A Loud Duel with Equal Accuracy Where Each Duelist Has Only a Probability of Possessing a Bullet. AUTH: M.A. Girshick, D.H. Blackwell PAGES: 5, DATE: 1949 COST: $ 4.00 KEYS: Duels; Game theory ABST: A consideration of optimum strategies dependent on the relative magnitude of the probabilities of possessing a bullet. 5 pp. RM-234-PR: A Note on the Monte Carlo Method and the Potential Equation. AUTH: R.E. Bellman PAGES: 4, DATE: 1949 COST: $ 4.00 ABST: No abstract available. 4 pp. RM-241-PR: Comparison of Reconnaissances. AUTH: D.H. Blackwell PAGES: 8, DATE: 1949 COST: $ 4.00 KEYS: Game theory; Reconnaissance ABST: A representation of every reconnaissance better than a given reconnaissance for the special case in which the opponent has two moves. 8 pp. RM-243-PR: On the Equality Min Max = Max Min, and the Theory of Games. AUTH: M. Shiffman PAGES: 17, DATE: 1949 COST: $ 4.00 KEYS: Game theory ABST: A new elementary proof of von Neumann's minimum-maximum theorem. The possibility of determining an approximate saddle-point to the original problem by the solution of a system of equations is presented. 17 pp. RM-250-PR: On a Particular Non-Zero-Sum Game. AUTH: R.E. Bellman, D.H. Blackwell PAGES: 17, DATE: 1949 COST: $ 4.00 KEYS: Game theory ABST: A detailed consideration of a particular non-zero-sum game of attrition. 17 pp. RM-252-PR: Composite Targets I, N Identical Elements. AUTH: H.H. Germond PAGES: 24, DATE: 1949 COST: $ 4.00 ABST: No abstract available. 24 pp. RM-271-PR: A Note on the Power Function of the Wald-Wolfowitz Tolerance Limits for a Normal Distribution. AUTH: A.W. Marshall PAGES: 7, DATE: 1949 COST: $ 4.00 KEYS: Statistical analysis ABST: An investigation of the power function of the Wald-Wolfowitz method. This method (1) constructs tolerance limits for a normal distribution, and (2) determines a method which approximates an integral with limits of integration that are random variables. 7 pp. RM-274-PR: Determination of Expected Coverage and of Expected Damage--Single Bomb of Large Lethal Area. AUTH: H.H. Germond PAGES: 18, DATE: 1949 COST: $ 4.00 ABST: No abstract available. 18 pp. RM-289-PR: Occurrence of Improbable States in a Modified Ehrenfest Model: Part I. AUTH: R.E. Bellman, T.E. Harris PAGES: 14, DATE: 1949 COST: $ 4.00 ABST: No abstract available. 14 pp. RM-302-PR: A Model for the Reliability of Complex Mechanisms. AUTH: T.E. Harris PAGES: 8, DATE: 1949 COST: $ 4.00 KEYS: Models; Reliability ABST: A report on determining how long it will be before all elements are simultaneously out of repair, when several elements are used in parallel in a complex mechanism. 8 pp. RM-306-PR: Expected Coverage with Conventional Bombs When Rectangular Patterns Are Employed Against Rectangular Targets. AUTH: H.H. Germond PAGES: 16, DATE: 1949 COST: $ 4.00 ABST: No abstract available. 16 pp. RM-309-PR: A Circular Probability Grid. AUTH: H.H. Germond PAGES: 6, DATE: 1948 COST: $ 4.00 ABST: No abstract available. 6 pp. RM-319-PR: Local Defense of Targets of Equal Value. AUTH: R.L. Belzer, M. Dresher, O. Helmer PAGES: 9, DATE: 1949 COST: $ 4.00 KEYS: Game theory; Targets NOTE: See also: RM-320, RM-329. ABST: An analysis to determine optimal attack and defense strategies. Both opponents know each other's capacities, but not each other's choice of strategies. (See also RM-320, RM-329.) 9 pp. RM-320-PR: Local Defense of Targets of Equal Value: Extension of Results. AUTH: M. Dresher, O.A. Gross PAGES: 18, DATE: 1950 COST: $ 4.00 KEYS: Game theory; Targets NOTE: See also: RM-329. ABST: A supplement to RM-319. (See also RM-329.) 18 pp. RM-321-PR: Occurrence of Improbable States in a Modified Ehrenfest Model: Part II. AUTH: R.E. Bellman, T.E. Harris PAGES: 7, DATE: 1950 COST: $ 4.00 ABST: No abstract available. 7 pp. RM-323-PR: On the Expected Damage from Single Bomb Drops. AUTH: W.E. Frye, E.V.B. Stearns PAGES: 39, DATE: 1950 COST: $ 4.00 ABST: No abstract available. 39 pp. RM-329-PR: Local Defense of Targets of Equal Value: Completion of Results. AUTH: O.A. Gross PAGES: 6, DATE: 1950 COST: $ 4.00 KEYS: Game theory; Targets ABST: A supplement to RM-319 and RM-320. 6 pp. RM-330-PR: The Circular Coverage Function. AUTH: H.H. Germond PAGES: 18, DATE: 1950 COST: $ 4.00 ABST: No abstract available. 18 pp. RM-339-PR: Table of Q Functions. AUTH: J.I. Marcum PAGES: 187, DATE: 1950 COST: $ 15.00 ABST: No abstract available. 187 pp. RM-357-PR: On Positive Transformations. AUTH: R.E. Bellman, T.E. Harris PAGES: 15, DATE: 1950 COST: $ 4.00 KEYS: Game theory; Markov processes ABST: A discussion on positive transformations encountered in connection with Markoff process and with games of timing. 15 pp. RM-359-PR: [N] Targets of Differing Vulnerability with Attack Stronger Than Defense. AUTH: O.A. Gross PAGES: 9, DATE: 1950 COST: $ 4.00 KEYS: Game theory; Targets ABST: A study of an attack-defense model with an interpretation by means of a numerical example. 9 pp. RM-366-PR: On the Min Max of a Bilinear Form. AUTH: S.S. Walters PAGES: 5, DATE: 1950 COST: $ 4.00 KEYS: Game theory ABST: A method which determines the minmax of a bilinear form is defined over the Cartesian product of two compact sets, each of which is in a Euclidean space. 5 pp. RM-370-PR: Estimation in Truncated Sampling Processes. AUTH: M. Halperin PAGES: 59, DATE: 1950 COST: $ 7.50 KEYS: Numerical methods and approximations; Statistical analysis ABST: An examination of estimation procedures for truncated sampling processes to determine which is asymptotically "best." Considered in the study are (1) processes with fixed points of truncation, (2) a truncated mortality process with renewal allowed, and (3) processes with random points of truncation. 59 pp. RM-376-PR: A Method for Choosing Among Optimum Strategies. AUTH: G.W. Brown PAGES: 5, DATE: 1950 COST: $ 4.00 KEYS: Decision-making; Game theory; Military strategy NOTE: See also: RM-386, RM-387. ABST: An extension of the minmax principle to determine a preferred optimum strategy in discrete games whose solutions are not unique. (See also RM-386, RM-387.) 5 pp. RM-386-PR: Best Strategies. AUTH: J.C.C. McKinsey PAGES: 8, DATE: 1950 COST: $ 4.00 KEYS: Game theory; Military strategy NOTE: See also: RM-376, RM-387. ABST: A study of "best" strategies which are optimum and take advantage of the mistakes of the opponent. (See also RM-376, RM-387.) 8 pp. RM-387-PR: Some Remarks on Best Strategies. AUTH: R.L. Belzer PAGES: 7, DATE: 1950 COST: $ 4.00 KEYS: Game theory; Military strategy NOTE: See also: RM-376, RM-386. ABST: A discussion of the geometrical significance of best strategies as defined by McKinsey and Brown. (See also RM-376, RM-386.) 7 pp. RM-388-PR: Human Factors in Systems Analysis. AUTH: H. Goldhamer PAGES: 29, DATE: 1950 COST: $ 4.00 KEYS: Group behavior; System analysis ABST: A systems-analysis approach to the relation between the optimization of certain critical parameters and organized human action. 29 pp. RM-408-PR: A Continuous Colonel Blotto Game. AUTH: O.A. Gross, R.A. Wagner PAGES: 13, DATE: 1950 COST: $ 4.00 KEYS: Game theory ABST: A Memorandum on a continuous two-person, zero-sum game. Colonel Blotto and the enemy are confronted with a situation in which (1) Blotto has at his disposal a total of B units of attack, (2) the enemy has E units of like character, and (3) they are to attack simultaneously and in full force a set of [n] hills of different values, with prescribed payoffs. (See supplement, RM-424.) 13 pp. RM-413-PR: The Expected Coverage of a Small Circular Target By a Number of Circular Bombs. AUTH: R.H. Dishington PAGES: 12, DATE: 1950 COST: $ 4.00 ABST: No abstract available. 12 pp. RM-414-PR: Solution of a Game with Constraints. AUTH: R.A. Wagner PAGES: 8, DATE: 1950 COST: $ 4.00 KEYS: Game theory ABST: An example of a game with constraints solved by finding fixed points in a mapping process. 8 pp. RM-424-PR: The Symmetric Blotto Game. AUTH: O.A. Gross PAGES: 7, DATE: 1950 COST: $ 4.00 KEYS: Game theory ABST: In this extension of RM-408, a method of constructing a solution for the general symmetric case is given. 7 pp. RM-427-PR: A Reduction of General Two-Person Games Without Side Payments. AUTH: D.H. Blackwell, H.F. Bohnenblust PAGES: 9, DATE: 1950 COST: $ 4.00 KEYS: Game theory ABST: A demonstration that the process of reduction of the payoff matrices of a two-person non-zero-sum game leads to a unique result, in which the Nash points are precisely those of the original game. 9 pp. RM-433-PR: Best Strategies for Continuous Games with a Continuous Payoff. AUTH: I.L. Glicksberg PAGES: 7, DATE: 1950 COST: $ 4.00 KEYS: Game theory; Military strategy ABST: A proof that best strategies exist for the continuous two-person zero-sum game with a continuous payoff function. 7 pp. RM-435-PR: Games Played Over Nonconvex Sets of Mixed Strategies. AUTH: I.L. Glicksberg PAGES: 3, DATE: 1950 COST: $ 4.00 KEYS: Game theory; Military strategy ABST: A demonstration of a necessary and sufficient condition that a finite game (or a continuous game with continuous payoff), played over closed sets of the sets of all mixed strategies, satisfies the minmax relation. 3 pp. RM-444-PR: A Remark on the Silent Duel with Positive Initial Accuracy, and on Associated Silent and Noisy Duels. AUTH: L.S. Shapley PAGES: 4, DATE: 1950 COST: $ 4.00 KEYS: Duels; Game theory ABST: A description of the solution of the silent duel with positive initial accuracy, and a discussion of a relationship between the solution of the silent duel and that of the associated noisy duel. 4 pp. RM-445-PR: The Silent Duel, One Bullet Versus Two, Equal Accuracy. AUTH: L.S. Shapley PAGES: 16, DATE: 1950 COST: $ 4.00 KEYS: Duels; Game theory ABST: A description of the solution, for the case of all accuracies equal and increasing monotonically from zero to one, of the duel in which the antagonists have one and two silent bullets, respectively. 16 pp. RM-447-PR: On the Roots of Markoffian Random Functions. AUTH: A.J. Siegert PAGES: 21, DATE: 1950 COST: $ 4.00 ABST: No abstract available. 21 pp. RM-448-PR: The Survival Probability Problem. AUTH: D.A. Darling PAGES: 8, DATE: 1950 COST: $ 4.00 ABST: No abstract available. 8 pp. RM-464-PR: Comments on the Modified Form of Aircraft Progress Function. AUTH: F. Hoffman PAGES: 15, DATE: 1950 COST: $ 4.00 KEYS: Airplanes; Learning curves ABST: An examination of the aircraft progress curve introduced by the Stanford Research Institute to determine whether this modification shows a clear superiority over the original and simpler form of the curve in terms of the fit of the curves to the observed data. 15 pp. RM-474-PR: Noisy Duel, One Bullet Each, with Simultaneous Fire and Unequal Worths. AUTH: I.L. Glicksberg PAGES: 14, DATE: 1950 COST: $ 4.00 KEYS: Duels; Game theory ABST: A consideration of the noisy duel in which the competitors have unequal worths. It is shown that a simple duel of this type has a value but that only one antagonist, in general, has an optimal strategy. 14 pp. RM-478-PR: Minimax Theorem for Upper and Lower Semicontinuous Payoffs. AUTH: I.L. Glicksberg PAGES: 5, DATE: 1950 COST: $ 4.00 KEYS: Game theory ABST: A proof of the minimax theorem for the game played over a pair of compact metric spaces, in which the payoff is an upper or lower semicontinuous function. 5 pp. RM-491-PR: Notes on the Game with Rational Payoff. AUTH: I.L. Glicksberg, O.A. Gross PAGES: 11, DATE: 1950 COST: $ 4.00 KEYS: Game theory NOTE: See also: RM-501. ABST: Some results on continuous games with rational payoff functions which relate to the existence of step-function solutions. (See also RM-501.) 11 pp. RM-501-PR: A Class of Games with Unique Density Function Solutions. AUTH: I.L. Glicksberg, O.A. Gross PAGES: 10, DATE: 1950 COST: $ 4.00 KEYS: Game theory ABST: A continuation of RM-491, with an example of a rational game in which the value is rational and yet there is a unique solution which is a pair of density functions. 10 pp. RM-502-PR: Games with Positive-Density Solutions. AUTH: O. Helmer PAGES: 7, DATE: 1950 COST: $ 4.00 KEYS: Game theory ABST: Proofs of some theorems about games with positive-density solutions and some examples. 7 pp. RM-510-PR: Continuous Games with Given Strategies. AUTH: I.L. Glicksberg, O.A. Gross PAGES: 9, DATE: 1951 COST: $ 4.00 KEYS: Game theory; Military strategy ABST: Two methods of constructing a continuous game with a given pair of distribution functions as a solution. 9 pp. RM-528-PR: Military Doctrine of Decision and the Von Neumann Theory of Games. AUTH: G. Haywood PAGES: 107, DATE: 1951 COST: $ 10.00 KEYS: Game theory ABST: An analysis of the military doctrine of command decision in the light of the theory of games. 107 pp. RM-534-PR: Moment Space Boundaries and Some Applications. AUTH: M. Dresher PAGES: 14, DATE: 1951 COST: $ 4.00 KEYS: Boundary value problems; Game theory ABST: A derivation of the properties of the boundary of the moment space from which is obtained by the mapping method the solution of polynomial-like games. It is shown how these boundaries are used in solving optimal strategies of polynomial games. RM-538-PR: A Class of Games with Unique Solutions. AUTH: I.L. Glicksberg, O.A. Gross PAGES: 8, DATE: 1951 COST: $ 4.00 KEYS: Game theory ABST: An illustration of the fact that in a game played over the unit square, if either player has a non-step-function optimal strategy, the opposing player has a unique optimal strategy. Examples are included which show that games with wellbehaved payoffs can have unique solutions which are more or less pathological. 8 pp. RM-549-PR: The Pathological Nature of Certain Games with Rational Payoff. AUTH: I.L. Glicksberg, O.A. Gross PAGES: 9, DATE: 1951 COST: $ 4.00 KEYS: Game theory ABST: A construction of an example of a continuous game with rational payoff in which the unique optimal strategy for one player has a countable set of jumps, the jumps occurring at a dense set of points. The example would seem to shatter the view that games with rational payoffs can be solved by methods similar to those used in polynomial games. RM-568-PR: The Pathological Nature of Certain Games with Rational Payoff: II. AUTH: I.L. Glicksberg, O.A. Gross PAGES: 6, DATE: 1951 COST: $ 4.00 KEYS: Game theory ABST: A construction of an example of a continuous game with rational payoff in which the unique optimal strategy for each player has a countable set of jumps, the jumps occurring at a dense set of points. RM-593-PR: Density of Games with Unique Solutions. AUTH: I.L. Glicksberg, O.A. Gross PAGES: 8, DATE: 1951 COST: $ 4.00 KEYS: Game theory ABST: A proof that the set of continuous games (played over the unit square) with unique solutions is dense in the space of all games with continuous payoffs. 8 pp. RM-595-PR: Machine Method: Iterative Solution of Games. AUTH: R.W. Bemer PAGES: 12, DATE: 1951 COST: $ 4.00 KEYS: Computers; Game theory ABST: A description of a machine method for the iterative solution of games. 12 pp. RM-597-PR: Games with Circular Symmetry. AUTH: L.J. Savage PAGES: 4, DATE: 1948 COST: $ 4.00 KEYS: Game theory ABST: A characterization of the effective strategies of a game with circular symmetry. 4 pp. RM-608-PR: Factorable Games. AUTH: O. Helmer PAGES: 6, DATE: 1951 COST: $ 4.00 KEYS: Game theory ABST: A discussion of two cases of finite games where the matrix is decomposed into submatrices and the solution can be found by solving the games represented by some of these submatrices. 6 pp. RM-610-PR: Moments of the Distribution of Outcomes of a Game. AUTH: I.L. Glicksberg, O.A. Gross PAGES: 2, DATE: 1951 COST: $ 4.00 KEYS: Game theory ABST: A derivation of the moments of the outcome distribution of a continuous game over the unit square with continuous payoff. 2 pp. RM-611-PR: A Game with Respective Optimal Spectra of Cardinality [C] and 1. AUTH: I.L. Glicksberg, O.A. Gross PAGES: 4, DATE: 1951 COST: $ 4.00 KEYS: Game theory ABST: A presentation of a counter-example to the conjecture that if either player in a game over the unit square with continu ous payoff has a step-function optimal strategy, then the same is true of his opponent. 4 pp. RM-614-PR: Note of the Formulation of the Study of Logistics. AUTH: O. Morganstern PAGES: 14, DATE: 1951 COST: $ 4.00 ABST: No abstract available. 14 pp. RM-615-PR: [N]-Person Games: An Example and a Proof. AUTH: J.F. Nash PAGES: 4, DATE: 1951 COST: $ 4.00 KEYS: Game theory ABST: A presentation of a duopoly example and a brief proof of the existence of equilibrium points yielding a simple proof of the main theorem of two-person zero-sum games. 4 pp. RM-620-PR: Continuous Games with Given Unique Solutions. AUTH: I.L. Glicksberg, O.A. Gross PAGES: 9, DATE: 1951 COST: $ 4.00 KEYS: Game theory ABST: A demonstration that given a pair of distributions over the unit interval, ([f, q]), there exists a game (with continuous payoff) over the unit square with the unique solution ([f, q]). 9 pp. RM-638-PR: On Determining the Full Set of Solutions of a Finite Game. AUTH: L.S. Shapley PAGES: 12, DATE: 1951 COST: $ 4.00 KEYS: Game theory ABST: A detailed account of a procedure for establishing whether a given set of solutions to a finite game is complete. 12 pp. RM-641-PR: The Noisy Duel: Existence of a Value in the Singular Case. AUTH: L.S. Shapley PAGES: 17, DATE: 1951 COST: $ 4.00 KEYS: Duels; Game theory ABST: A presentation of a simple example and a formal method of solving an indeterminate duel, with a characterization of the formal solution as the limit of an iterative process that is intuitively plausible. (See also RM-3672-1). 17 pp. RM-647-PR: On a General Class of Problems Involving Sequential Analysis. AUTH: R.E. Bellman PAGES: 7, DATE: 1951 COST: $ 4.00 ABST: No abstract available. 7 pp. RM-654-PR: Sums of Games. AUTH: J.W. Milnor PAGES: 6, DATE: 1951 COST: $ 4.00 KEYS: Game theory ABST: A demonstration that a certain class of two-person zero-sum perfect information games, without chance moves, form a group under a suitable composition law. 6 pp. RM-655-PR: Games Concave on Each Side of the Unit Square Diagonal. AUTH: I.L. Glicksberg, O.A. Gross PAGES: 10, DATE: 1951 COST: $ 4.00 KEYS: Game theory ABST: A derivation of a simple relationship between the spectra of optimal strategies for a certain class of games with continuous payoff. 10 pp. RM-656-PR: Notes on the [N]-Person Game: I, Characteristic-Point Solutions of the Four-Person Game. AUTH: L.S. Shapley PAGES: 14, DATE: 1951 COST: $ 4.00 KEYS: Game theory ABST: A presentation of a family of solutions, covering all zero-sum four-person games, which behave continuously under perturbation of the characteristic function. RM-660-PR: Tables in Brief--Mathematical Tables for Use with Desk Calculators. AUTH: W. White PAGES: 50, DATE: 1951 COST: $ 4.00 ABST: No abstract available. 50 pp. RM-670-PR: Notes on the [N]-Person Game: II, The Value of an [N]-Person Game. AUTH: L.S. Shapley PAGES: 18, DATE: 1951 COST: $ 4.00 KEYS: Game theory NOTE: See also: RM-656, RM-817, RM-881, and RM-1005. ABST: A deduction of a "value" for the essential [n]-person game and the establishment of a number of simple properties of the value. RM-677-PR: The Determination of Decision Regions for a Simplified Two-Plane Bombing Model. AUTH: H.N. Shapiro PAGES: 17, DATE: 1951 COST: $ 4.00 ABST: No abstract available. 17 pp. RM-679-PR: Games Against Nature. AUTH: J.W. Milnor PAGES: 25, DATE: 1951 COST: $ 4.00 KEYS: Game theory ABST: An axiomatic study of various criteria for playing games against nature; and a discussion of the concept of an equilibrium point for [n]-person games against nature. RM-686-PR: A Stochastic Development of "Ballantyne's Integral Equation.". AUTH: R.P. Peterson PAGES: 4, DATE: 1951 COST: $ 4.00 ABST: No abstract available. 4 pp. RM-693-PR: Some Remarks on the Double Description Method. AUTH: B.H. Jacobs, R.M. Thrall, R.A. Wagner PAGES: 22, DATE: 1952 COST: $ 4.00 KEYS: Game theory ABST: An application of the double description method to games with linear constraints on the strategy space of one or both players. In addition, an adaptation of the method for use with IBM equipment is described. 22 pp. RM-705-PR: A Game Value Characterization of Algebraic Numbers. AUTH: O.A. Gross PAGES: 7, DATE: 1951 COST: $ 4.00 KEYS: Game theory ABST: A proof that a necessary and sufficient condition for a real number to be the value of a polynomial game over the unit square, with only integral coefficients in the payoff, is that it be an algebraic number. RM-706-PR: A Note on Payoffs Which Vanish Almost Everywhere. AUTH: O.A. Gross PAGES: 4, DATE: 1951 COST: $ 4.00 KEYS: Game theory ABST: A proof that one can find a game over the unit square whose payoff vanishes almost everywhere, such that a given distribution function over the closed unit interval is the unique optimal strategy for one of the players. RM-709-PR: Report of a Seminar on Organization Science. AUTH: M.M. Flood PAGES: 58, DATE: 1951 COST: $ 7.50 KEYS: Organization--Theory NOTE: See also: RM-789-1, P-256, P-258, P-263, P-312, P-346. ABST: Several talks presented at a seminar held in Santa Monica, California (August 1951), to discuss current RAND research on organization problems. (See also RM-789-1, P-256, P-258, P-263, P-312, P-346.) 58 pp. RM-718-PR: An Infinite-Dimensional Extension of a Symmetric Blotto Game. AUTH: O.A. Gross PAGES: 6, DATE: 1951 COST: $ 4.00 KEYS: Game theory ABST: A consideration of a two-person zero-sum game over a function space and with discontinuous payoff, which has an optimal strategy for either player, consisting of randomizing over a certain two-parameter family of functions. 6 pp. RM-721-PR: Short Proof of a Theorem of Gross. AUTH: J.G. Wendel PAGES: 3, DATE: 1951 COST: $ 4.00 ABST: No abstract available. 3 pp. RM-724-PR: A Generalization of Numerical Utilities: I. AUTH: R.M. Thrall, N.C. Dalkey PAGES: 30, DATE: 1951 COST: $ 4.00 KEYS: Utility theory ABST: A generalization of the von Neumann-Morgenstern theory of utility, with applications to decisionmaking and game theory. 30 pp. RM-734-PR: Prolegomena to a Theory of Organization. AUTH: O. Morganstern PAGES: 122, DATE: 1951 COST: $ 10.00 KEYS: Organization--Theory ABST: A discussion of a framework within which to make initial descriptive analyses of organizations, the framework dealing solely with the centrally directed organizations. 122 pp. RM-736-PR: Continuous Blotto. AUTH: M.P. Peisakoff PAGES: 6, DATE: 1951 COST: $ 4.00 KEYS: Game theory ABST: A presentation of the value and one-parameter continuous optimal strategies for a continuous Blotto game. 6 pp. RM-737-PR: Note on Games over a Function Space with Homogeneous Kernels. AUTH: W.H. Fleming PAGES: 4, DATE: 1951 COST: $ 4.00 KEYS: Game theory ABST: A proof that certain games with functions defined on the closed unit interval (0, 1) as pure strategies, and payoffs which involve a homogeneous kernel and a function assigning various weights to points of (0, 1) can be reduced to games of the same type in which every point of (0, 1) is weighted equally in the payoff. 4 pp. RM-745-PR: On Weak Convergence of Strategies in Certain Games over a Function Space. AUTH: W.H. Fleming PAGES: 9, DATE: 1951 COST: $ 4.00 KEYS: Game theory; Military strategy ABST: A proof that, for a certain class of games over a function space, mixed strategies are weak limits of pure strategies. 9 pp. RM-747-PR: Two Examples Concerning Behavior Strategies. AUTH: F.B. Thompson, R.A. Wagner PAGES: 7, DATE: 1951 COST: $ 4.00 KEYS: Game theory; Military strategy ABST: A discussion of two examples by means of which some questions concerning properties of behavior strategies in finite games are answered. 7 pp. RM-752-PR: A Second Note on Payoffs Which Vanish Almost Everywhere. AUTH: O.A. Gross PAGES: 4, DATE: 1952 COST: $ 4.00 KEYS: Game theory ABST: A proof that, given a pair ([f, q]) of distribution functions over (0, 1), there is a game over the square with payoff vanishing almost everywhere which has ([f, q]) as its unique solution. (See also RM-706). 4 pp. RM-753-PR: A Statistical Theory of Target Detection by Pulsed Radar: Mathematical Appendix. AUTH: J.I. Marcum PAGES: 126, DATE: 1948 COST: $10.00 ABST: No abstract available. 126 pp. RM-754-PR: A Statistical Theory of Target Detection by Pulsed Radar. AUTH: J.I. Marcum PAGES: 90, DATE: 1947 COST: $7.50 ABST: No abstract available. 90 pp. RM-759-PR: Equivalence of Games in Extensive Form. AUTH: F.B. Thompson PAGES: 13, DATE: 1952 COST: $ 4.00 KEYS: Game theory ABST: A characterization of four simple transformations which are sufficient to carry any two equivalent games in extensive form one into the other. Application is made to the problem of simplification of a game in extensive form. 13 pp. RM-769-PR: Behavior Strategies in Finite Games. AUTH: F.B. Thompson PAGES: 18, DATE: 1952 COST: $ 4.00 KEYS: Game theory; Military strategy ABST: A development of the relation between behavior strategies and mixed strategies with a characterization of those game structures solvable by behavior strategies. 18 pp. RM-780-PR: A Preference Experiment. AUTH: M.M. Flood PAGES: 15, DATE: 1952 COST: $ 4.00 KEYS: Utility theory ABST: An investigation to determine if a set of objects can have exactly the same monetary value but differ widely and inconsistently in personal utilities attached to them by subjects. Thirteen subjects made sealed bids on 24 objects, each object being a chance at stated odds at a specified sum of money. 15 pp. RM-789-1-PR: Some Experimental Games. AUTH: M.M. Flood PAGES: 44, DATE: 1952 COST: $ 4.00 KEYS: Game theory ABST: A study of several experimental games to test the applicability and usefulness of the axiomatic structures developed by von Neumann, Morgenstern, and others. 44 pp. RM-791-PR: A Pursuit Game with Incomplete Information. AUTH: R. Isaacs PAGES: 29, DATE: 1952 COST: $ 4.00 KEYS: Games ABST: An analysis of a simple, nontrivial example of a pursuit game lacking full information. 29 pp. RM-814-PR: Minmax Theorem for a Class of Games Over a Function Space. AUTH: W.H. Fleming PAGES: 19, DATE: 1952 COST: $ 4.00 KEYS: Game theory ABST: A demonstration of the existence of a value and optimal mixed strategies for certain two-person games played over a space of bounded measurable functions. 19 pp. RM-817-PR: Notes on the [N]-Person Game: III, Some Variants of the Von Neumann-Morgenstern Definition of Solution. AUTH: L.S. Shapley PAGES: 10, DATE: 1952 COST: $ 4.00 KEYS: Game theory ABST: An introduction of the concept of "G-stability," from which several new definitions of "solution" are obtained. Some theorems are proved, and a number of examples are given. 10 pp. RM-857-PR: A Model for Partial Damage to Point Targets. AUTH: M.R. Mickey PAGES: 9, DATE: 1952 COST: $ 4.00 ABST: No abstract available. 9 pp. RM-858-PR: Remark on a Theorem of Danskin. AUTH: J.G. Wendel PAGES: 4, DATE: 1952 COST: $ 4.00 KEYS: Game theory ABST: A demonstration that the Brown-Robinson-Danskin iterative process for finding the value of a continuous game also "yields" solutions of the game. 4 pp. RM-859-PR: Some Functional Equations Related to Dynamic Programming Problems Involving Non-Commutative Operations. AUTH: O.A. Gross PAGES: 19, DATE: 1952 COST: $ 4.00 KEYS: Programming (mathematics) ABST: A study of a type of functional equation relating to dynamic programming. A computation method for obtaining approximate and, in some cases, actual solutions is described. The associated decision procedures involve a fixed finite number of fixed choices at each stage. Illus.c RM-863-PR: The Generalized Outcome of a Class of Machine Gun Duels. AUTH: G.F. Gompf PAGES: 81, DATE: 1952 COST: $ 7.50 ABST: No abstract available. 81 pp. RM-881-PR: Notes on the [N]-Person Game: IV, A Theorem on C-Stable Sets. AUTH: L.S. Shapley PAGES: 7, DATE: 1952 COST: $ 4.00 KEYS: Game theory ABST: Solutions for the following set-equation, relavant to [n]-person game theory: X = C - (X = R), where C and R are, respectively, a convex set and a cone in an [n]-dimensional vector space, satisfying certain conditions. 7 pp. RM-884-PR: More on Games of Survival. AUTH: M.O. Peisakoff PAGES: 21, DATE: 1952 COST: $ 4.00 KEYS: Game theory ABST: A demonstration that the game of survival, which is a repetition of a normalized finite zero-sum two-person game with each entry a nonzero integer, is inessential and has some easily described optimal strategies. 21 pp. RM-889-PR: Optimal Sets for Games over the Square. AUTH: I.L. Glicksberg, O.A. Gross PAGES: 7, DATE: 1952 COST: $ 4.00 KEYS: Game theory ABST: A proof that every nonvoid "weak" closed convex set of distributions on the unit interval is the set of all optimal strategies for one player in some game with continuous payoff over the square. 7 pp. RM-890-PR: The Systems Research Laboratory and Its Program. AUTH: R.L. Chapman, W.C. Biel, J.L. Kennedy, A. Newell PAGES: 25, DATE: 1952 COST: $ 4.00 KEYS: Air defenses; Interception; Man machine systems; Systems research KEYS: laboratory ABST: A description of (1) a research program involving man-machine systems, (2) the laboratory in which the program is being pursued, and (3) a generalized model for organizational research. 25 pp. RM-894-PR: A Characterization of the Normal Distribution. AUTH: J.G. Wendel PAGES: 6, DATE: 1952 COST: $ 4.00 ABST: No abstract available. 6 pp. RM-897-PR: Reduction of Certain Games Over Function Space. AUTH: W.H. Fleming, O.A. Gross PAGES: 8, DATE: 1952 COST: $ 4.00 KEYS: Game theory ABST: A study of a class of two-person zero-sum games over a space of measurable functions. Mixed-strategy solutions involving uniform translates of pure strategy are determined by reducing these games to games over the squares. 8 pp. RM-898-PR: An Example of an Infinite, Nonconstant-Sum Game. AUTH: L.S. Shapley PAGES: 9, DATE: 1952 COST: $ 4.00 KEYS: Game theory ABST: A simple example illustrating some of the questions which arise when an infinite general-sum game is solved for equilibrium points. 9 pp. RM-900-PR: Quantitative Theory of Human Behavior: The Single Individual. AUTH: E.W. Barankin PAGES: 93, DATE: 1952 COST: $ 7.50 KEYS: Behavior; Probability ABST: A discussion of a new concept of probability (constructed from a theory of behavior) which determines the comparative behavioristic significance of convergence in probability and almost sure convergence. 93 pp. RM-901-PR: Solution Sets for Games on the Square. AUTH: I.L. Glicksberg, O.A. Gross PAGES: 14, DATE: 1952 COST: $ 4.00 KEYS: Game theory ABST: A study of some necessary and sufficient conditions which show that a pair of nonvoid "weak" closed convex sets of strategies form the solution set of a game with continuous payoff on the square. 14 pp. RM-913-PR: Aerial Bombing Tactics: General Considerations (A World War II Study). AUTH: M.M. Flood PAGES: 40, DATE: 1952 COST: $ 4.00 ABST: No abstract available. 40 pp. RM-916-PR: Reasonable Outcomes for [N]-Person Games. AUTH: J.W. Milnor PAGES: 17, DATE: 1952 COST: $ 4.00 KEYS: Game theory ABST: A description of upper and lower bounds for the payoff which each coalition should get in any "reasonable" play of an [n]-person game. 17 pp. RM-921-PR: A Mathematical Treatment of Learning Models. AUTH: S. Karlin PAGES: 29, DATE: 1952 COST: $ 4.00 ABST: No abstract available. 29 pp. RM-922-PR: Observations and Comments on the Organization Studies of the Systems Research Laboratory. AUTH: H.A. Simon PAGES: 35, DATE: 1952 COST: $ 4.00 KEYS: Air defenses; Interception; Man machine systems; Systems research KEYS: laboratory ABST: A summary of discussions with the Systems Research Laboratory staff concerning the concepts from organization theory which might be useful in analyzing data on the Ground Controlled Intercept Station experiment. 35 pp. RM-933-PR: Decision Processes and Functional Equations. AUTH: S. Karlin, H.N. Shapiro PAGES: 11, DATE: 1952 COST: $ 4.00 ABST: No abstract available. 11 pp. RM-948-PR: Some Experimental [N]-Person Games. AUTH: G. Kalisch, J.W. Milnor, J.F. Nash, E.D. Nering PAGES: 46, DATE: 1952 COST: $ 4.00 KEYS: Game theory ABST: An analysis of [n]-person coalition games. The pattern of behavior of the players is described, together with the relationship between the observed outcome of the games and various theoretical concepts. 46 pp. RM-949-PR: Some Simple Nonlinear Models. AUTH: S. Karlin, H.N. Shapiro PAGES: 8, DATE: 1952 COST: $ 4.00 ABST: A discussion of some nonlinear models of dynamic programming which are susceptible to complete analysis. RM-971-PR: Duality in Dynamic Programming. AUTH: S. Karlin PAGES: 10, DATE: 1952 COST: $ 4.00 ABST: No abstract available. 10 pp. RM-1142-PR: Order Matrices: I. AUTH: L.S. Shapley PAGES: 10, DATE: 1953 COST: $ 4.00 KEYS: Game theory; Matrices--Theory NOTE: See also: RM-1145, RM-3672-1. ABST: A definition of the order matrix of a two-person matrix game. Its maximal undominated submatrix, or saddle, is described, and a method is given for locating elements of the saddle. RM-1145-PR: Order Matrices: II. AUTH: L.S. Shapley PAGES: 11, DATE: 1953 COST: $ 4.00 KEYS: Game theory NOTE: See also: RM-1142, RM-3672-1. ABST: A proof that the center of an order matrix (defined as the smallest carrier for the solutions of all the associated numerical matrices) lies between the residual set and the saddle, provided that the order matrix contains no equal elements. P-44: Some Tests on the Randomness of a Million Digits. AUTH: B.B. Brown PAGES: 15, DATE: 1948 COST: $ 4.00 KEYS: Mathematics; Numerical methods and approximations; Stochastic processes NOTE: See also: P-113. ABST: A report on the randomness of a million digits produced by a random digit generator. They are examined for randomness by (1) the Frequency test, (2) the Poker test, (3) the Serial test, and (4) the Run test. (See also P-113.) 15 pp. P-47: Isomorphism of Games, and Strategic Equivalence. AUTH: J.C.C. McKinsey PAGES: 41, DATE: 1948 COST: $ 4.00 KEYS: Games ABST: A detailed proof that a certain precise mathematical condition that is necessary for strategic equivalence in the theory of games implies another precise mathematical condition that is recognized as sufficient for strategic equivalence. 41 pp. P-57: Solutions of Discrete, Two-Person Games. AUTH: L.S. Shapley, S. Karlin, H.F. Bohnenblust PAGES: 29, DATE: 1949 COST: $ 4.00 KEYS: Game theory ABST: A study of the fundamental relationship between the dimensions of optimal strategy sets. Also discussed in the paper are (1) the set of games with unique solutions, (2) the construction of a game matrix with a given solution, and (3) the solution of matrices with special diagonal properties. 29 pp. P-61: Some Nonparametric Tests of Whether the Largest Observations of a Set Are Too Large or Too Small. AUTH: J.E. Walsh PAGES: 8, DATE: 1950 COST: $ 4.00 KEYS: Statistical analysis ABST: A presentation of some nonparametric tests of whether the [r] largest observations of the set are too large or too small to be consistent with the hypothesis that these populations have a common median value. The observations are statistically independent and are drawn from continuous symmetrical population. (Published in [The Annals of Mathematical Statistics], December 1950. 8 pp. P-65: Some Estimates and Tests Based on [R] Smallest Values in a Sample. AUTH: J.E. Walsh PAGES: 4, DATE: 1950 COST: $ 4.00 KEYS: Statistical analysis ABST: An analysis of a situation in which only the [r] smallest values of a sample of size are available. Properties of some well-known nonparametric point estimates, confidence intervals, and significance tests for the 100[p] percent point of the population are examined. (Published in [The Annals of Mathematical Statistics], September 1950.) 4 pp. P-66: Games with Continuous, Convex Payoff. AUTH: H.F. Bohnenblust, S. Karlin, L.S. Shapley PAGES: 19, DATE: 1949 COST: $ 4.00 KEYS: Game theory ABST: A study of special class of games in which the strategies of one player form a compact and convex region [B] of finite-dimensional Euclidean space while those of the other form an arbitrary set [A]. 19 pp. P-78: Some Notes on Computation of Games Solutions. AUTH: G.W. Brown PAGES: 6, DATE: 1949 COST: $ 4.00 KEYS: Game theory NOTE: See also: P-154. ABST: A presentation of several dynamical systems whose steady-state solutions yield solutions to a discrete game matrix. Considered in the report are (1) various systems of differential equations for a symmetric game, (2) related systems of difference equations for digital computation, and (3) the linear programming problem represented as a symmetric game. (See also P-154.) 6 pp. P-80: On the Power Function of the 'Best' [T]-Test Solution of the Behrens-Fisher Problem. AUTH: J.E. Walsh PAGES: 4, DATE: 1949 COST: $ 4.00 KEYS: Statistical analysis ABST: A comparison of the power function of the Scheffe test with the power function of the corresponding most powerful test for the case in which the ratio of variances is known. (Published in [The Annals of Mathematical Statistics], December 1949.) 4 pp. P-84: Some Two-Person Games Involving Bluffing. AUTH: R.E. Bellman, D.H. Blackwell PAGES: 10, DATE: 1949 COST: $ 4.00 KEYS: Game theory NOTE: See also: P-168. ABST: A study of a class of games which may be handled by uniform techniques. (See also P-168.) 10 pp. P-85: On a Theorem of Ville. AUTH: H.F. Bohnenblust, S. Karlin PAGES: 8, DATE: 1949 COST: $ 4.00 KEYS: Game theory ABST: An extension of the theorems of Ville and Kakutani under certain conditions to infinite-dimensional spaces. The results are utilized in the theory of nondiscrete games. 8 pp. P-86: Large-Sample Tests and Confidence Intervals for Mortality Rates. AUTH: J.E. Walsh PAGES: 11, DATE: 1949 COST: $ 4.00 KEYS: Mortality; Statistical analysis ABST: A presentation of methods which determine some valid large sample tests and confidence intervals for the mortality rate. Differences are examined between customary "unit" deaths estimated by policy coverage and actual mortality governed solely by deaths of individuals. (Published in the [Journal of the American Statistical Association], June 1950.) 11 pp. P-88: Stochastic (Monte Carlo) Attenuation Analysis. AUTH: H. Kahn PAGES: 21, DATE: 1949 COST: $ 4.00 ABST: No abstract available. 21 pp. P-90: Tables of Hermite Polynomials and the Derivations of the Error Function. AUTH: J.I. Marcum PAGES: 241, DATE: 1948 COST: $ 20.00 ABST: No abstract available. 241 pp. P-91: On the Power Function of Tests of Percentage Points Based on the Noncentral [T]-Statistics. AUTH: J.E. Walsh PAGES: 3, DATE: 1949 COST: $ 4.00 KEYS: Statistical analysis ABST: A study of the power function of one-sided tests. An approximate expression, with desirable properties from the viewpoint of power functon comparisons, is determined for the power function. 3 pp. P-92: Some Comments on the Efficiency of Significance Tests. AUTH: J.E. Walsh PAGES: 10, DATE: 1949 COST: $ 4.00 KEYS: Statistical analysis ABST: A discussion of an estimate method which determines the efficiency of a significance test. This process associates a statistic with the test and defines the efficiency of the test to be the efficiency of the statistic considered as an estimate. Its power function implications are examined for several cases in which uniformly most powerful tests exist. (Published in [Human Biology].) 10 pp. P-93: The Prediction of Social and Technological Events. AUTH: A. Kaplan, A.L. Skogstad, M.A. Girshick PAGES: 31, DATE: 1949 COST: $ 4.00 KEYS: Delphi method; Forecasting; Technology ABST: A report on a pilot study of the prediction of social and technological events. From questioning twenty-six predictors, certain criteria were estimated: (1) the success of such prediction, (2) its possible improvement, and (3) the prior appraisal of the success to be expected. 31 pp. P-94: Integral of the Guassian Distribution Over an Offset Ellipse. AUTH: H.H. Germond PAGES: 13, DATE: 1949 COST: $ 4.00 ABST: No abstract available. 13 pp. P-96: The Future of Mathematical Statistics and Quality Control. AUTH: G.W. Brown PAGES: 7, DATE: 1949 COST: $ 4.00 KEYS: Industry; Production; Statistics ABST: A discussion of a few specific areas of activity in mathematical statistics in the field of quality control. (Published in the [Bulletin of the International Statistical Institute], Part 2, Vol. XXXII, 1950.) 7 pp. P-97: Geometry and Reduced Moment Spaces. AUTH: S. Karlin, L.S. Shapley PAGES: 7, DATE: 1949 COST: $ 4.00 ABST: No abstract available. 7 pp. P-100: Polynomial Games. AUTH: M. Dresher, S. Karlin, L.S. Shapley PAGES: 28, DATE: 1950 COST: $ 4.00 KEYS: Game theory ABST: A presentation of a basis for a theory of two-person zero-sum games in which the payoff is a polynomial function of the two strategy variables. 28 pp. P-102: On a Generalization of the Behrens-Fisher Problem. AUTH: J.E. Walsh PAGES: 11, DATE: 1949 COST: $ 4.00 KEYS: Numerical methods and approximations; Statistical analysis ABST: A generalization which may be approximated by many practical situations. A solution is presented for the generalized situation, and some efficiency properties of this solution are investigated. (Published in [Human Biology], May 1950.) 11 pp. P-105: Planning Defense Production. AUTH: C.J. Hitch PAGES: 12, DATE: 1949 COST: $ 4.00 KEYS: Accounting and budgets ABST: A talk delivered in late 1949 on the production problems of an advanced defense economy. The method considered is one in which the defense resources or budget is allocated among the production of the various goods and services contributing to the nation's security. 12 pp. P-106: Total Reconnaissance with Total Countermeasures: Simplified Model. AUTH: S. Sherman PAGES: 2, DATE: 1949 COST: $ 4.00 KEYS: Game theory; Reconnaissance ABST: Proof of a theorem and two corollaries on a simplified model of total reconnaissance with total countermeasures. (Also published as RM-202.) 2 pp. P-112: Concerning the Effect of Small Correlation on Certain Large-Sample Tests and Confidence Intervals for the Mean. AUTH: J.E. Walsh PAGES: 7, DATE: 1949 COST: $ 4.00 KEYS: Statistical analysis ABST: A study of statistical tests and confidence intervals for the population mean. The case considered is one in which the random sample requirement is violated and the number of observations is large. (Published in the [Journal of the American Statistical Association], March 1951.) 7 pp. P-113: History of RAND's Random Digits: Summary. AUTH: G.W. Brown PAGES: 5, DATE: 1949 COST: $ 4.00 KEYS: Mathematics; Numerical methods and approximations; Stochastic processes ABST: Described are (1) the random digit generator, (2) various tests applied to the digits, and (3) the method of alteration of the digits to remove a bias. (Published in the [Applied Mathematics Series-12], June 1951. See also P-44.) 5 pp. P-116: Efficient Allocation of Resources. AUTH: T.C. Koopmans PAGES: 14, DATE: 1949 COST: $ 4.00 ABST: No abstract available. 14 pp. P-129: A Large Sample [T]-Statistic Which Is Insensitive to Nonrandomness. AUTH: J.E. Walsh PAGES: 7, DATE: 1950 COST: $ 4.00 KEYS: Mathematics; Statistical analysis; Stochastic processes ABST: A study of statistical tests and confidence intervals for the population mean. The case considered is one in which the random sample requirement is violated and the number of observations is large. (Published in the [Journal of the American Statistical Association].) 7 pp. P-131: On Games of Timing. AUTH: M. Shiffman PAGES: 39, DATE: 1949 COST: $ 4.00 KEYS: Game theory ABST: An analysis of a symmetric game of timing. The report shows (1) that there is a unique strategy which is either a density from some point [a] to 1, or there is a jump at 0 and a density from [a] to 1; and (2) that determining the density function depends on the solution of a certain integral equation with positive kernel. 39 pp. P-133: Some Tests for Comparing Percentage Points of Two Arbitrary Continuous Populations. AUTH: A.W. Marshall, J.E. Walsh PAGES: 13, DATE: 1950 COST: $ 4.00 KEYS: Statistical analysis ABST: A comparison of samples from two continuous populations. 13 pp. P-139: On a Theorem of DOOB. AUTH: T.E. Harris PAGES: 9, DATE: 1950 COST: $ 4.00 ABST: A justification for the interchange of limiting process required in the heuristic approach of Doob to the Kolmogorov limiting distribution of the maximum deviation between a theoretical and an empirical distribution function. P-140: A Simplification of Games in Extensive Form. AUTH: W.D. Krentel, J.C.C. McKinsey, W.V. Quine PAGES: 32, DATE: 1951 COST: $ 4.00 KEYS: Game theory ABST: A study of game theory in extensive form applicable to military situations. The problem of a necessary and sufficient condition for the equivalence of two patterns of information is also discussed. 32 pp. P-141: Recurrence Times for the Ehrenfest Model. AUTH: R.E. Bellman, T.E. Harris PAGES: 18, DATE: 1950 COST: $ 4.00 ABST: No abstract available. 18 pp. P-142: Solutions of Games by Differential Equations. AUTH: G.W. Brown, J. VonNeumann PAGES: 11, DATE: 1950 COST: $ 4.00 KEYS: Differential equations; Game theory ABST: A presentation of a new proof for the existence of a value and of good strategies for a zero-sum two-person game. 11 pp. P-152: Some Mathematical Models for Branching Processes. AUTH: T.E. Harris PAGES: 53, DATE: 1950 COST: $ 7.50 ABST: No abstract available. 53 pp. P-159: On the General Moment Problem. AUTH: R.E. Bellman, D.H. Blackwell PAGES: 14, DATE: 1950 COST: $ 4.00 ABST: A method which theoretically resolves the general moment problem and provides the solution to the problem of characterizing the moment space of characteristic functions. P-168: On Games Involving Bluffing. AUTH: R.E. Bellman, D.H. Blackwell PAGES: 32, DATE: 1950 COST: $ 4.00 KEYS: Game theory NOTE: See also: P-84. ABST: An investigation of some sets of heuristic axioms of play for simple card games in order to determine the general pattern which contributes to the solution of the mathematical problem of the solution of maximizing or minimizing the expectation of a player in a many-moved two-person game. (See also P-84.) 32 pp. P-172: Two-Person Cooperative Games. AUTH: J.F. Nash PAGES: 12, DATE: 1950 COST: $ 4.00 KEYS: Game theory ABST: A definition of the concepts of a general two-person cooperative game with the development of a concept of a solution. 12 pp. P-179: A Large-Sample Test of the Hypothesis That One of Two Random Variables Is Stochastically Larger Than the Other. AUTH: A.W. Marshall PAGES: 13, DATE: 1951 COST: $ 4.00 KEYS: Statistical analysis; Stochastic processes ABST: A presentation of a large-sample nonparametric test using grouped data. (Published in the [Journal of the American Statistical Association], September 1951.) 13 pp. P-180: Some Non-Parametric Results for Experimental Designs. AUTH: J.E. Walsh PAGES: 12, DATE: 1950 COST: $ 4.00 KEYS: Experimental design; Statistical analysis ABST: Some nonparametric results which are usually valid for a well-known type of experimental design. (Published in the [Journal of the American Statistical Association], September 1952.) 12 pp. P-183: An Analysis of Some Failure Data. AUTH: D.J. Davis PAGES: 42, DATE: 1952 COST: $ 4.00 ABST: No abstract available. 42 pp. P-188: On Certain Games with Transcendental Values. AUTH: O.A. Gross PAGES: 2, DATE: 1950 COST: $ 4.00 KEYS: Game theory ABST: An observation that for certain games with transcendental values there is no optimal strategy consisting of a step function of finitely many steps. 2 pp. P-189: Optimal Inventory Policy. AUTH: K.J. Arrow, T.E. Harris, J. Marschak PAGES: 47, DATE: 1950 COST: $ 4.00 ABST: No abstract available. 47 pp. P-193: A Further Generalization of the Kakutani Fixed-Point Theorem, with Applications to Nash Equilibrium Points. AUTH: I.L. Glicksberg PAGES: 8, DATE: 1951 COST: $ 4.00 KEYS: Game theory ABST: A proof of the analogue of the Tychonoff extension of the fixed-point theorem of Brouwer for the Kakutani fixed-point theorem. The Kakutani theorem is extended to convex Hausdorff linear topological spaces. With this, the existence of equilibrium points in the general [n]-person continuous game, with continuous payoffs, is demonstrated. 8 pp. P-204: A Formal Theory of the Employment Relationship. AUTH: H.A. Simon PAGES: 18, DATE: 1950 COST: $ 4.00 ABST: No abstract available. 18 pp. P-207: First-Passage and Recurrence Distributions. AUTH: T.E. Harris PAGES: 26, DATE: 1951 COST: $ 4.00 KEYS: Markov processes; Statistical analysis ABST: A discussion of first passage and recurrence distributions for the states of an irreducible Markov chain. (Published in the [Proceedings of the Institute of Mathematical Statistics], September 1951, and in the [Transactions of the American Mathematical Society], 1952.) 26 pp. Ref. P-219: A Comparison of Organization Theories. AUTH: H.A. Simon PAGES: 21, DATE: 1951 COST: $ 4.00 ABST: A paper suggesting a framework that permits a comparison of the economist's theory of the firm and the administrator's theory of organizational equilibrium. P-222: A Comparison of Treatments of a Duopoly Situation. AUTH: J.P. Mayberry, J.F. Nash, M. Shubik PAGES: 21, DATE: 1951 COST: $ 4.00 KEYS: Game theory ABST: An examination on the basis of each of several theories, of the behavior of two firms in competition, with explicit cost functions and an explicit demand function. 21 pp. P-227: Geometry and Moment Spaces. AUTH: S. Karlin, L.S. Shapley PAGES: 98, DATE: 1952 COST: $ 7.50 ABST: No abstract available. 98 pp. P-230: On Some Dynamic Linear Programming Problems. AUTH: R.E. Bellman PAGES: 11, DATE: 1951 COST: $ 4.00 ABST: No abstract available. 11 pp. P-234: On the Application of Servomechanism Theory in the Study of Production Control--A Study in the Theory of Organization. AUTH: H.A. Simon PAGES: 30, DATE: 1951 COST: $ 4.00 ABST: An application of the servomechanism theory to the analysis and design of decisional procedures for controlling the rate of manufacturing activity. P-238: The First Passage Problem for a Continuous Markoff Process. AUTH: D.A. Darling, A.J.F. Siegert PAGES: 31, DATE: 1953 COST: $ 4.00 ABST: No abstract available. 31 pp. P-241: Reduction of Certain Classes of Games to Integral Equations. AUTH: S. Karlin PAGES: 42, DATE: 1951 COST: $ 4.00 KEYS: Game theory; Integral equations ABST: An investigation of the relationship of certain classes of games with corresponding integral equations. 42 pp. P-248: The Theory of Infinite Games. AUTH: S. Karlin PAGES: 53, DATE: 1951 COST: $ 7.50 KEYS: Game theory ABST: A development of the general theory of infinite games, with a presentation of some new examples of determinate games. 53 pp. P-252: Moment Spaces and Inequalities. AUTH: M. Dresher PAGES: 22, DATE: 1952 COST: $ 4.00 ABST: A geometrical interpretation of an integral inequality as a condition that a given point lie in a space defined by the convex hull of a given curve. By characterizing the boundaries of various dimensions, integral inequalities are derived from the requirement that points of the space lie within elements of the boundaries. P-254: On a Class of Games. AUTH: S. Karlin PAGES: 13, DATE: 1951 COST: $ 4.00 KEYS: Game theory ABST: A qualitative description of the nature of optimal strategies for a payoff kernel satisfying a certain condition on its partial derivatives. 13 pp. P-255: Solutions of Convex Games as Fixed-Points. AUTH: M. Dresher, S. Karlin PAGES: 16, DATE: 1951 COST: $ 4.00 KEYS: Game theory ABST: A derivation of some general dimensional properties of solutions for games played over arbitrary convex sets, using a fixed-point interpretation of an optimal strategy. 16 pp. P-256: A Preference Experiment. AUTH: M.M. Flood PAGES: 43, DATE: 1951 COST: $ 4.00 KEYS: Group behavior ABST: A study of a preference experiment conducted to develop a theory adequate to predict (1) the group preference in any single trial, in terms of data available prior to the trial, and (2) the interesting features of group activity encountered in the choice process. The experiment described consists of a group of individuals asked to select one from a set of alternatives. (See also RM-709, RM-789-1, P-258, P-263, P-312, P-346. 43 pp. P-257: Games of Pursuit. AUTH: R. Isaacs PAGES: 14, DATE: 1951 COST: $ 4.00 KEYS: Game theory ABST: A discussion of several examples of games of pursuit. 14 pp. P-258: A Preference Experiment (Series 2, Trial 1). AUTH: M.M. Flood PAGES: 42, DATE: 1951 COST: $ 4.00 ABST: No abstract available. 42 pp. P-263: A Preference Experiment (Series 2, Trials 2, 3, 4). AUTH: M.M. Flood PAGES: 24, DATE: 1952 COST: $ 4.00 ABST: No abstract available. 24 pp. P-265: Equivalence of Information Patterns and Essentially Determinate Games. AUTH: N.C. Dalkey PAGES: 33, DATE: 1952 COST: $ 4.00 KEYS: Game theory ABST: Derivations of a necessary and sufficient condition for the equivalence of information patterns in general games and of a necessary and sufficient condition for essential determinateness. 33 pp. P-266: The Uses and Limitations of Mathematical Models, Game Theory and Systems Analysis in Planning and Problem Solution. AUTH: J.L. Kennedy PAGES: " 21, DATE: 1952 COST: $ 4.00 KEYS: Game theory; Game theory; Planning; Problem solving ABST: A discussion of how to deal scientifically with a complex system; i.e., "an assemblage of objects united by some form of regular interaction or interdependence, an organic or organized whole." 21 pp. P-267: Use of the Learning Curve. AUTH: D. Novick PAGES: 6, DATE: 1951 COST: $ 4.00 KEYS: Cost estimating; Learning curves ABST: A discussion of the learning curve (a concept of estimating changes in unit labor cost as increasing quantities of an article are produced) and of some of the things to be considered in using the curve for prediction purposes. 6 pp. P-280: On the Asymptotic Efficiency of Certain Non-Parametric Two-Sample Tests. AUTH: A.M. Mood PAGES: 17, DATE: 1952 COST: $ 4.00 KEYS: Statistical analysis ABST: The computation of certain asymptotic efficiencies for given two-sample tests against normal alternatives to the null hypothesis. Published in [The Annals of Mathematical Statistics], September 1954.) 17 pp. P-295: A Value for [N]-Person Games. AUTH: L.S. Shapley PAGES: 15, DATE: 1952 COST: $ 4.00 KEYS: Game theory ABST: An examination of a number of elementary properties of a value for the "essential" case. This value is deduced from a set of three axioms, having simple intuitive interpretations. 15 pp. P-297: Quota Solutions of [N]-Person Games. AUTH: L.S. Shapley PAGES: 24, DATE: 1952 COST: $ 4.00 KEYS: Game theory ABST: A presentation of a family of solutions for a class Q ("quota games") of [n]-person games which embraces all constant-sum four-person games and a not inconsiderable array of higher games. In addition, some related, more complicated solutions to Q games are described, as well as an extension of the results to a wider class of games. 24 pp. P-305: On the Detection of a Sine Wave in Gaussian Noise. AUTH: E. Reich, P. Swerling PAGES: 27, DATE: 1952 COST: $ 4.00 ABST: No abstract available. 27 pp. P-309: A Survey of Input-Output Research. AUTH: R.W. Shephard PAGES: 80, DATE: 1952 COST: $ 7.50 ABST: No abstract available. 80 pp. P-326: Suboptimization in Operations Problems. AUTH: C.J. Hitch PAGES: 24, DATE: 1952 COST: $ 4.00 KEYS: Operations research; Optimization ABST: An analysis of the possibilities, limitations, and dangers of suboptimizing. In addition, the utility of certain concepts and postulates of economic theory for improving the selection of criteria in operations research problems is examined. 24 pp. P-329: On a Functional Equation Occurring in the Theory of Dynamic Programming. AUTH: R.E. Bellman PAGES: 23, DATE: 1952 COST: $ 4.00 ABST: No abstract available. 23 pp. P-337: Methods of Reducing Sample Size in Monte Carlo Computations. AUTH: H. Kahn, A.W. Marshall PAGES: 18, DATE: 1953 COST: $ 4.00 KEYS: Monte carlo method; Statistical analysis ABST: This paper formulates the general problem of Monte Carlo computations within the framework of mathematical statistics and indicates briefly its relation to the theory of estimation and the design of experiments. (Published in the [Journal of the Operations Research Society of America], November 1953.) 18 pp. P-346: On Game-Learning Theory and Some Decision-Making Experiments. AUTH: M. Flood PAGES: 39, DATE: 1952 COST: $ 4.00 ABST: No abstract available. 39 pp. P-354: Conflicts with Imprecise Payoffs. AUTH: J.D. Williams PAGES: 13, DATE: 1952 COST: $ 4.00 KEYS: Game theory ABST: A discussion of game theory to illustrate conflict situations in which imprecise payoffs appear. 13 pp. P-365: Behavioral Model of Rational Choice. AUTH: H.A. Simon PAGES: 16, DATE: 1953 COST: $ 4.00 ABST: No abstract available. 16 pp. P-379: A Derivative Test for Finite Solutions of Games. AUTH: I.L. Glicksberg PAGES: 7, DATE: 1953 COST: $ 4.00 KEYS: Game theory ABST: A proof that in a game over the square with continuous payoff [M], the minimizing ([y]) player has an optimal strategy using at most [n]/2 points (counting 0 and 1 as half points), and the maximizing player has an optimal strategy using at most [n] points. 7 pp. P-380: On Some Variational Problems Occurring in the Theory of Dynamic Programming. AUTH: R.E. Bellman, I.L. Glicksberg, O.A. Gross PAGES: 50, DATE: 1953 COST: $ 4.00 ABST: No abstract available. 50 pp. P-382: Studies in Functional Equations Occurring in Decision Processes. AUTH: R.E. Bellman, H.N. Shapiro, T.E. Harris PAGES: 62, DATE: 1953 COST: $ 7.50 KEYS: Functional equations ABST: A collection of three papers which discuss various functional equations arising from certain decision-making models. P-386: Suboptimization Criteria and Operations Research. AUTH: R.N. McKean PAGES: 20, DATE: 1953 COST: $ 4.00 KEYS: Operations research; Optimization ABST: An extension of the discussion presented in P-326. This paper discusses criteria prerequisite to (1) suboptimizations that lead to improved operations within a given institutional framework, (2) institutional changes devised for increasing efficiency, and (3) descriptive or consumers' research useful to high-level suboptimization. 20 pp. P-402: Optimal Two- and Three-Stage Production Schedules with Setup Time Included. AUTH: S.M. Johnson PAGES: 10, DATE: 1953 COST: $ 4.00 ABST: No abstract available. 10 pp. P-405: On a Class of Games over Function Space and Related Variational Problems. AUTH: W.H. Fleming PAGES: 36, DATE: 1953 COST: $ 4.00 KEYS: Game theory ABST: A study of a certain class of two-person zero-sum games in which the players have functions as pure strategies. A notion of mixed strategy is defined for such games, and a theorem is proved ensuring the existence of solutions in mixed strategies. 36 pp. P-407: Bottleneck Problems and Dynamic Programming. AUTH: R.E. Bellman PAGES: 8, DATE: 1953 COST: $ 4.00 ABST: No abstract available. 8 pp. P-410: Some Functional Equations in the Theory of Dynamic Programming. AUTH: R.E. Bellman PAGES: 9, DATE: 1953 COST: $ 4.00 ABST: No abstract available. 9 pp. P-414: A Simple Derivation of the Poisson Distribution. AUTH: R.E. Kalaba PAGES: 2, DATE: 1953 COST: $ 4.00 ABST: No abstract available. 2 pp. P-419: Passage of Stationary Processes Through Linear and Nonlinear Devices. AUTH: A.J.F. Siegert PAGES: 26, DATE: 1953 COST: $ 4.00 ABST: No abstract available. 26 pp. P-423: Computational Problems in the Theory of Dynamic Programming. AUTH: R.E. Bellman PAGES: 21, DATE: 1953 COST: $ 4.00 KEYS: Programming (mathematics) ABST: A formulation in terms of the dynamic programming approach, of a simple problem involving a sequence of decisions. The resultant functional equation is used to illustrate a number of approximation techniques, employing the particularly important concept of approximation in strategy space. P-433: A Functional Equation in the Theory of Dynamic Programming and Its Generalizations. AUTH: R.E. Bellman, R.S. Lehman PAGES: 71, DATE: 1953 COST: $ 7.50 ABST: No abstract available. 71 pp. P-435: Comments on J. Von Neumann's "The Problem of Optimal Assignment on a Two-Person Game.". AUTH: G.B. Dantzig PAGES: 5, DATE: 1952 COST: $ 4.00 ABST: A simplification of certain arguments in J. von Newmann's paper reducing the optimal assignment problem to a two-person game. P-436: On the Continuous Gold-Mining Equation. AUTH: R.E. Bellman, R.S. Lehman PAGES: 8, DATE: 1953 COST: $ 4.00 ABST: No abstract available. 8 pp. P-440: The Product Form for the Inverse in the Simplex Method. AUTH: G.B. Dantzig, W. Orchard-Hays PAGES: 7, DATE: 1953 COST: $ 4.00 ABST: No abstract available. 7 pp. P-444: Military Implications of Nuclear Weapon Developments. AUTH: B. Brodie PAGES: 21, DATE: 1953 COST: $ 4.00 KEYS: Nuclear weapons ABST: An appraisal of the military importance of thermonuclear weapons. The author attempts to indicate the present or future transportability of thermonuclear weapons in existing types of aircraft, their energy yield or probable range of yields, and their cost per unit to produce, particularly in relation to the resources involved in manufacturing fission bombs. (Published in [Foreign Affairs], January 1954.) 21 pp. P-454: Dynamic Programming and a New Formalism in the Calculus of Variations. AUTH: R.E. Bellman PAGES: 7, DATE: 1953 COST: $ 4.00 ABST: No abstract available. 7 pp. P-455: Some Problems in the Theory of Dynamic Programming. AUTH: R.E. Bellman PAGES: 20, DATE: 1953 COST: $ 4.00 ABST: No abstract available. 20 pp. P-456: Some Combinatorial Problems Arising in the Theory of Multistage Processes. AUTH: R.E. Bellman, O.A. Gross PAGES: 14, DATE: 1953 COST: $ 4.00 ABST: No abstract available. 14 pp. P-457: On Some Applications of the Theory of Dynamic Programming to Logistics. AUTH: R.E. Bellman PAGES: 23, DATE: 1953 COST: $ 4.00 ABST: No abstract available. 23 pp. P-468: Notes on Parametric Linear Programming. AUTH: A.S. Manne PAGES: 7, DATE: 1953 COST: $ 4.00 ABST: No abstract available. 7 pp. P-470: Notes on the Optimal Choice of Weapons. AUTH: J. Marschak, M.R. Mickey PAGES: 36, DATE: 1951 COST: $ 4.00 ABST: No abstract available. 36 pp. P-473: On a New Iterative Algorithm for Finding the Solutions of Games and Linear Programming Problems. AUTH: R.E. Bellman PAGES: 15, DATE: 1953 COST: $ 4.00 KEYS: Games ABST: A discussion of an iterative procedure which yields the value of a game very rapidly. 15 pp. RM-1011/PR: Report on a Preliminary Systems Analysis for Strategic Targets. AUTH: N.C. Dalkey, O. Helmer, F.B. Thompson PAGES: 91, DATE: 1953 COST: $ 7.50 ABST: A status report on a pilot study concerned with the planning of a target system analysis, designed to synthesize such aspects of the targeting problem as operational factors, physical vulnerability, economic consequences of physical destruction, and military consequences of economic damage. RM-1169/PR: The Feasibility of Using the F84G for Air-to-Air Toss Bombing with Atomic Weapons. AUTH: J.L. Jenkins PAGES: 12, DATE: 1953 COST: $ 4.00 ABST: A brief analysis of the feasibility of using the F-84G for air-to-air bombing with the MK-7 bomb. The mission considered is evaluated for one representative set of parameters, and only minor changes in the fire control systems are assumed. RM-260-1-PR: Reliability of Progress Curves in Airframe Production. AUTH: A.A. Alchian PAGES: 33, DATE: 1950 COST: $ 4.00 KEYS: Aerospace industry and trade; Airframes; Learning curves; Reliability; KEYS: Statistics ABST: A presentation of statistical tests which determine the similarity of the functions among various airframe manufacturers based on World War II data. An assessment of the prediction reliability is made with these curves. 33 pp. RM-481-PR: Reliability of Cost Estimates: Some Evidence. AUTH: A.A. Alchian PAGES: 11, DATE: 1950 COST: $ 4.00 KEYS: Cost estimating; Reliability ABST: A presentation of data from several sources on the reliability of cost estimates. It is presented as an aid which can be used as a yardstick for gauging the reliability of other cost estimates or predictions. RM-563-PR: Estimating Output from Floor Space: Feasibility. AUTH: A.A. Alchian, A.L. Skogstad, N. Hanunian PAGES: 18, DATE: 1951 COST: $ 4.00 KEYS: Airframes; Production ABST: No abstract available. 18 pp. RM-224: A Mathematical Model of an Air Transportation System. AUTH: T.W. Anderson, K.J. Arrow, J.E. Walsh PAGES: 8, DATE: 1949 COST: $ 4.00 KEYS: Transportation--Mathematical models ABST: A development of a mathematical model of an air transportation system in order to study the most efficient program of operations for transporting a given amount of goods between two fixed locations per unit of time. 8 pp. RM-284-PR: Some Statistical Problems Connected with Stochastic Processes. AUTH: T.W. Anderson, D.A. Darling PAGES: 13, DATE: 1949 COST: $ 4.00 KEYS: Statistical analysis; Stochastic processes ABST: A treatment of the problem of testing the hypothesis that a sample of [n] independent, identically distributed random variables has the common continuous distribution function [F(x)] specified in advance. The method used reduces the problems to considerations in the theory of continuous Gaussian stochastic processes. 13 pp. P-169: Some Statistical Problems Connected with Stochastic Processes. AUTH: T.W. Anderson, D.A. Darling PAGES: 20, DATE: 1950 COST: $ 4.00 KEYS: Statistical analysis; Stochastic processes ABST: A treatment of the statistical problem of testing the hypothesis that a sample of [n] independent, identically distributed, random variables has the common continuous distribution function [F(x)] fixed in advance. (Published in [The Annals of Mathematical Statistics], June 1952.) 20 pp. RM-456-PR: Methodology Problems in Airframe Cost-Performance Studies. AUTH: K.J. Arrow, S.S. Arrow PAGES: 33, DATE: 1950 COST: $ 4.00 KEYS: Airframes; Cost analysis ABST: A study of the possible approaches to the problem of establishing a relation between the cost and the performance of airframes which will be useful for such predictive purposes as estimating costs incurred by altered specifications. 33 pp. P-239: Comparison of Input-Output and Alternative Projections, 1929-1939. AUTH: S.S. Arrow PAGES: 17, DATE: 1951 COST: $ 4.00 ABST: An attempt to compare four alternative techniques of forecasting under the hypothesis that all the basic data necessary for each method are available. The errors are examined in each set of projections of industry outputs from 1929 to 1939. RM-645-PR: On a Geometrical Game Connected with Sequential Analysis. AUTH: R.E. Bellman PAGES: 13, DATE: 1951 COST: $ 4.00 KEYS: Bombing; Game theory ABST: A consideration of a game which has its origins in some strategic bombing models. 13 pp. RM-1069: On an Application of the Theory of Dynamic Programming to Bottleneck Problems in Production and Allocation. AUTH: R.E. Bellman PAGES: 8, DATE: 1953 COST: $ 4.00 ABST: The title describes the aim and content of this publication. RM-1131: A Survey of the Current Status of the Electronic Reliability Problem. AUTH: R.R. Carhart PAGES: 136, DATE: 1953 COST: $ 10.00 ABST: An evaluation of reliability as a systems problem. The study examines (1) the general background of the problem, (2) tube, component, and system reliability, (3) personnel and organizational factors, (4) the theory of reliability, and (5) the application of the theory to military electronics. The concept of critical complexity is introduced, and reliability control is suggested as an effective means of achieving and maintaining reliability in the development, production, and use of complex electronic systems. No abstract available. 145 pp. RM-818-PR: Another Proof of the Minmax Theorem for Continuous Payoff. AUTH: J.M. Danskin, J.M. Danskin PAGES: 4, DATE: 1952 COST: $ 4.00 KEYS: Game theory ABST: The convergence for continuous games of the Brown-Robinson iterative process is used to prove the minmax theorem for these games. 4 pp. P-235: A Game over Function Space. AUTH: J.M. Danskin, L. Gillman PAGES: 15, DATE: 1953 COST: $ 4.00 KEYS: Game theory ABST: A proof of the existence of a saddle-point in an example of a nonlinear game over function space and a derivation of an explicit formula for the solution. 15 pp. P-293: An Extension of the Brown-Robinson Iterative Process for Finding the Value of a Game. AUTH: J.M. Danskin, J.M. Danskin PAGES: 13, DATE: 1952 COST: $ 4.00 KEYS: Game theory ABST: A proof that the process corresponding to the Brown-Robinson iterative method is valid for zero-sum two-person games with continuous payoffs, played over the unit square. 13 pp. RM-1265: Notes on Linear Programming--Part II: Duality Theorems. AUTH: G.B. Dantzig, A. Orden, A. Orden PAGES: 4, DATE: 1953 COST: $ 4.00 ABST: A demonstration that the simplex procedure itself yields as a natural by-product proofs of several important theorems concerned with duality in the field of linear inequalities. RM-1266: Notes on Linear Programming--Part III: Computational Algorithm of the Revised Simplex Method. AUTH: G.B. Dantzig PAGES: 7, DATE: 1953 COST: $ 4.00 ABST: An extension of RM-1264 and RM-1265, Parts I and II, respectively, of Notes on Linear Programming. The present study presents the computational procedure. RM-1094: Distributions of Surviving Bombers in Certain Air Battle Models. AUTH: W.J. Dixon PAGES: 35, DATE: 1953 COST: $ 4.00 ABST: A comparison of alternative approximations for the distribution and expected value of the number of surviving bombers in a homogeneous cell. This cell is subjected to successive waves of attacks identical with respect to both the number of attackers and the effectiveness of each attacker. No abstract available. 36 pp. RM-1102: A Production-Line Assignment Problem. AUTH: D.R. Fulkerson, I.L. Glicksberg, O.A. Gross, I.L. Glicksberg, O.A. Gross PAGES: 3, DATE: 1953 COST: $ 4.00 KEYS: Production ABST: A description of a production-line problem of the bottleneck type. Its solution is given by relating it to the optimal assignment problem solved by J. von Neumann, G. B. Dantzig, and others. No abstract available. 4 pp. RM-1171: A Tactical Air Game. AUTH: D.R. Fulkerson, S.M. Johnson, S.M. Johnson PAGES: 20, DATE: 1953 COST: $ 4.00 ABST: A formulation of a discrete, linear analogue of Mengel's model of a tactical air war as a game (described in RM-1068). The symmetric case in which the attrition rates are the same for both sides is solved for both finite and infinite campaigns. No abstract available. 21 pp. RM-684-PR: Decision Functions for Bombing Models. AUTH: M. Hausner PAGES: 5, DATE: 1951 COST: $ 4.00 ABST: No abstract available. 5 pp. RM-776-PR: Games of Survival. AUTH: M. Hausner PAGES: 8, DATE: 1952 COST: $ 4.00 KEYS: Games ABST: A proof that in general a 2 x 2 zero-sum game of survival has a solution. It is shown that the two motives, of survival or of ruin of the opponent, are equivalent. 8 pp. RM-777-PR: Optimal Strategies in Games of Survival. AUTH: M. Hausner PAGES: 6, DATE: 1952 COST: $ 4.00 KEYS: Games ABST: A presentation of a simple procedure for calculating the optimal strategies and the survival probability for a general class of games of survival. 6 pp. RM-1058: Chain Reliability: A Simple Failure Model for Complex Mechanisms. AUTH: W.J. Howard PAGES: 35, DATE: 1953 COST: $ 4.00 ABST: A discussion of a simple example of a chain supporting a weight to determine how the reliability of a complex mechanism depends on the reliability of its components. The chain, consisting of several links, represents a complex mechanism composed of similar components, and the weight is analogous to a type of environmental stress which the mechanism must withstand without failure. No abstract available. 35 pp. R-249: Capabilities and Operating Costs of Possible Future Transport Airplanes. AUTH: T.V. Jones, AircraftDesignSection PAGES: 195, DATE: 1953 COST: $ 15.00 KEYS: Air transportation; Transport airplanes ABST: An attempt to determine the capabilities and operating costs of potential transport aircraft. This report (1) illustrates how aircraft should be compared in performing a logistics job by providing a sample operational analysis of transport airplane use and (2) discusses the design and analysis of many possible future transport aircraft which could be operational in 8 to 10 years if the necessary engine and airframe development were carried on from the present time. A 1953 attempt to determine the capabilities and operating costs of potential transport aircraft. This report (1) illustrates how aircraft should be compared in performing a logistics job by providing a sample operational analysis of transport airplane use and (2) discusses the design and analysis of many possible future transport aircraft. 202 pp. RM-189-PR: Note on Some Historic Principles of Target Selection. AUTH: C. Kaysen PAGES: 1, DATE: 1949 COST: $ 4.00 ABST: No abstract available. 1 pp. R-0165: Notes on Strategic Air Intelligence in World War II (ETO). AUTH: C. Kaysen PAGES: vii, 32, DATE: 1949 COST: |c$4.00 KEYS: World War, 1939-1945--Aerial operations; World War, 1939-1945--Military KEYS: intelligence RM-1140: Algebraic Solution of Linear-Programming Problems. AUTH: J.G. Kemeny PAGES: 43, DATE: 1953 COST: $ 4.00 ABST: An illustration of certain algebraic solutions for linear-programming problems in order to show that in the case of reasonably simple problems these techniques are superior to the usual machine-methods. No abstract available. 44 pp. RM-1068: Optimum Tactics in an Air Superiority Campaign. AUTH: A.S. Mengel PAGES: 26, DATE: 1953 COST: $ 4.00 ABST: An application of the calculus of variations to an investigation of the optimum tactics in an air superiority campaign described by a simple set of Lanchester-type differential equations. This study determines: (1) a straightforward definition of air superiority, (2) the numerical advantage required to obtain it, and (3) a simple rule for allocating sorties between counter-air and counter-surface missions to maximize the relative support given the ground troops. No abstract available. 27 pp. R-251-AEC: Worldwide Effects of Atomic Weapons: Project SUNSHINE. AUTH: PhysicsDepartment PAGES: 107, DATE: 1953 COST: $ 10.00 KEYS: Fallout; Nuclear weapons effects; Radiation ABST: A presentation of a 1953 estimate of the fallout problem. The report discusses the various aspects of long-range contamination due to the detonation of large numbers of nuclear devices. An improved methodology for assessing the human hazard is developed, and an extensive experimental program is proposed. An amended, unclassified version of R-251-AEC, which presents the 1953 estimate of the fallout problem. The report discusses the various aspects of long-range contamination due to the detonation of large numbers of nuclear devices. An improved methodology for assessing the human hazard is developed, and an extensive experimental program is proposed. 107 pp. RM-1005: N-Person Games--V: Stable-Set Solutions Including an Arbitrary Closed Component. AUTH: L.S. Shapley PAGES: 10, DATE: 1952 COST: $ 4.00 KEYS: Game theory ABST: A proof of a stable-set solution to a simple n-person game, which includes an arbitrary closed subset of a certain (n - 3)-dimensional convex region in the simplex of imputations, at a finite distance from the rest of the solution. A proof of a stable-set solution to a simple [n]-person game, which includes an arbitrary closed subset of a certain ([n] -3)-dimensional convex region in the simplex of imputations, at a finite distance from the rest of the solution. (Also published as P-888.) 11 pp. RM-279-PR: Notes on ([m] X 2) Evaluation Matrices for Special Systems Analysis Applications. AUTH: J.C. Wylie PAGES: 33, DATE: 1950 COST: $ 4.00 KEYS: Games ABST: A method to determine the optimal strategy of general ([m] x 2) matrices arising in game-theory problems in order to facilitate the application of this field of mathematics to practical systems analyses. This evaluation indicates the effects of parameter shifts and suggests general mathematical solutions for game theory problems. 33 pp. RM-1203-AEC: Polynomial Approximations to Neutron-Deuteron Differential Angular Cross Sections. AUTH: H. Zirin PAGES: 17, DATE: 1953 COST: $ 4.00 KEYS: Differential equations; Mathematics; Neutrons; Polynomials ABST: An attempt to describe the experimental measurements of (n, d) angular cross sections for computational purposes. The differential cross sections are approximated by a series of Legendre polynomials with energy-dependent coefficients, and smooth curves are drawn for the coefficients at various energies of incidence. 18 pp. R-0266: Selection and Use of Strategic Air Bases. AUTH: A.J. Wohlstetter, F. Hoffman, R.J. Lutz, H.S. Rowen PAGES: 426, DATE: 1954 COST: $ 25.00 KEYS: Bases; Strategic air command ABST: An examination of the critical factors in strategic-base selection and an application of this analysis to the basing of the 1956-1961 bombing force. The principal factors considered are the distances from bases to targets, to favorable entry points into enemy defenses, to the source of base supply, and to the points from which the enemy can attack these bases. In addition, the study discusses the joint effects of these factors on the costs of extending bomber radius, the enemy deployment of defenses, the numbers of our bombers lost to enemy fighters, logistics costs, base vulnerability, and our probable bomber loss on the ground. RM-1344-AEC: Equation of State of Air on the Statistical Model. AUTH: R. Latter PAGES: 35, DATE: 1954 COST: $ 4.00 KEYS: Atmosphere; Equations of state; Models; Temperature; Thermodynamics ABST: An estimate of the equation of state (for an oxygen, nitrogen, and argon mixture occurring in air) for the temperature range from 5000 degree K upward and for densities from 1/2,000 to 50 times normal density. These results are compared with those of Bethe, Fuchs, and others. P-311: An Application of Markov Processes to the Study of the Epidemiology of Mental Disease. AUTH: A.W. Marshall, H. Goldhamer PAGES: 51, DATE: 1954 COST: $ 7.50 KEYS: Mental health; Statistics ABST: A presentation of several methods (developed in studies of mental disease) for determining certain epidemiological parameters that are not directly observable or that can be secured only by expensive and time-consuming field surveys. The simple models of the process involved in the passage from sanity to insanity, hospitalization and death provide some picture of the underlying process that generates a given incidence rate. 51 pp. P-328: A Bayes Model in Sequential Design. AUTH: S.M. Johnson, S. Karlin PAGES: 30, DATE: 1954 COST: $ 4.00 ABST: A study to determine the optimal procedure for maximizing the expected number of successes in a given number of trials. P-466: The Effect of Reliability of "Supervisory" Equipment on the Accuracy of a "Supervised" System. AUTH: A.W. Boldyreff PAGES: 6, DATE: 1954 COST: $ 4.00 ABST: No abstract available. 6 pp. P-482: Computational Experience in Solving Linear Programming Problems. AUTH: W. Orchard-Hays PAGES: 19, DATE: 1954 COST: $ 4.00 ABST: No abstract available. 19 pp. P-483: Bottleneck Problems, Functional Equations and Dynamic Programming. AUTH: R.E. Bellman PAGES: 23, DATE: 1954 COST: $ 4.00 ABST: No abstract available. 23 pp. P-486: A General Survey of the Theory of Dynamic Programming. AUTH: R.E. Bellman PAGES: 59, DATE: 1954 COST: $ 7.50 ABST: No abstract available. 59 pp. P-490: Some Applications of the Theory of Dynamic Programming. AUTH: R.E. Bellman PAGES: 18, DATE: 1954 COST: $ 4.00 ABST: A description of the theory of dynamic programming. To illustrate the general principles, two particular problems-one of deterministic type and one of stochastic type-are treated. Published in the Journal of the Society for Industrial and Applied Mathematics. P-491: The Theory of Dynamic Programming as Applied to a Smoothing Problem. AUTH: R.E. Bellman, I.L. Glicksberg, O.A. Gross PAGES: 10, DATE: 1954 COST: $ 4.00 ABST: No abstract available. 10 pp. P-510: Solution of a Large-Scale Traveling-Salesman Problem. AUTH: G.B. Dantzig, D.R. Fulkerson, S.M. Johnson PAGES: 35, DATE: 1954 COST: $ 4.00 ABST: No abstract available. 35 pp. P-513: Monotone Convergence in Dynamic Programming and the Calculus of Variations. AUTH: R.E. Bellman PAGES: 8, DATE: 1954 COST: $ 4.00 ABST: No abstract available. 8 pp. P-530: Which Program Do We Mean in Program Budgeting? AUTH: D. Novick PAGES: " 22, DATE: 1954 COST: $ 4.00 KEYS: Accounting and budgets ABST: A discussion of the meaning and development of the word "program" as it is used in denoting government activities. Against this background, the author presents a fuller definition and discusses it in relation to "program budgeting." 22 pp. P-531: The Use of Multistage Sampling Schemes in Monte Carlo Computations. AUTH: A.W. Marshall PAGES: 20, DATE: 1954 COST: $ 4.00 KEYS: Monte carlo method; Probability ABST: A review of importance sampling, a technique whereby Monte Carlo computations are made more efficient--provided the probability distribution, from which the sample observations are drawn, is judiciously chosen. (Published in H. A. Meyer (ed.), [Symposium on Monte Carlo Methods], John Wiley & Sons, Inc., New York, 1956.) 20 pp. P-537: Systems Engineering. AUTH: A.W. Boldyreff PAGES: 13, DATE: 1954 COST: $ 4.00 ABST: No abstract available. 13 pp. P-550: The Theory of Dynamic Programming. AUTH: R.E. Bellman PAGES: 23, DATE: 1954 COST: $ 4.00 ABST: No abstract available. 23 pp. P-556: Univariate Two-Population Distribution-Free Discrimination. AUTH: D.S. Stoller PAGES: 11, DATE: 1954 COST: $ 4.00 KEYS: Statistical analysis; Stochastic processes ABST: An examination of an asymptotically optimum distribution-free procedure for classifying a univariate random variable into one of two subpopulations. (Published in the [Journal of the American Statistical Association], December 1954.) 11 pp. P-557: A Rational Game on the Square. AUTH: O.A. Gross PAGES: 6, DATE: 1954 COST: $ 4.00 KEYS: Game theory ABST: An example of a two-person zero-sum game on a closed unit square having as payoff a continuous rational function with rational coefficients. It is shown that the only optimal strategy available to either player is the Cantor function. 6 pp. P-561: The Problem of Routing Aircraft--A Mathematical Solution. AUTH: G.B. Dantzig, A.R. Ferguson PAGES: 18, DATE: 1954 COST: $ 4.00 ABST: No abstract available. 18 pp. P-562: Revisions and Extensions to the Simplex Method (With Side Lights on Programming Techniques). AUTH: W. Orchard-Hays PAGES: 22, DATE: 1954 COST: $ 4.00 ABST: No abstract available. 22 pp. P-564: Constructive Proof of the Min-Max Theorem. AUTH: G.B. Dantzig PAGES: 17, DATE: 1954 COST: $ 4.00 KEYS: Game theory ABST: An algebraic proof of the fundamental game theorem that is elementary and constructive. An example illustrates the method. 17 pp. P-566: Some Functional Equations in the Theory of Dynamic Programming--I: Functions of Points and Point Transformations. AUTH: R.E. Bellman PAGES: 36, DATE: 1954 COST: $ 4.00 ABST: No abstract available. 36 pp. P-568: Decisionmaking in the Face of Uncertainty--I: Uncertain Outcome. AUTH: R.E. Bellman PAGES: 7, DATE: 1954 COST: $ 4.00 ABST: No abstract available. 7 pp. P-572: On the Optimal Inventory Equation. AUTH: R.E. Bellman, I.L. Glicksberg, O.A. Gross PAGES: 6, DATE: 1954 COST: $ 4.00 ABST: No abstract available. 6 pp. P-574: Dynamic Programming and a New Formalism in the Theory of Integral Equations. AUTH: R.E. Bellman PAGES: 7, DATE: 1954 COST: $ 4.00 ABST: A proof that the functional equation technique of the dynamic programming theory may derive functional differential equations for the characteristic values of a certain integral equation, similar to those obtained for differential equation eigenvalues. P-575: On a Quasi-Linear Equation. AUTH: R.E. Bellman PAGES: 9, DATE: 1954 COST: $ 4.00 ABST: No abstract available. 9 pp. P-576: Upper Bounds, Secondary Constraints, and Block Triangularity in Linear Programming. AUTH: G.B. Dantzig PAGES: 22, DATE: 1954 COST: $ 4.00 ABST: No abstract available. 22 pp. P-579: Gaming as a Technique of Analysis. AUTH: A.M. Mood, R.D. Specht PAGES: 14, DATE: 1954 COST: $ 4.00 KEYS: Games ABST: A discussion of gaming as an activity in which a set of rules is established to represent the context of the problem considered. 14 pp. P-586: A Problem in the Sequential Design of Experiments. AUTH: R.E. Bellman PAGES: 17, DATE: 1954 COST: $ 4.00 ABST: No abstract available. 17 pp. P-589: Dynamic Programming and Multistage Decision Processes of Stochastic Type. AUTH: R.E. Bellman PAGES: 19, DATE: 1954 COST: $ 4.00 ABST: No abstract available. 19 pp. P-590: A Note on the Mean Value of Random Determinants. AUTH: R.E. Bellman PAGES: 4, DATE: 1954 COST: $ 4.00 ABST: No abstract available. 4 pp. P-593: Decisionmaking in the Face of Uncertainty--II. AUTH: R.E. Bellman PAGES: 11, DATE: 1954 COST: $ 4.00 ABST: No abstract available. 11 pp. P-602: Concepts and Computing Procedures for Certain X Programming Problems. AUTH: H.M. Markowitz PAGES: 44, DATE: 1954 COST: $ 4.00 ABST: No abstract available. 44 pp. P-605: Maximal Flow Through a Network. AUTH: L.R. Ford, D.R. Fulkerson PAGES: 12, DATE: 1954 COST: $ 4.00 ABST: No abstract available. 12 pp. P-609: A Linear-Programming Solution to Dynamic Leontief Type Models. AUTH: H.M. Wagner PAGES: 51, DATE: 1954 COST: $ 7.50 ABST: No abstract available. 51 pp. P-899: War Gaming as a Technique of Analysis. AUTH: A.M. Mood PAGES: 13, DATE: 1954 COST: $ 4.00 KEYS: Games ABST: A discussion of war gaming techniques, devised to deal with problems whose analysis requires appreciable context. 13 pp. R-0249: Capabilities and Operating Costs of Possible Future Transport Airplanes: Turbofan Engine Supplement. AUTH: T.V. Jones PAGES: 82, DATE: 1954 COST: $ 7.50 KEYS: Air transportation; Transport airplanes ABST: Data on transport airplanes powered by turbofan and "bypass turbojet" powerplants. The study compares turbofan-powered transports with turbojet- and turboprop-powered aircraft, states the assumptions considered in this 1954 analysis, and discusses the characteristics of the turbofan-powered transport. 82 pp. RM-1268-PR: Notes on Linear Programming: Part V-A--Product-Form Tableau for Revised Simplex Method. AUTH: G.B. Dantzig, W. Orchard-Hays, G. Waters PAGES: 20, DATE: 1954 COST: $ 4.00 ABST: No abstract available. 20 pp. RM-1341: On the Solution of an Approximate Equation in the Theory of Optimal Allocation. AUTH: D.R. Anderson PAGES: 13, DATE: 1954 COST: $ 4.00 ABST: A discussion of a certain functional equation, the solution of which is useful in approximating to the solution of a more general functional equation. No abstract available. 14 pp. P-587: Social Interaction. AUTH: R.F. Bales PAGES: 22, DATE: 1954 COST: $ 4.00 ABST: A paper which describes a systematic procedure for analyzing social interaction and compares what is known about the interaction process with some features of an air defense network. RM-1415: A Two-Machine-Gun Duel with the Bomber Turret Vulnerable. AUTH: F.P. Ballantyne PAGES: 12, DATE: 1954 COST: $ 4.00 KEYS: Aerial combat; Duels; Game theory ABST: An analysis of a two-machine-gun duel in which the sole motive of the fighter is to kill the bomber and the goal of the bomber is survival. It is assumed that the bomber defends itself with a tail turret and that the fighter, bomber, and bomber turret are each considered a singly vulnerable area. An analysis of a two-machine-gun duel in which the sole motive of the fighter is to kill the bomber and the goal of the bomber is survival. It is assumed that the bomber defends itself with a tail turret and that the fighter, bomber, and bomber turret are each considered a singly vulnerable area. 13 pp. RM-1241: On the Limiting Behavior of Discrete Dynamic-Programming Processes--I (The Gold-Mining Problem). AUTH: R.E. Bellman PAGES: 9, DATE: 1954 COST: $ 4.00 ABST: One of several studies in which the limiting behavior of certain classes of dynamic programming processes is examined, as various parameters defining the processes tend to zero. In particular, the gold-mining problem is considered. RM-1242: On the Limiting Behavior of Discrete Dynamic-Programming Processes--II (A Direct Proof of Convergence). AUTH: R.E. Bellman PAGES: 8, DATE: 1954 COST: $ 4.00 ABST: A direct proof of a certain convergence which is given independently of the concept of a continuous process. RM-1243: On the Limiting Behavior of Discrete Dynamic-Programming Processes--III (The Generalized Gold-Mining Problem). AUTH: R.E. Bellman PAGES: 5, DATE: 1954 COST: $ 4.00 ABST: A generalization of the gold-mining problem, considered in RM-1241 of the same title. In the limit the generalized version is shown to reduce to the simpler version. RM-1336: On the Computational Solution of Some Functional Equations in the Theory of Dynamic Programming. AUTH: R.E. Bellman PAGES: 6, DATE: 1954 COST: $ 4.00 ABST: A proof that various functional equations, occurring in the theory of optimal inventory and allocation, may be solved by simple iterative processes under certain conditions. No abstract available. 6 pp. RM-1337: On Multi-Stage Games with Imprecise Payoff. AUTH: R.E. Bellman PAGES: 6, DATE: 1954 COST: $ 4.00 KEYS: Games ABST: A proof that under certain natural conditions the play of a multi-stage game is to a great extent independent of the payoff function. A proof that under certain natural conditions the play of a multistage game is to a great extent independent of the payoff function. 7 pp. P-597: Dynamic Programming and a New Formalism in the Calculus of Variations--I. AUTH: R.E. Bellman PAGES: 28, DATE: 1954 COST: $ 4.00 ABST: An investigation of various problems in the calculus of variations as continuous decision processes. It is shown how the methods of dynamic programming theory may be utilized to yield functional equations of a new type and successive approximations of the monotone type to the solutions. RM-1363-AEC: Numerical Solutions of Spherical Blast Waves. AUTH: H.L. Brode PAGES: 35, DATE: 1954 COST: $ 4.00 KEYS: Atmosphere; Geophysics; Wave mechanics ABST: An attempt to solve the problem of a spherical blast in air by employing an artificial viscosity as a mechanism for avoiding shock-front discontinuities. This study considers overpressure, density, particle velocity, and position as functions of time and space. In addition, dynamic pressure, static overpressure, durations of pressure and velocity, and shock values of all quantities are described for various times and radial distances. An attempt to solve the problem of a spherical blast in air by employing an artificial viscosity as a mechanism for avoiding shock-front discontinuities. This study considers overpressure, density, particle velocity, and position as functions of time and space. In addition, dynamic pressure, static overpressure, durations of pressure and velocity, and shock values of all quantities are described for various times and radial distances. 36 pp. RM-1264: Notes on Linear Programming--Part I: The Generalized Simplex Method for Minimizing a Linear Form under Linear Inequality Restraints. AUTH: G.B. Dantzig, A. Orden, P. Wolfe, A. Orden, P.S. Wolfe PAGES: 17, DATE: 1954 COST: $ 4.00 ABST: The first of a series of papers on the determination of optimum solutions to systems of linear inequalities. The present paper develops a theory for avoiding assumptions regarding rank of underlying matrices which has import in applications where little or nothing is known about the rank of some linear inequality system requiring solution. RM-1268A: Notes on Linear Programming--Part V: A Product-Form Tableau for Revised Simplex Method--Computing Appendix for RM-1268. AUTH: G.B. Dantzig, W. Orchard-Hays, G. Waters PAGES: 19, DATE: 1954 COST: $ 4.00 ABST: A computing appendix for RM-1268, Notes on Linear Programming--Part V: Alternate Algorithm for the Revised Simplex Method Using Product Form for the Inverse. The method considered is applied to a linear programming problem (requiring the minimization of a given functional subject to linear restraints) in order to illustrate the tableau. A description of a finite iterative procedure, using a product form for the inverse. RM-1270: Notes on Linear Programming--Part VII: The Dual Simplex Algorithm. AUTH: G.B. Dantzig PAGES: 10, DATE: 1954 COST: $ 4.00 ABST: A procedure for solving the dual problem by means of variables associated with a basis that may have negative as well as positive values in the iterative process before an optimum is reached. RM-1274: Notes on Linear Programming--Part XI: Composite Simplex-Dual Simplex Algorithm--I. AUTH: G.B. Dantzig PAGES: 16, DATE: 1954 COST: $ 4.00 ABST: A proposal for avoiding certain undesirable features of Phase I of the simplex method (i.e., by the introduction of vectors on the basis that they are likely to be in the optimal solution of Phase II). RM-1281: Notes on Linear Programming--Part XIII: Optimal Solution of a Dynamic Leontief Model with Substitution. AUTH: G.B. Dantzig PAGES: 13, DATE: 1954 COST: $ 4.00 ABST: An examination of a dynamic Leontief system of the discrete type. Alternative substitute type activities are allowed; a bill of goods is given over time; and the unknown quantities of activities satisfying the system are determined in order to minimize a specified linear objective function. RM-1290: Notes on Linear Programming--Part XIV: A Computational Procedure for a Scheduling Problem of Edie. AUTH: G.B. Dantzig PAGES: 13, DATE: 1954 COST: $ 4.00 ABST: A presentation of two methods for assigning workers optimally to jobs in a dynamic situation. It is assumed that the number of men on the job varies to meet a specified (nonconstant) work load throughout the day and that the work pattern of each worker varies as to starting and leaving time, providing breaks for rests and meals. No abstract available. 14 pp. RM-1328: Notes on Linear Programming--Part XV: Minimizing the Number of Carriers to Meet a Fixed Schedule. AUTH: G.B. Dantzig, D.R. Fulkerson, D.R. Fulkerson PAGES: 12, DATE: 1954 COST: $ 4.00 ABST: A proof that the problem of determining the minimum number of carriers required to meet a fixed schedule of transportation can be made into a linear programming problem. No abstract available. 13 pp. RM-1367: Notes on Linear Programming--Parts VIII, IX, and X: Upper Bounds, Secondary Constraints, and Block Triangularity in Linear Programming. AUTH: G.B. Dantzig PAGES: 22, DATE: 1954 COST: $ 4.00 ABST: An attempt to develop short-cut computational methods for solving systems whose matrices may be described as block triangular. No abstract available. 23 pp. RM-1374: Notes on Linear Programming--Part XVII: Linear Programming under Uncertainty. AUTH: G.B. Dantzig PAGES: 19, DATE: 1954 COST: $ 4.00 ABST: A study of a class of linear programming models where the activities are divided into two or more stages. The quantities of activities in the first stage are determined in advance, and those in the second and later stages are dependent on the outcome of random events. No abstract available. 20 pp. RM-1375: Notes on Linear Programming--Part XVIII: Status of Solution of Large-Scale Linear-Programming Problems. AUTH: G.B. Dantzig PAGES: 10, DATE: 1954 COST: $ 4.00 ABST: A discussion of the need to compute large-scale systems of linear-programming problems. Various characteristics of some practical models, promising to lead to short-cut procedures, are indicated. No abstract available. 11 pp. RM-1335: Optimal Tactics in a Multistrike Air Campaign. AUTH: M. Dresher PAGES: 17, DATE: 1954 COST: $ 4.00 KEYS: Aerial combat--Tactics; Combat models; Games ABST: An analysis of a tactical air campaign model, consisting of a finite number of counterair and countersurface missions, as a multimove continuous game. The optimal tactics are derived as a function of the attrition parameters. An analysis of a tactical air compaign model, consisting of a finite number of counterair and countersurface missions, as a multimove continuous game. The optimal tactics are derived as a function of the attrition parameters. 18 pp. RM-1369: Notes on Linear Programming--Part XVI: The Problem of Routing Aircraft--a Mathematical Solution. AUTH: A.R. Ferguson, G.B. Dantzig, G.B. Dantzig PAGES: 18, DATE: 1954 COST: $ 4.00 KEYS: Programming (mathematics) ABST: An application of linear programming to a transportation problem in which a method is presented for assigning a given fleet of various aircraft types to carry an anticipated traffic load over several routes at minimum cost. 23 pp. RM-1400: Notes on Linear Programming--Part XX: Maximal Flow Through a Network. AUTH: L.R. Ford, D.R. Fulkerson, L.R. Ford, D.R. Fulkerson PAGES: 12, DATE: 1954 COST: $ 4.00 ABST: A proof of the minimal cut theorem, for a general network, which determines a simple computational procedure for achieving a maximal flow in planar networks. RM-1420-AEC: Solutions of the Temperature-Perturbed Thomas-Fermi Equation. AUTH: J.J. Gilvarry, G.H. Peebles, G.H. Peebles PAGES: 17, DATE: 1954 COST: $ 4.00 KEYS: Atoms--Properties; Differential equations; Equations of state; Quantum KEYS: mechanics ABST: An analytical solution of the temperature-perturbed Thomas-Fermi equation in order to determine boundary and initial parameters, corresponding to seven neutral-atomic zero-temperature solutions given by Slater and Krutter. An extension in directly-fitted range is presented, and the effects of the temperature perturbation on the equation of state are shown graphically for this extended range. An analytical solution of the temperature-perturbed Thomas-Fermi equation in order to determine boundary and initial parameters, corresponding to seven neutral-atomic zero-temperature solutions given by Slater and Krutter. An extension in directly-fitted range is presented, and the effects of the temperature perturbation on the equation of state are shown graphically for this extended range. 17 pp. RM-1286: The Derivatives of the Value of a Game. AUTH: O.A. Gross PAGES: 4, DATE: 1954 COST: $ 4.00 KEYS: Game theory; Military strategy ABST: A proof that the right- and left-hand derivates of the value of a finite, two-person, zero-sum game, with respect to an element of the payoff, exist and are expressible in terms of the optimal strategies. 5 pp. RM-1383: Notes on Linear Programming--Part XIX: The Fixed-Charge Problem. AUTH: W.M. Hirsch, G.B. Dantzig, G.B. Dantzig PAGES: 21, DATE: 1954 COST: $ 4.00 ABST: A discussion of the properties of a general solution to a fundamental unsolved problem in the programming area. This problem is one in which various activities have fixed charges (e.g., set-up time charges) if operating at a positive level. No abstract available. 22 pp. RM-1391: Differential Games--I: Introduction. AUTH: R. Isaacs, R.P. Isaacs PAGES: 33, DATE: 1954 COST: $ 4.00 KEYS: Games ABST: A discussion of the general scope and applications of differential games. The basic concepts are presented in terms of such military applications as pursuit, battle, and aiming games. A discussion of the general scope and applications of differential games. The basic concepts are presented in terms of such military applications as pursuit, battle, and aiming games. 34 pp. RM-1399: Differential Games--II: The Definition and Formulation. AUTH: R. Isaacs, R.P. Isaacs PAGES: 31, DATE: 1954 COST: $ 4.00 KEYS: Games ABST: A continuation of RM-1391, Differential Games--I: Introduction. The present study examines the mathematical definition and concept of a differential game. A continuation of RM-1391, the present study examines the mathematical definition and concept of a differential game. 32 pp. RM-1411: Differential Games--III: The Basic Principles of the Solution Process. AUTH: R. Isaacs, R.P. Isaacs PAGES: 21, DATE: 1954 COST: $ 4.00 KEYS: Differential equations; Game theory ABST: A discussion of (1) the differential equation technique for solving differential games and (2) the verification theorem for proving that the answers obtained are the correct solutions. A discussion of (1) the differential equation technique for solving differential games, and (2) the verification theorem for proving that the answers obtained are the correct solutions. (See also RM-1391, RM-1399, RM-1486.) 22 pp. RM-1208-AEC: Hydrogen Wave-Functions. AUTH: R. Latter PAGES: 57, DATE: 1954 COST: $ 7.50 KEYS: Atoms--Properties; Hydrogen; Wave mechanics ABST: A graphical presentation of the results of detailed hydrogenic wave-function calculations. 57 pp. RM-1416-AEC: Atomic Energy Levels for the Thomas-Fermi and Thomas-Fermi-Dirac Potential. AUTH: R. Latter PAGES: 32, DATE: 1954 COST: $ 4.00 KEYS: Atoms--Properties; Differential equations; Electrons; Quantum mechanics ABST: A study to determine the Schrèodinger equation for the Thomas-Fermi and Thomas-Fermi-Dirac potentials. Electron self-interactions are considered by modifying the potentials to give asymptotically the field of a unit charge, and all levels from 1s to 7d are examined for a range of Z-values sufficient to permit easy interpolation. A study to determine the Schrodinger equation for the Thomas-Fermi and Thomas-FermiDirac potentials. Electron self-interactions are considered by modifying the potentials to give asymptotically the field of a unit charge, and all levels from ls to 7d are examined for a range of Z-values sufficient to permit easy interpolation. 32 pp. RM-1386: On the Continuous Simplex Method. AUTH: R.S. Lehman PAGES: 57, DATE: 1954 COST: $ 7.50 ABST: A study which develops the continuous simplex method and applies it to several bottleneck problems. This method is defined as a systematic technique for solving a class of problems arising in the dynamic programming theory. RM-1238: Detection Range of an Active Radar Seeker. AUTH: J.D. Mallett, P. Swerling, P. Swerling PAGES: 36, DATE: 1954 COST: $ 4.00 ABST: An analysis of the effect of various factors on the detection range of an active radar seeker. An attempt is made to (1) determine the theoretical range of a seeker, (2) present graphs which show how these factors affect detection range and which aid in choosing optimum parameters, and (3) apply these results to several cases representative of actual or proposed seekers. RM-1379: Optimization in Dynamic Allocation Problems by a Modified Calculus of Variations Technique. AUTH: A.S. Mengel PAGES: 14, DATE: 1954 COST: $ 4.00 ABST: A direct proof that modified Euler equations solve linear-type problems that can not be optimized by the classical calculus of variations technique. The method considered applies to nonlinear equations as well as to minimax problems if a saddle-point exists. No abstract available. 14 pp. RM-1326: Continuous Iteration Method for Solution of Differential Games. AUTH: J. Nash, J.F. Nash PAGES: 8, DATE: 1954 COST: $ 4.00 KEYS: Computers; Game theory ABST: An iterative method for solving such differential games as simple air war games. This method is stated in a continuous form, but may be applied in a discrete approximation for use with a high-speed digital computing machine. An iterative method for solving such differential games as simple air war games. This method is stated in a continuous form, but may be applied in a discrete approximation for use with a high-speed digital computing machine. 9 pp. RM-1275: Notes on Linear Programming--Part XII: A Composite Simplex Algorithm--II. AUTH: W. Orchard-Hays PAGES: 15, DATE: 1954 COST: $ 4.00 ABST: A proposal which combines the normal and dual algorithms, with some modifications, in order to determine an optimal solution in fewer iterations than by other methods. The present study separates the nonsingularity of a basis matrix and the feasibility and the optimality of the solution. RM-1433: Background, Development, and Extensions of the Revised Simplex Method. AUTH: W. Orchard-Hays PAGES: 66, DATE: 1954 COST: $ 7.50 ABST: A discussion of the development of the present form of the simplex method, as used in the RAND codes for the IBM 701 calculator. In addition, some results of computational experience are given, and numerous parametric variations are examined. No abstract available. 67 pp. RM-1368: On the Convergence of Discrete Stochastic Decision Processes to Their Continuous Analogues. AUTH: H.A. Osborn PAGES: 25, DATE: 1954 COST: $ 4.00 ABST: A direct proof of the convergence of the discrete gold-mining process to the continuous process discussed in P-433, A Functional Equation in the Theory of Dynamic Programming and Its Generalizations, and R-271, Dynamic Programming of Continuous Processes. No abstract available. 26 pp. RM-1320: Games with Information Lag. AUTH: H. Scarf, L.S. Shapley, H.E. Scarf, L.S. Shapley PAGES: 7, DATE: 1954 COST: $ 4.00 KEYS: Games ABST: A study to determine a set of conditions for the existence of a value and optimal strategies for a two-person game in which each player has a denumerable sequence of choices to make. A study to determine a set of conditions for the existence of a value and optimal strategies for a two-person game in which each player has a denumerable sequence of choices to make. 8 pp. RM-1257: Electronic Reliability and Supply Improvement Based on Failure Reporting and Presentation. AUTH: L.W. Sepmeyer, F.A. Hadden, F.A. Hadden PAGES: 60, DATE: 1954 COST: $ 7.50 ABST: A summary of the results of RM-958-1, A Field Trial on an Air Force Electronic Equipment Reliability Study Program. The present study describes a method which reports field failure and replacements in an attempt to provide a tool for controlling equipment reliability. RM-1338: Analytic Formulation of a Theater Air-Ground Warfare System (1953 Techniques). AUTH: C.P. Siska, L.A. Giamboni, J.R. Lind, L.A. Giamboni, J.R. Lind PAGES: 54, DATE: 1954 COST: $ 7.50 KEYS: Aerial combat--Tactics; Combat models; Conventional warfare; War KEYS: games ABST: An attempt to determine the interactions of opposing tactical air and ground forces and the resultant effect on the movement of a main resistance line by studying a set of differential equations. These have been programmed on a Reeves Electronic Analogue Computer, so that a tactical theater war game may be simulated. (See also RM-1428.) 54 pp. RM-1220: Statistical Theory of Navigation Employing Independent Inertial and Velocity Measurements. AUTH: P. Swerling, E. Reich, E. Reich PAGES: 56, DATE: 1954 COST: $ 7.50 ABST: A theoretical study of optimum determination of position by a navigation device employing independent inertial and velocity measurements, which are subject to random errors. This problem is related to the theory of statistical estimation as well as to filtering theory. 57 pp. RM-1321: Statistical Theory of Navigation Employing Independent Inertial and Velocity Measurements: Minimum Rms Error in Computed Position. AUTH: P. Swerling, E. Reich, E. Reich PAGES: 26, DATE: 1954 COST: $ 4.00 ABST: A continuation of RM-1220, Statistical Theory of Navigation Employing Independent Inertial and Velocity Measurements. The present study gives (1) explicit formulas for minimum rms error in computed position as a function of time of flight and (2) curves based on these formulas to determine the results for numerous illustrative cases. No abstract available. 27 pp. RM-1217: Probability of Detection for Fluctuating Targets. AUTH: P. Swerling PAGES: 38, DATE: 1954 COST: $ 4.00 ABST: An analysis of the probability of detection of a target by a pulsed search radar, when the target has a fluctuating cross section. Formulas for detection probability and curves of detection probability versus range are considered for several models of target fluctuation. 44 pp. RM-1317: Notes on the Analysis of "Immersed" Variance. AUTH: J.W. Tukey PAGES: 34, DATE: 1954 COST: $ 4.00 KEYS: Statistical analysis ABST: A technique for studying the variance of a concealed parameter. In particular, the case is examined where the variance components associated with the parameter are emphasized. 34 pp. RM-1357: Confidence Intervals for Poisson Parameters in Logistics Research. AUTH: J.W.T. Youngs, M.A. Geisler, A.R. Mirkovich, M.A. Geisler, A.R. Mirkovich PAGES: 8, DATE: 1954 COST: $ 4.00 KEYS: Logistics; Statistical analysis ABST: A presentation of (1) the method of confidence intervals for Poisson parameters, and (2) some tables for estimating the confidence intervals for useful Poisson distribution values. Such data help to determine the demand pattern at airbase level for each of, or a sum of, many types of supply items. 9 pp. RM-1412-AEC: Effect of Correlations on the Equation of State of an Electron Gas. AUTH: R.A. Ferrell PAGES: 8, DATE: 1955 COST: $ 4.00 KEYS: Equations of state; Temperature; Thermodynamics ABST: An attempt to apply quantitatively the equation of state of a free electron gas to relatively low temperatures in order to emphasize correlation effects. RM-1598-PR: A Condition for the Existence of Saddle-Points. AUTH: L.S. Shapley PAGES: 5, DATE: 1955 COST: $ 4.00 KEYS: Game theory NOTE: See also: RM-3672-1. ABST: A study which relates the occurrence of saddle-points in zero-sum two-person games to their occurrence in subgames. (See also RM-3672-1.) 5 pp. P-580: On the Optimal Inventory Equation. AUTH: R.E. Bellman, I.L. Glicksberg, O.A. Gross PAGES: 40, DATE: 1955 COST: $ 4.00 ABST: No abstract available. 40 pp. P-596: Linear Programming under Uncertainty. AUTH: G.B. Dantzig PAGES: 19, DATE: 1955 COST: $ 4.00 ABST: No abstract available. 19 pp. P-610: A Production Smoothing Problem. AUTH: S.M. Johnson, G.B. Dantzig PAGES: 28, DATE: 1955 COST: $ 4.00 ABST: No abstract available. 28 pp. P-629: Markets as Cooperative Games. AUTH: L.S. Shapley PAGES: 6, DATE: 1955 COST: $ 4.00 KEYS: Competition; Game theory ABST: A description of how numerous market situations can be formulated as cooperative games in the von Neumann-Morgenstern theory. The solutions of several examples are discussed, and an abstract market game is defined generally. 6 pp. P-631: Notes in the Theory of Dynamic Programming--II: A Functional Equation Arising in Allocation Theory. AUTH: R.E. Bellman PAGES: 8, DATE: 1955 COST: $ 4.00 ABST: No abstract available. 8 pp. P-632: Notes in the Theory of Dynamic Programming--III: Equipment Replacement Policy. AUTH: R.E. Bellman PAGES: 7, DATE: 1955 COST: $ 4.00 ABST: No abstract available. 7 pp. P-640: Notes in the Theory of Dynamic Programming--IV: A Variational Problem with Constraints. AUTH: R.E. Bellman PAGES: 24, DATE: 1955 COST: $ 4.00 ABST: No abstract available. 24 pp. P-642: The Problem of Aiming and Evasion. AUTH: R. Isaacs PAGES: 42, DATE: 1955 COST: $ 4.00 KEYS: Game theory ABST: A discussion of the general evasion game with a time lag in the information that the marksman has as to the target position. An example is presented in which the marksman has no optimal strategy. (A condensed version of RM-1385.) 42 pp. P-646: The Application of Statistical Methods to the Design and Analysis of Experiments. AUTH: D.S. Stoller PAGES: 11, DATE: 1955 COST: $ 4.00 KEYS: Experimental design; Statistical analysis ABST: A survey of the criteria, designs, and analyses of tests (in statistics and operations research) which are applicable to experimental design and analysis. (Published in H. C. Carroll and W. A. Wildhack (eds.), [Proving Ground Instrumentation, 1955], American Ordnance Association, Washington, D.C., June 1955.) 11 pp. P-651: Mathematical Aspects of Scheduling Theory. AUTH: R.E. Bellman PAGES: 61, DATE: 1955 COST: $ 7.50 ABST: No abstract available. 61 pp. P-659: Description of the Air-Defense Experiments--II: The Task Environment. AUTH: A. Newell PAGES: 4, DATE: 1955 COST: $ 4.00 ABST: No abstract available. 4 pp. P-661: Description of the Air-Defense Experiments--I: The Physical and Cultural Environments. AUTH: W.C. Biel PAGES: 6, DATE: 1955 COST: $ 4.00 ABST: No abstract available. 6 pp. P-669: The Influence of Mass Destruction Weapons on Strategy. AUTH: B. Brodie PAGES: 23, DATE: 1955 COST: $ 4.00 KEYS: Military strategy; Nuclear weapons; Nuclear weapons--Tactical use ABST: A lecture (presented before the Army War College, Carlisle Barracks, Pennsylvania, March 1955) concerning the influence of thermonuclear weapons in terms of strategic and tactical use. The author states that with the speed and magnitude of destruction available through the steadily growing stockpiles of nuclear weapons, any unrestricted war between the major powers must have a character and a conclusion that are predetermined by the war plans existing at the outset. 23 pp. P-671: Functional Equations in the Theory of Dynamic Programming--II: Nonlinear Differential Equations. AUTH: R.E. Bellman PAGES: 5, DATE: 1955 COST: $ 4.00 ABST: No abstract available. 5 pp. P-685: Linear Programming and Economic Theory. AUTH: P.A. Samuelson PAGES: 17, DATE: 1955 COST: $ 4.00 ABST: No abstract available. 17 pp. P-688: Computing Experience with Linear Programming and Its Variants. AUTH: W. Orchard-Hays PAGES: 13, DATE: 1955 COST: $ 4.00 ABST: No abstract available. 13 pp. P-689: Criteria for the Selection of Water-Resource Projects. AUTH: R.N. McKean PAGES: 15, DATE: 1955 COST: $ 4.00 ABST: No abstract available. 15 pp. P-696: Some Aspects of the Theory of Dynamic Programming. AUTH: R.E. Bellman PAGES: 13, DATE: 1955 COST: $ 4.00 ABST: No abstract available. 13 pp. P-699: An Appreciation of Systems Analysis. AUTH: C.J. Hitch PAGES: 26, DATE: 1955 COST: $ 4.00 KEYS: System analysis ABST: A description of military systems analysis as a framework for combining the knowledge of experts in many fields to reach solutions which transcend any individual expert's judgment. 26 pp. P-700: Remarks on the Design, Conduct, and Analysis of Large Air Exercises. AUTH: N.C. Peterson PAGES: 21, DATE: 1955 COST: $ 4.00 KEYS: United States. Air Force; Air operations; Experimental design ABST: A transcript of a talk presented before the Tenth Operations Analysis Technical Conference at Eglin Air Force Base, Florida, May 10, 1955. The ideal practices to use in large Air Force exercises are discussed with particular reference to those exercises connected with the study of tactics for offensive forces. P-704: Functional Equations in the Theory of Dynamic Programming, V: Positivity and Quasi-Linearity. AUTH: R.E. Bellman PAGES: 6, DATE: 1955 COST: $ 4.00 ABST: No abstract available. 6 pp. P-710: Some Observations on Factor Analysis. AUTH: H.H. Harman PAGES: 8, DATE: 1955 COST: $ 4.00 KEYS: Psychology; Statistical analysis; Statistics ABST: An attempt to trace the origin and growth of the psychological theories and mathematical foundations of factor analysis and to appraise its present status. 8 pp. P-714: On a Class of Variational Problems. AUTH: R.E. Bellman PAGES: 13, DATE: 1955 COST: $ 4.00 ABST: No abstract available. 13 pp. P-717: On Differential Games with Integral Payoff. AUTH: L.D. Berkovitz, W.H. Fleming PAGES: 33, DATE: 1955 COST: $ 4.00 KEYS: Differential equations; Game theory ABST: A paper which, by using methods of the calculus of variations, obtains the necessary conditions such that differential games of a certain type have a saddle-point. By strengthening the necessary conditions, sufficient conditions for the existence of a saddle-point and a method of constructing the saddle-point are derived. 33 pp. P-718: The Problem of Continuous Programs. AUTH: H.A. Osborn PAGES: 18, DATE: 1955 COST: $ 4.00 ABST: No abstract available. 18 pp. P-721: Notes on the Theory of Dynamic Programming, V: Maximization Over Discrete Sets. AUTH: R.E. Bellman PAGES: 6, DATE: 1955 COST: $ 4.00 ABST: No abstract available. 6 pp. P-724: Cargo Density Variations: A Challenge to Air Transport. AUTH: R.E. Bickner PAGES: 20, DATE: 1955 COST: $ 4.00 KEYS: Airlift; Transport airplanes ABST: Condensed version of a 1955 study (RM1380) of means of improving the efficiency of airlift operations. The author deals with: (1) the significance of cargo densities in the various phases of airlift operations; (2) the mistakes resulting from the assumption that densities are constant; and (3) the methods by which cargo densities can be appropriately considered. 20 pp. P-725: A Note on Randomized Branch Sampling. AUTH: A.W. Marshall PAGES: 6, DATE: 1955 COST: $ 4.00 KEYS: Monte carlo method; Stochastic processes ABST: A discussion of the operation of randomized branch sampling, the relation between this sampling plan and importance sampling developed in Monte Carlo calculations, and some improvements to Jessen's theory based on the identity of these methods. 6 pp. P-728: The Existence of Stationary Measures for Certain Markov Processes. AUTH: T.E. Harris PAGES: 29, DATE: 1955 COST: $ 4.00 ABST: No abstract available. 29 pp. P-731: A New Technique for Eigenvalue Problems. AUTH: H.A. Osborn PAGES: 21, DATE: 1955 COST: $ 4.00 ABST: No abstract available. 21 pp. P-738: A Systematic Approach to a Class of Problems in the Theory of Noise and Other Random Phenomena. AUTH: D.A. Darling, A.J.F. Siegert PAGES: 20, DATE: 1955 COST: $ 4.00 ABST: No abstract available. 20 pp. P-742: On Differential Games with Survival Payoffs. AUTH: H.E. Scarf PAGES: 18, DATE: 1955 COST: $ 4.00 KEYS: Game theory NOTE: See also: RM-1480. ABST: A proof that under certain conditions the upper and lower values of approximating games converge actually to the same function. A class of survival games in an arbitrary [n]-dimensional region R and with an arbitrary payoff function [f(x)] on the boundary is considered. It is assumed that neither player can force the state of the game to proceed in any direction. (See also RM-1480.) 18 pp. P-748: A Fruitful Application of Static Marginal Analysis. AUTH: H.W. Karr, M.A. Geisler PAGES: 23, DATE: 1955 COST: $ 4.00 ABST: No abstract available. 23 pp. P-756: An Introductory Note for the Proceedings of the Gainsville, Florida, Symposium on Monte Carlo Methods. AUTH: A.W. Marshall PAGES: 17, DATE: 1955 COST: $ 4.00 ABST: A discussion of (1) the progress of Monte Carlo techniques from 1949 to the present and (2) the papers presented before the Symposium on Monte Carlo Methods at Gainesvill, Florida, March 16-17, 1954. Monte Carlo is defined as a random sampling procedure for treating mathematical problems of either deterministic or probabilistic type. P-764: Functional Equations in the Theory of Dynamic Programming--VI: A Direct Convergence Proof. AUTH: R.E. Bellman PAGES: 18, DATE: 1955 COST: $ 4.00 ABST: No abstract available. 18 pp. P-765: Notes on Control Processes--I: On the Minimum of Maximum Deviation. AUTH: R.E. Bellman PAGES: 9, DATE: 1955 COST: $ 4.00 ABST: No abstract available. 9 pp. P-766: Use of Different Monte Carlo Sampling Techniques. AUTH: H. Kahn PAGES: 41, DATE: 1955 COST: $ 4.00 ABST: A discussion of designing and using such variance-reducing techniques in Monte Carlo problems as importance sampling, Russian roulette and splitting, use of expected values, correlation and regression, and systematic and stratified sampling. In addition, the author examines how these techniques may be applied to the Monte Carlo evaluation of definite integrals. P-767: Transient Markov Chains with Stationary Measures. AUTH: T.E. Harris PAGES: 11, DATE: 1955 COST: $ 4.00 ABST: A presentation of conditions for the existence of nonnegative solutions Q<> of certain stationary equations where the quantities P<> are the transition probabilities, from state <> to state <>, of a transient markov chain. P-771: Notes on the Theory of Dynamic Programming, VII: Transportation Models. AUTH: R.E. Bellman PAGES: 11, DATE: 1955 COST: $ 4.00 ABST: No abstract available. 11 pp. P-773: Notes on the Theory of Dynamic Programming--VI: The Warehousing Model. AUTH: R.E. Bellman PAGES: 6, DATE: 1955 COST: $ 4.00 ABST: No abstract available. 6 pp. P-780: Dynamic Programming and the Numerical Solution of Variational Problems. AUTH: R.E. Bellman PAGES: 23, DATE: 1955 COST: $ 4.00 ABST: No abstract available. 23 pp. P-783: An Abstract Setting for the Notion of Dynamic Programming. AUTH: D.O. Ellis PAGES: 12, DATE: 1955 COST: $ 4.00 ABST: No abstract available. 12 pp. P-784: Eigenvalues and Functional Equations. AUTH: R.E. Bellman PAGES: 8, DATE: 1955 COST: $ 4.00 ABST: No abstract available. 8 pp. P-826: On the Max Flow Min Cut Theorem of Networks. AUTH: G.B. Dantzig, D.R. Fulkerson PAGES: 12, DATE: 1955 COST: $ 4.00 ABST: No abstract available. 12 pp. RM-1460/PR: Performance of a Scientific Satellite. AUTH: E.C. Heffern, H.A. Koch, H.A. Lieske, R.T. Oelschlager, H.T. Ponsford PAGES: 34, DATE: 1955 COST: $ 4.00 ABST: An investigation, from a flight economy viewpoint, of the feasibility of a scientific satellite for use in 1958. This study considers such alternatives as a modified Navajo booster with an Aerobee-Hi, a modified Series A intercontinental ballistic missile test vehicle with an Aerobee-Hi, and a modified Series B intercontinental ballistic missile test vehicle. P-647: An Optimal Inventory Policy for a Military Organization. AUTH: E.B. Berman, A.J. Clark PAGES: 83, DATE: 1955 COST: $ 7.50 ABST: No abstract available. 83 pp. RM-1428: Narrative Description of an Analytic Theater Air-Ground Warfare System. AUTH: J.R. Brom PAGES: 29, DATE: 1955 COST: $ 4.00 KEYS: Aerial combat--Tactics; Combat models; Conventional warfare; Logistics; KEYS: War games ABST: A discussion of the theater war formulated in the tactical air-ground study. The analysis considers the detail inherent in the mathematical model and the relationship of the technique to the overall planning problem. In addition, air, ground, and logistic network operations are examined, together with the nature, functions, and simulated performance of the forces. (See also RM-1338). 30 pp. RM-1447-AEC: Stark Fields from Ions in a Plasma. AUTH: A.A. Broyles PAGES: 23, DATE: 1955 COST: $ 4.00 KEYS: Electromagnetic spectra; Field theory; Spectroscopy ABST: A method to determine the probability of obtaining a given electric field on an ion in a plasma. This quantity is essential for computing the broadening of spectral lines from neighboring ions and for their contribution to the opacity. 24 pp. P-735: On the Partition of the Vertices of an N-Cube by an (N-1)-Plane. AUTH: S.S. Cairns PAGES: 18, DATE: 1955 COST: $ 4.00 ABST: A discussion of a problem arising in connection with airlift and machine scheduling. This study attempts to determine how to characterize the convex hull of the vertices of an n-cube that lie on one side of an (n - 1)-plane. P-658: Description of the Air-Defense Experiments--III: Data Collection and Processing. AUTH: R.L. Chapman PAGES: 5, DATE: 1955 COST: $ 4.00 ABST: A description of data collection and data processing techniques which influence the methodology of the Systems Research Laboratory studies. In addition, various problems involved in the experiment are considered. P-753: Cogwheel: A Film Story of Systems Research Laboratory's Activities. AUTH: R.L. Chapman, M.G. Weiner PAGES: 2, DATE: 1955 COST: $ 4.00 KEYS: Air defenses; Group behavior ABST: A discussion of [Cogwheel], a sound film showing a 40-man Air Force crew operating an air-defense direction center in the RAND Systems Research Laboratory. This film describes the development of the [Cogwheel] crew as an organization, the complexities of direction-center operations, some problems of studying systems in a laboratory, and the realism in human behavior and environment building attained in such laboratory studies. 2 pp. P-634: A Stockpiling Problem: Mathematical Treatment. AUTH: J.M. Danskin, J.M. Danskin PAGES: 24, DATE: 1955 COST: $ 4.00 ABST: A presentation of necessary conditions on the solution, if there is one, for the general case of a stockpiling problem. A complete solution is obtained for a special case. RM-1475: Notes on Linear Programming--Part XXII: Recent Advances in Linear Programming. AUTH: G.B. Dantzig PAGES: 31, DATE: 1955 COST: $ 4.00 ABST: A discussion of such developments in linear programming as uncertainty, combinatorial problems, and large-scale systems. No abstract available. 32 pp. P-734: Comments on Future Military Air Transport Requirements. AUTH: S.E. Eastman PAGES: 7, DATE: 1955 COST: $ 4.00 KEYS: Airlift; Logistics ABST: A 1955 discussion of logistic studies of the movement of passengers and cargo for the military establishment overseas, with special emphasis on the MATS mission in war and in peace. 7 pp. RM-1430: A Resource Allocation Problem in Continuous Form. AUTH: W.H. Fleming PAGES: 19, DATE: 1955 COST: $ 4.00 ABST: A study to determine the solution of a simple optimal resource allocation problem by considering the general methods developed in P-639, Variational Problems with Constraints. No abstract available. 20 pp. RM-1526: Discrete Approximations to Some Differential Games. AUTH: W.H. Fleming PAGES: 8, DATE: 1955 COST: $ 4.00 KEYS: Differential equations; Game theory ABST: A proof of the convergence of the values of time-discrete multistage games as the maximum time between successive moves shrinks to 0. It is assumed that the functional equation describing the limiting process has a continuously differentiable solution. A proof of the convergence of the values of time-discrete multistage games as the maximum time between successive moves shrinks to 0. It is assumed that the functional equation describing the limiting process has a continuously differentiable solution. 10 pp. RM-1604: Notes on Linear Programming--Part XXIX: A Simple Algorithm for Finding Maximal Network Flows and an Application to the Hitchcock Problem. AUTH: L.R. Ford, D.R. Fulkerson, L.R. Ford, D.R. Fulkerson PAGES: 22, DATE: 1955 COST: $ 4.00 KEYS: Programming (mathematics); Transportation ABST: A solution for finding a maximal flow and minimal cut in a transportation network in order to determine an efficient computational routine for the Hitchcock distribution problem. No abstract available. 23 pp. RM-1489: Notes on Linear Programming--Part XXVI: Computation of Maximal Flows in Networks. AUTH: D.R. Fulkerson, G.B. Dantzig, G.B. Dantzig PAGES: 17, DATE: 1955 COST: $ 4.00 ABST: A proposal of a simple computational method--based on the simplex algorithm of linear programming--to determine a maximal flow between two given points in a transportation network. No abstract available. 18 pp. RM-1446-AEC: The Lindemann and Grèuneisen Laws. AUTH: J.J. Gilvarry PAGES: 32, DATE: 1955 COST: $ 4.00 KEYS: Nuclear physics; Thermodynamics; X-rays ABST: A proof that the Lindemann fusion law can be derived from the theory of the temperature dependence of Bragg reflection of X rays. This law together with the Grèuneisen theory of solids is used in order to determine the Grèuneisen constant of the solid at melting in terms of fusion parameters. A proof that the Lindemann fusion law can be derived from the theory of the temperature dependence of Bragg reflection of X-rays. This law, together with the Gruneisen theory of solids, is used in order to determine the Gruneisen constant of the solid at melting in terms of fusion parameters. 35 pp. RM-1457-AEC: Grèuneisen's Law and the Fusion Curve at High Pressure. AUTH: J.J. Gilvarry PAGES: 30, DATE: 1955 COST: $ 4.00 KEYS: Differential equations; Equations of state; Lattice theory; Nuclear KEYS: physics; Thermodynamics ABST: A method which determines the corrections, corresponding to the lattice contributions, in thermo-dynamic functions obtained from the Thomas-Fermi model. It is assumed that the lattice contribution to the pressure is small and that the equation of state of the solid can be approximated by results of the statistical Thomas-Fermi atom model for the electron pressure. A method that determines the corrections, corresponding to the lattice contributions, in thermodynamic functions obtained from the Thomas-Fermi model. It is assumed that the lattice contribution to the pressure is small and that the equation of state of the solid can be approximated by results of the statistical Thomas-Fermi atom model for the electron pressure. 31 pp. RM-1496-AEC: The Equation of the Fusion Curve. AUTH: J.J. Gilvarry PAGES: 23, DATE: 1955 COST: $ 4.00 KEYS: Atoms--Properties; Equations of state; Lattice theory; Nuclear physics; KEYS: Thermodynamics ABST: A generalization of the Lindemann law, used in connection with the Murnaghan equation of state for a solid. A law of reduced states for fusion is derived which is valid for the case of classical excitation of the lattice vibrations at melting. A generalization of the Lindemann law, used in connection with the Murnaghan equation of state for a solid. A law of reduced states for fusion is derived that is valid for the case of classical excitation of the lattice vibrations at melting. 25 pp. RM-1556-AEC: The Grèuneisen Parameter for an Einstein Solid and under Finite Strain. AUTH: J.J. Gilvarry PAGES: 27, DATE: 1955 COST: $ 4.00 KEYS: Equations of state; Models ABST: A study to determine the Grèuneisen constant, as evaluated from the equation of state, for an Einstein solid. The presence of a state of finite hydrostatic pressure is considered by Murnaghan's theory of finite strain in order to determine the Grèuneisen parameters on the Debye and Einstein models. A study to determine the Gruneisen constant, as evaluated from the equation of state, for an Einstein solid. The presence of a state of finite hydrostatic pressure is considered by Murnaghan's theory of finite strain in order to determine the Gruneisen parameters on the Debye and Einstein models. 28 pp. RM-1153-AEC: Ionization of Radioactive Particles in the Free Air. AUTH: S.M. Greenfield PAGES: 14, DATE: 1955 COST: $ 4.00 KEYS: Atmosphere; Ionization; Radiation ABST: A study of the possibility of particles becoming ionized as they undergo radioactive decay. The resulting charge of either sign, existing for a relatively small time period, is shown to be statistically negligible. A study of the possibility of particles becoming ionized as they undergo radioactive decay. The resulting charge of either sign, existing for a relatively small time period, is shown to be statistically negligible. 14 pp. RM-1560: Notes on Linear Programming--Part XXVIII: A Simple Linear-Programming Problem Explicitly Solvable in Integers. AUTH: O.A. Gross PAGES: 8, DATE: 1955 COST: $ 4.00 KEYS: Programming (mathematics) ABST: A solution (by recursion formulas) of a simple linear minimization problem, involving a cycle set of inequalities. A modification of these formulas yields a solution in the case where the unknown variables are restricted to assume only integer values. No abstract available. 9 pp. RM-1603: A Search Problem Due to Bellman. AUTH: O.A. Gross PAGES: 9, DATE: 1955 COST: $ 4.00 KEYS: Mathematics ABST: A presentation of two interpretations of a general search problem posed by R. Bellman. Solutions are given in certain special cases. No abstract available. 10 pp. RM-1541: The Effectiveness of Alternative Flyaway Kits. AUTH: W. Hamburger PAGES: 15, DATE: 1955 COST: $ 4.00 KEYS: Operations research; Statistics ABST: An attempt to determine the effectiveness of alternative flyaway kits by comparing several methods of their selection. This comparison is limited to a single kit size, one definition of "best," and one set of circumstances. Such data are considered as the predictability of demands for spare parts, the amount of activity to be supported by the kit, and the demand-rate and weight of each spare part. An attempt to determine the effectiveness of alternative flyaway kits by comparing several methods of their selection. This comparison is limited to a single kit size, one definition of "best," and one set of circumstances. Such data are considered as the predictability of demands for spare parts, the amount of activity to be supported by the kit, and the demand-rate and weight of each spare part. 16 pp. RM-1553: Notes on Linear Programming--Part XXVII: Dilworth's Theorem on Partially Ordered Sets. AUTH: A.J. Hoffman, G.B. Dantzig PAGES: 11, DATE: 1955 COST: $ 4.00 ABST: A description of a linear programming approach to the finite case of a theorem of Dilworth on the decomposition of a partially ordered set as a union of chains. It is demonstrated that the problem of finding the mutually unrelated elements is equivalent to the dual of that problem. No abstract available. 12 pp. RM-1432: Notes on Linear Programming--Part XXIII: A Production Smoothing Problem. AUTH: S.M. Johnson, G.B. Dantzig, G.B. Dantzig PAGES: 28, DATE: 1955 COST: $ 4.00 ABST: An attempt to determine a production schedule for a single type item over numerous time periods in order to satisfy a given requirement schedule while minimizing total cost. It is assumed that the costs per unit for production, storage, and change in production rate are known functions of time. No abstract available. 29 pp. RM-1575: The Contextual Map. AUTH: J.L. Kennedy PAGES: 9, DATE: 1955 COST: $ 4.00 KEYS: Contextual maps; Decision-making ABST: A description of the use of the "contextual map" as a tool for assisting decisionmakers in dealing with large, complex interacting system problems. The map is a display of information, prepared in such a way that the viewer may comprehend the totality of a complex problem before breaking it up into components. (Revision published as P-965.) 9 pp. P-740: The Background and Implications of the Systems Research Laboratory Studies. AUTH: J.L. Kennedy, R.L. Chapman PAGES: 17, DATE: 1955 COST: $ 4.00 KEYS: Group behavior; Man machine systems ABST: A discussion of the contribution of the Systems Research Laboratory in not only designing and operating complex man-machine systems, but also developing a theory of organizational behavior. 17 pp. RM-1492-AEC: Equation of State of Water. AUTH: A.L. Latter, R. Latter, R. Latter PAGES: 4, DATE: 1955 COST: $ 4.00 KEYS: Atoms--Properties; Equations of state; Models; Temperature; Thermodynamics ABST: A generalization of the Fermi-Thomas model for application of mixtures. This study attempts to determine the equation of state of water up to pressure of 10,000 megabars and temperatures of several thousand electron-volts. A generalization of the Fermi-Thomas model for application of mixtures. This study attempts to determine the equation of state of water up to pressure of 10,000 megabars and temperatures of several thousand electron volts. 4 pp. RM-1574-AEC: The Equation of State of Water on the Thomas-Fermi Model. AUTH: A.L. Latter, R. Latter, R. Latter PAGES: 29, DATE: 1955 COST: $ 4.00 KEYS: Atoms--Properties; Equations of state; Models; Temperature; Thermodynamics ABST: Methods for extending the Thomas-Fermi model of a compressed atom to molecules or mixtures of the type <>. These methods are applied to HÒO at zero temperature in order to determine (1) the pressure and internal energy as functions of the density, (2) the position of the protons relative to the oxygen nucleus, and (3) the electrostatic potential distribution within the molecule. Methods for extending the Thomas-Fermi model of a compressed atom to molecules or mixtures of the type Z Z . These methods are applied to H 0 at zero temperature in order to determine (1) the pressure and internal energy as functions of the density, (2) the position of the protons relative to the oxygen nucleus, and (3) the electrostatic potential distribution within the molecule. 30 pp. RM-1453-AEC: Relativistic and Nonrelativistic Energy Levels in Uranium. AUTH: R. Latter PAGES: 8, DATE: 1955 COST: $ 4.00 KEYS: Atoms--Properties; Differential equations; Quantum mechanics; Uranium ABST: A method for computing the relativistic and nonrelativistic energy levels in uranium. The eigen-values obtained in the statistical potentials with the Hartree energies and the experimental energy levels are compared. In addition, the energy levels for large atomic numbers are obtained in the Thomas-Fermi potential using both the Schrèodinger and Dirac equations. A method for computing the relativistic and nonrelativistic energy levels in uranium. The eigenvalues obtained in the statistical potentials with the Hartree energies and the experimental energy levels are compared. In addition, the energy levels for large atomic numbers are obtained in the Thomas-Fermi potential, using both the Schrodinger and Dirac equations. 9 pp. RM-1452: Notes on Linear Programming--Part XXV: The Elimination Form of the Inverse and Its Application to Linear Programming. AUTH: H.M. Markowitz PAGES: 19, DATE: 1955 COST: $ 4.00 ABST: A discussion of a particular product form of matrix inverse which is closely related to the Gaussian elimination method of solving a set of simultaneous equations. No abstract available. 20 pp. RM-1470: Notes on Linear Programming--Part XXIV: The Modification of the Right-Hand Side of a Linear Programming Problem. AUTH: H.M. Markowitz PAGES: 4, DATE: 1955 COST: $ 4.00 ABST: A method to determine in one iteration a basic feasible solution in the simplex method for solving linear programming problems when the right-hand side of an equation is altered. No abstract available. 5 pp. RM-1537-AEC: Crystal Structures and Atomic Volumes of the Elements. AUTH: W.G. McMillan PAGES: 13, DATE: 1955 COST: $ 4.00 KEYS: Atoms--Properties; Lattice theory; Thermodynamics ABST: Data on the crystal structures of the common modifications of the elements at zero pressure. Data on the crystal structures of the common modification of the elements at zero pressure. 13 pp. RM-1487-AEC: Line Broadening by Electrons: The Validity of Simple Theories. AUTH: R.E. Meyerott, H. Margenau, H. Margenau PAGES: 12, DATE: 1955 COST: $ 4.00 KEYS: Electrons; Spectroscopy ABST: A comparison of the simple impact theories of line broadening by electrons with the detailed computations of Kivel, Bloom, and Margenau. A comparison of the simple impact theories of the line broadening by electrons with the detailed computations of Kivel, Bloom, and Margenau. 13 pp. RM-1578-AEC: Photoelectric K and L Shell Absorption Coefficients for Highly Ionized Atoms. AUTH: S.A. Moszkowski, R.E. Meyerott, R.E. Meyerott PAGES: 20, DATE: 1955 COST: $ 4.00 KEYS: Atoms--Properties; Ionization; Radiation ABST: A method for calculating numerical values of K and L shell photoelectric absorption coefficients (averaged over subshells) for highly ionized atoms. This study considers (1) the photoelectric effect for hydrogen-like atoms, (2) the absorption from atoms using the customary screening approximation, (3) the effect of screening on the form of the wave-functions, and (4) a comparison of the various methods described. A method for calculating numerical values of K and L shell photoelectric absorption coefficients (averaged over subshells) for highly ionized atoms. This study considers (1) the photoelectric effect for hydrogenlike atoms, (2) the absorption from atoms using the customary screening approximation, (3) the effect of screening on the form of the wave functions, and (4) a comparison of the various methods described. 21 pp. RM-1511-AEC: Abstract Compendium on Theoretical Equation of State for Solids. AUTH: C.P. Nash PAGES: 32, DATE: 1955 COST: $ 4.00 KEYS: Atoms--Properties; Bibliography; Equations of state; Lattice theory; KEYS: Thermodynamics ABST: A compendium of literature on the theoretical equation of state for solids. Part I considers nonmetals while Part II discusses the general lattice theory. A compendium of literature on the theoretical equation of state for solids. Part I considers nonmetals, while Part II discusses the general lattice theory. 33 pp. RM-1440: Notes on Linear Programming--Part VI: The RAND Code for the Simplex Method (SX4) (For the IBM 701 Electronic Computer). AUTH: W. Orchard-Hays PAGES: 79, DATE: 1955 COST: $ 7.50 ABST: A description of the fourth in a series of codes for the IBM 701 computer which perform the simplex method. While several modifications of the basic simplex procedure are given, only the code, as assembled for the revised simplex method on a primal system as opposed to its dual, is considered. No abstract available. 80 pp. RM-1480: The Convergence of the Discrete Analogues of Differential Games: Part I. AUTH: H.E. Scarf PAGES: 17, DATE: 1955 COST: $ 4.00 KEYS: Differential equations; Game theory ABST: An examination of a class of survival games in an arbitrary n-dimensional region R and with an arbitrary payoff function f(x) on the boundary. It is assumed that the players cannot force the state of the game to proceed in any direction. An examination of a class of survival games in an arbitrary [n]-dimensional region [R] and with an arbitrary payoff function [f(x)] on the boundary. It is assumed that the players cannot force the state of the game to proceed in any direction. (See also P-742.) 18 pp. RM-1533: A Symmetric Market Game. AUTH: L.S. Shapley PAGES: 23, DATE: 1955 COST: $ 4.00 KEYS: Games ABST: A study which describes a family of solutions to an (m + n)-person game and presents various significant properties of the general solutions. The game is interpreted heuristically as a symmetrical market. A study which describes a family of solutions and presents various significant properties of the general solutions. The game is interpreted heuristically as a symmetrical market. 24 pp. Book-020505: Studies in the Economics of Transportation. AUTH: M. Beckmann, C.B. Mcguire, C.B. Winsten PAGES: 375, DATE: 1956 COST: $ 25.00 KEYS: Transportation ABST: An examination of the theoretical aspects of highway and railroad systems. Concepts and methods are developed for assessing the capabilities and efficiency of existing and projected traffic systems. (Published by Yale University Press, 1956. Available only from booksellers or the publisher.) (Non-RAND book based on a RAND study, RM-1488, published in 1955 under the same title.) 375 pp. Book-020530: Dynamic Programming. AUTH: R.E. Bellman PAGES: 367, DATE: 1956 COST: $ 25.00 KEYS: Programming (mathematics) ABST: An introduction to the mathematical theory of multistage decision processes. The study involves a certain conceptual framework which furnishes a new and versatile mathematical tool for the treatment of many novel and interesting problems in dynamic programming and in various parts of classical analysis. This book may be of aid to graduate students in mathematics, economics, and engineering, as well as to research workers in operations analysis and systems analysis. (Published by Princeton University Press, 1957. Available only from booksellers or the publisher.) 367 pp. RM-1688-PR: Communication Networks--II: Interoffice Trunking Problems. AUTH: R.E. Kalaba, M.L. Juncosa PAGES: 30, DATE: 1956 COST: $ 4.00 ABST: No abstract available. 30 pp. RM-1754-PR: A Revised Data Processing System for Managing War Reserve Stocks of Aircraft Spare Parts. AUTH: H.W. Nelson, J.D. Tupac PAGES: 52, DATE: 1956 COST: $ 7.50 ABST: A description of a new data-processing system, developed jointly by the Air Force and RAND, for management of war reserve stocks of aircraft spare parts. Initiated because the Air Force was experiencing difficulty with its manual and punched card system, this new system offers substantial advantages. Illus. RM-1785-PR: Costs and Benefits in Mathematical Programming. AUTH: A.S. Manne PAGES: 25, DATE: 1956 COST: $ 4.00 NOTE: Also published as P-936. ABST: An application of linear programming methods to month-to-month airlift planning within the U.S. Military Air Transport Service. Linear programming methods are substituted for trial-and-error calculations in an attempt (1) to diminish the time required to adapt plans to radical changes in the airlift problem and (2) to increase the productivity of MATS' resources. Illus. RM-1836-PR: Economic Comparisons of Military Air Transport Fleets, Details of the Method Used in R-294 (U). AUTH: C.B. Mcguire PAGES: 87, DATE: 1956 COST: $ 7.50 KEYS: Logistics--Transport ABST: A method for economic comparisons of alternative military air transport fleets in general terms so that the method may be applied to other problems of systematic fleet selection. The author considers the wartime requirement of alternative military air transport fleets, the problem of finding the minimum cost fleet, the principles of fleet computation in mathematical terms, the derivation of one of the fleets presented in R-294, and new estimates of total fleet costs. P-511: Allocation of Indirect Costs. AUTH: G.H. Fisher PAGES: 16, DATE: 1956 COST: $ 4.00 KEYS: Accounting and budgets; Cost analysis ABST: An attempt to solve the cost distribution problem arising when the operating costs of interdependent indirect (support) activities are to be allocated to end product (direct) activities. 16 pp. P-622: On Games of Survival. AUTH: J.W. Milnor, L.S. Shapley PAGES: 44, DATE: 1956 COST: $ 4.00 KEYS: Game theory; Survival ABST: A proof (using semi-martingale theory) of the existence of a value and optimal strategies in a game of survival. A simple exponential approximation to the solution is also discussed, together with many examples. 44 pp. P-676: Functional Equations in the Theory of Dynamic Programming--III: Multistage Games. AUTH: R.E. Bellman PAGES: 31, DATE: 1956 COST: $ 4.00 ABST: An attempt to determine existence and uniqueness theorems for a class of functional equations occurring in the theory of multistage games. (Published in [Rendiconti del Circolo Matematico di Palermo], Series II, Vol. V, 1956.) 31 pp. P-711: On the Solution of Discrete Programming Problems. AUTH: A.S. Manne, H.M. Markowitz PAGES: 45, DATE: 1956 COST: $ 4.00 ABST: No abstract available. 45 pp. P-777: On a Generalization of the Fundamental Identity of Wald. AUTH: R.E. Bellman PAGES: 7, DATE: 1956 COST: $ 4.00 ABST: No abstract available. 7 pp. P-787: Dynamic Programming. AUTH: R.E. Bellman PAGES: 4, DATE: 1956 COST: $ 4.00 ABST: No abstract available. 4 pp. P-794: Weapon System Cost Analysis. AUTH: D. Novick PAGES: 24, DATE: 1956 COST: $ 4.00 KEYS: Cost analysis; Weapon systems--Procurement ABST: A summary of the methodology for computing Air Force weapon system costs used at Rand as of the winter of 1955. The methodology presented considers each factor entering into an Air Force weapon system, provides the demand measurements for economic resources, identifies the additional or incremental expenditures resulting from the use of a proposed new equipment, and distinguishes between the one-time or investment outlays and the recurring or annual operating expenses. (Published in [IRE] [Transactions on Engineering Management], July 1956. Presented before the Institute of Radio Engineers at Los Angeles, California, January 18, 1956.) 24 pp. P-796: Dynamic Programming and Its Application to Variational Problems in Mathematical Economics. AUTH: R.E. Bellman PAGES: 49, DATE: 1956 COST: $ 4.00 ABST: No abstract available. 49 pp. P-797: Games with Partial Information. AUTH: H.E. Scarf, L.S. Shapley PAGES: 27, DATE: 1956 COST: $ 4.00 KEYS: Game theory NOTE: See also: RM-1320. ABST: A discussion of a particular class of games with partial information in which each player is informed of his opponent's moves a fixed amount of time after they are made. In addition, some of the properties of games with perfect information are generalized to games with positive time lags. (See also RM-1320.) 27 pp. P-799: The Design of Military Supply Tables for Spare Parts. AUTH: M.A. Geisler, H.W. Karr PAGES: 17, DATE: 1956 COST: $ 4.00 ABST: No abstract available. 17 pp. P-807: On the Application of the Theory of Dynamic Programming to the Study of Control Processes. AUTH: R.E. Bellman PAGES: 21, DATE: 1956 COST: $ 4.00 ABST: No abstract available. 21 pp. P-810: Evolution of Computer Codes for Linear Programming. AUTH: W. Orchard-Hays PAGES: 51, DATE: 1956 COST: $ 7.50 ABST: No abstract available. 51 pp. P-811: Nuclear Weapons and Changing Strategic Outlooks. AUTH: B. Brodie PAGES: 27, DATE: 1956 COST: $ 4.00 KEYS: International relations; Military strategy; Nuclear weapons ABST: A composite of two lectures, one presented before the Naval War College at Newport, Rhode Island, February 6, 1956, and the other before the Army War College at Carlisle Barracks, Pennsylvania, February 20, 1956. This paper examines the problems arising from the fact that no substitute for force in the government of international affairs has been discovered. (Published in the [Bulletin of the Atomic Scientists], February 1957.) 27 pp. P-818: Maintenance of a Group of Machines Utilized Intermittently and Subject to Several Types of Malfunction--I: Operational Requirements and Resource Allocations. AUTH: W.P. Sewell PAGES: 8, DATE: 1956 COST: $ 4.00 ABST: No abstract available. 8 pp. P-819: Some Queueing Problems in Machine Maintenance. AUTH: D.S. Stoller PAGES: 8, DATE: 1956 COST: $ 4.00 ABST: No abstract available. 8 pp. P-820: The Relevance of Costs in Operations Research. AUTH: M.W. Hoag PAGES: 18, DATE: 1956 COST: $ 4.00 KEYS: Operations research ABST: This paper divides operations research into studies in which costs are largely irrelevant, a measure of real cost internal to the analysis is required, and real costs must be approximated by money costs. 18 pp. P-823: Weapon-System Cost Analysis. AUTH: G.H. Fisher PAGES: 20, DATE: 1956 COST: $ 4.00 KEYS: Weapon systems ABST: A method for estimating cost inputs for weapon-systems analyses and a discussion of the characteristics of this method. In addition, its use as a tool in Air Force planning and programming of future weapons systems is examined. (Published in [The] [Journal of the Operations Research] [Society of America], October 1956. 20 pp. P-824: Thoughts on Linear Programming and Automation. AUTH: G.B. Dantzig PAGES: 16, DATE: 1956 COST: $ 4.00 ABST: No abstract available. 16 pp. P-837: Multidimensional Maximization, Dynamic Programming, and Economic Lot Size. AUTH: R.E. Bellman PAGES: 20, DATE: 1956 COST: $ 4.00 ABST: No abstract available. 20 pp. P-841: Strategy Versus Tactics in a Nuclear Age. AUTH: B. Brodie PAGES: 26, DATE: 1956 COST: $ 4.00 KEYS: Military strategy; Nuclear weapons; United states--Foreign relations ABST: A discourse on the roles of strategy and tactics in a world that possesses both thermonuclear weapons and the experience of almost unlimited war. The author states that the defense problem is more likely to be solved by strategy and national policy than by tactics. (Presented before the Graduate Institute of International Studies at Geneva, Switzerland, May 1956. Published in Thursfield, Barclay, and Yool (eds.), [Brassey's Annual: The Armed Forces Yearbook], Macmillan, New York, 1956.) 26 pp. P-842: Manual for the RAND-IBM Code for Linear Programming on the 704. AUTH: W. Orchard-Hays, L. Cutler, H.A. Judd PAGES: 50, DATE: 1956 COST: $ 4.00 KEYS: Programming (mathematics) ABST: No abstract available. 50 pp. P-844: Optimal Utilization and Extension of Interoffice Trunking Facilities. AUTH: R.E. Kalaba, M.L. Juncosa PAGES: 21, DATE: 1956 COST: $ 4.00 ABST: No abstract available. 21 pp. P-845: Notes on the Theory of Dynamic Programming--VIII. AUTH: R.E. Bellman PAGES: 5, DATE: 1956 COST: $ 4.00 ABST: No abstract available. 5 pp. P-846: Priority Assignment on a Waiting Line. AUTH: S.A. Dressin, E. Reich PAGES: 7, DATE: 1956 COST: $ 4.00 ABST: No abstract available. 7 pp. P-856: Best Exploration for Maximum Is Fibonaccian. AUTH: S.M. Johnson PAGES: 8, DATE: 1956 COST: $ 4.00 ABST: No abstract available. 8 pp. P-859: Functional Equations in the Theory of Dynamic Programming--VII: An Integro-Differential Equation for the Fredholm Resolvent. AUTH: R.E. Bellman PAGES: 9, DATE: 1956 COST: $ 4.00 ABST: No abstract available. 9 pp. P-861: Information in Games with Finite Resources. AUTH: D. Gale PAGES: 9, DATE: 1956 COST: $ 4.00 KEYS: Game theory ABST: A proof that, in games with finite resources, the uniform mixed strategy is optimal. Therefore, a player is not helped by knowing the strategies available to his opponent. 9 pp. Also published as RM-1542. P-863: Birth-Death Processes and Tandem Queues. AUTH: E. Reich PAGES: 5, DATE: 1956 COST: $ 4.00 ABST: No abstract available. 5 pp. P-866: On a Dynamic Programming Approach to the Caterer Problem--I. AUTH: R.E. Bellman PAGES: 18, DATE: 1956 COST: $ 4.00 ABST: No abstract available. 18 pp. P-869: Dynamic Programming and LaGrange Multipliers. AUTH: R.E. Bellman PAGES: 6, DATE: 1956 COST: $ 4.00 ABST: No abstract available. 6 pp. P-870: Professor Koopmans on Fallacies: A Comment. AUTH: C.J. Hitch PAGES: 8, DATE: 1956 COST: $ 4.00 ABST: No abstract available. 8 pp. P-883: Rain Scavenging of Radioactive Particulate Matter from the Atmosphere. AUTH: S.M. Greenfield PAGES: 29, DATE: 1956 COST: $ 4.00 KEYS: Atmosphere; Meteorology ABST: A derivation of a physical model to explain the removal of radioactive particulate matter from the atmosphere by rain. The processes considered quantitatively are the direct pickup of radioactive particles by rain and the scavenging by raindrops of cloud droplets which have already collected the smaller radioactive particles. 29 pp. P-885: A Comparison of Linear Programming and Dynamic Programming. AUTH: S.E. Dreyfus PAGES: 15, DATE: 1956 COST: $ 4.00 ABST: No abstract available. 15 pp. P-888: A Solution Containing an Arbitrary Closed Component. AUTH: L.S. Shapley PAGES: 10, DATE: 1956 COST: $ 4.00 KEYS: Game theory ABST: A discussion of an [n]-person game solution constructed around an arbitrary closed set. It is shown that there is practically no limit to the possible complexity of solutions. (Also published as RM-1005.) 10 pp. P-890: Hitchcock Transportation Problem. AUTH: D.R. Fulkerson PAGES: 29, DATE: 1956 COST: $ 4.00 ABST: No abstract available. 29 pp. P-891: The Simplex Method. AUTH: G.B. Dantzig PAGES: 31, DATE: 1956 COST: $ 4.00 ABST: A discussion of the simplex method, for solving a linear program, which first transforms the original system to an equivalent system of m equations in canonical form by eliminating ma of the n unknowns. If the right choice of m variables is made, an optimal solution is obtained to the original problem by equating the remaining variables to zero. If not, the method produces an improved set of m variables and a corresponding canonical form. The procedure is iterted until an optimum solution is determined. P-892: The Central Mathematical Problem. AUTH: G.B. Dantzig PAGES: 19, DATE: 1956 COST: $ 4.00 ABST: No abstract available. 19 pp. P-893: Formulating a Linear Programming Model. AUTH: G.B. Dantzig PAGES: 11, DATE: 1956 COST: $ 4.00 ABST: No abstract available. 11 pp. P-907: The Storage Allocation of the Linear Programming Code. AUTH: H.A. Judd PAGES: 12, DATE: 1956 COST: $ 4.00 ABST: No abstract available. 12 pp. P-908: Adaptability of the Linear Programming Codes. AUTH: W. Orchard-Hays PAGES: 20, DATE: 1956 COST: $ 4.00 ABST: No abstract available. 20 pp. P-909: Operating the Linear Programming Codes. AUTH: L. Cutler PAGES: 27, DATE: 1956 COST: $ 4.00 ABST: A method of operating an elaborate set of computer codes. The checks used and the types of error expected are discussed, together with the procedure for computing after machine or problem error has occurred. It is shown that with adequate written instructions the problems can be run on the high-speed computer by any machine operator. P-911: The Revised Simplex Method. AUTH: W. Orchard-Hays PAGES: 29, DATE: 1956 COST: $ 4.00 ABST: No abstract available. 29 pp. P-914: Preparation of Input for the Linear Programming Code. AUTH: H.A. Judd PAGES: 11, DATE: 1956 COST: $ 4.00 ABST: No abstract available. 11 pp. P-916: The Complete Dualized System of the Simplex Method. AUTH: W. Orchard-Hays PAGES: 12, DATE: 1956 COST: $ 4.00 ABST: No abstract available. 12 pp. P-917: On Some Applications of Dynamic Programming to Matrix Theory. AUTH: R.E. Bellman PAGES: 10, DATE: 1956 COST: $ 4.00 ABST: No abstract available. 10 pp. P-923: Network Flow Theory. AUTH: L.R. Ford PAGES: 13, DATE: 1956 COST: $ 4.00 ABST: No abstract available. 13 pp. P-924: Computational Aspects of Dynamic Programming. AUTH: S.E. Dreyfus PAGES: 3, DATE: 1956 COST: $ 4.00 ABST: No abstract available. 3 pp. P-925: Printing and Checking for Linear Programming Codes. AUTH: H.A. Judd PAGES: 27, DATE: 1956 COST: $ 4.00 ABST: No abstract available. 27 pp. P-928: Gradient Methods for Constrained Maxima. AUTH: K.J. Arrow, L. Hurwicz PAGES: 12, DATE: 1956 COST: $ 4.00 ABST: An application of certain computational methods to evaluate constrained extrema, maxima, or minima. Although the solution of nonlinear games is discussed, the application of the gradient method to constrained maxima is emphasized. P-932: An Analytic Solution of the Warehouse Problem. AUTH: S.E. Dreyfus PAGES: 9, DATE: 1956 COST: $ 4.00 ABST: No abstract available. 9 pp. P-939: A Systematic Approach to a Class of Problems in the Theory of Noise and Other Random Phenomena--III: Examples. AUTH: A.J.F. Siegert PAGES: 39, DATE: 1956 COST: $ 4.00 ABST: No abstract available. 39 pp. P-949: On the Role of Dynamic Programming in Statistical Communication Theory. AUTH: R.E. Bellman, R.E. Kalaba PAGES: 20, DATE: 1956 COST: $ 4.00 ABST: No abstract available. 20 pp. P-950: Linear Programming. AUTH: R.E. Kalaba PAGES: 16, DATE: 1956 COST: $ 4.00 ABST: No abstract available. 16 pp. P-965: A Display Technique for Planning. AUTH: J.L. Kennedy PAGES: 10, DATE: 1956 COST: $ 4.00 KEYS: Contextual maps; Display systems; Planning; Research and development ABST: A description of a display technique which may be used by teams of planners and decisionmakers when faced with the complexities of developing large interacting systems. In particular, it is proposed that the contextual map will substantially assist decisionmaking in Air Force research and development. 10 pp. P-968: Scientific Progress and Political Science. AUTH: B. Brodie PAGES: 21, DATE: 1956 COST: $ 4.00 KEYS: Decision-making; Political science; Security measures ABST: A speech delivered before the American Association for the Advancement of Science at New York City, December 26, 1956, on the deficiency of political scientists in coping with policy decisions affecting national security in an atomic age. The causes for this deficiency are enumerated (e.g., the security barrier, the exaggeration of the esoteric nature of the military art, the rampant technology in the art, and the weight of tradition in determining scope and method in political science). 21 pp. P-972: Soviet Economic Aid in Southeast Asia: Threat or Windfall? AUTH: C. Wolf PAGES: 15, DATE: 1956 COST: $ 4.00 KEYS: Southeast asia; United states--Economic assistance; United states--Foreign KEYS: relations; Soviet Union--Economics ABST: Comments on Soviet diplomacy in Asia during the mid-fifties. The author suggests that Soviet Bloc aid to nonallied countries might entail windfall benefits as well as threats to U.S. interests and create interesting complications in U.S. policies toward SEATO allies. 15 pp. P-977: A Dynamic Programming Solution to a Cascading Problem Arising in Heavy Water Production. AUTH: R.E. Bellman PAGES: 7, DATE: 1956 COST: $ 4.00 ABST: No abstract available. 7 pp. P-991: Some Principles for a Data-Processing System in Logistics. AUTH: M.A. Geisler PAGES: 20, DATE: 1956 COST: $ 4.00 ABST: No abstract available. 20 pp. P-994: Theory of Games of Strategy. AUTH: M. Dresher PAGES: 14, DATE: 1956 COST: $ 4.00 KEYS: Game theory ABST: A survey of the mathematical theory of zero-sum two-person games. In particular, this study describes games with a finite number of strategies, the solution of finite games, games with infinite strategies, and examples of infinite games. 14 pp. P-995: Queueing with Balking. AUTH: F.A. Haight PAGES: 25, DATE: 1956 COST: $ 4.00 ABST: No abstract available. 25 pp. RM-1741: On the Optimal Use of Guided Missiles--I: Allocation of Missiles. AUTH: R.E. Bellman PAGES: 11, DATE: 1956 COST: $ 4.00 ABST: The first of a series of studies concerned with mathematical problems arising in the use of guided missiles. The present study deals with the optimal allocation of missiles against a given target system. It is shown that the computational solution of these problems can be greatly simplified by means of the functional-equation technique of dynamic programming. The method proposed is applicable to a large class of problems involving the allocation of resources, both economic and military. No abstract available. 11 pp. RM-1742: On the Optimal Use of Guided Missiles--II: Dummy Missiles. AUTH: R.E. Bellman PAGES: 12, DATE: 1956 COST: $ 4.00 ABST: A continuation of RM-1741, which considered the optimal allocation of missiles against a given target system, assuming that dummy missiles are allowable. The present study deals with the same problem, first under the assumption that dummy missiles are to be used, and second under the assumption that the amount of fissile material available is limited. An attempt is made to present a computational technique that can treat, in a routine fashion, target systems with hundreds of targets, some independent and some in target clusters, under realistic assumptions concerning probabilility of survival of the individual missile and the type of defense employed. 12 pp. RM-1745: On the Computational Solution of Dynamic-Programming Processes--I: On a Tactical Air-Warfare Model of Mengel. AUTH: R.E. Bellman, S.E. Dreyfus, S.E. Dreyfus PAGES: 21, DATE: 1956 COST: $ 4.00 ABST: The first of a series of studies concerned with the computational solution of dynamic programming processes. The functional equation approach is used to treat a tactical air-warfare model that A. Mengel previously considered by means of classical variational techniques. No abstract available. 22 pp. RM-1746: On the Computational Solution of Dynamic-Programming Processes--II: On a Cargo-Loading Problem. AUTH: R.E. Bellman, S.E. Dreyfus, S.E. Dreyfus PAGES: 9, DATE: 1956 COST: $ 4.00 ABST: A presentation of the numerical solution of a cargo-loading problem in which the difficulty arises from indivisibility requirements. A dynamic programming formulation is used. No abstract available. 9 pp. RM-1842: Implications of Nuclear Weapons in Total War. AUTH: B. Brodie PAGES: 34, DATE: 1956 COST: $ 4.00 KEYS: Air power; Military strategy; Nuclear warfare ABST: Part of a broader investigation concerned with the general theory of air strategy in a nuclear age. The present Memorandum states that (1) an unrestricted strategic air campaign in a war in which the United States is engaged will be decisive, (2) strategic bombing will prove other kinds of military operations unfeasible, and (3) those surviving strategic attack will be far more important in the national recovery following hostilities rather than in controlling the subsequent course of the war. (Also published as P-1118.) 34 pp. RM-1710: Application of Dynamic Programming to the Airplane Minimum Time-to-Climb Problem. AUTH: T.F. Cartaino, S.E. Dreyfus, S.E. Dreyfus PAGES: 20, DATE: 1956 COST: $ 4.00 ABST: An application of the dynamic programming technique to the solution of the airplane minimum time-to-climb problem. A typical case is solved. No abstract available. 21 pp. RM-1621: A Technique for Optimal Distribution of Available Stocks to Bases. AUTH: A. Clark, A.J. Clark PAGES: 67, DATE: 1956 COST: $ 7.50 ABST: A technique for distributing available stocks of Air Force property among bases in an optimal fashion. The level of system stocks, the uncertainty of demand for parts, and the costs not only of holding and processing Air Force property, but also of the effects of a shortage of a part when it is needed are considered. The technique is particularly applicable to aircraft spare parts. No abstract available. 68 pp. RM-1709: Notes on Linear Programming--Part XXXI: A Primal-Dual Algorithm. AUTH: G.B. Dantzig, L.R. Ford, D.R. Fulkerson, L.R. Ford, D.R. Fulkerson PAGES: 16, DATE: 1956 COST: $ 4.00 ABST: A procedure for solving transportation problems which is a natural extension of the Kuhn-Egervâary method for solving assignment problems. The present paper extends this procedure to the general linear programming case. No abstract available. 17 pp. RM-1832: Notes on Linear Programming--Part XXXV: Discrete-Variable Extremum Problems. AUTH: G.B. Dantzig PAGES: 27, DATE: 1956 COST: $ 4.00 ABST: A review of some recent successes in the use of linear programming methods for solving discrete-variable extremum problems. One example of the use of the multistage approach of dynamic programming is also discussed. No abstract available. 28 pp. P-803: The Value of Airlift in Defensive, Local, or Peripheral Wars After 1960. AUTH: S.E. Eastman PAGES: 15, DATE: 1956 COST: $ 4.00 KEYS: Airlift ABST: A discussion of the value of airlift to the U.S. Air Force in a situation sometime after 1960 involving something less than all-out general war. Military requirements for intercontinental air transportation are discussed, along with U.S. capacity to engage in limited war operations. 15 RM-1744: The Distribution of Radial Error and Its Statistical Application in War Gaming. AUTH: H.P. Edmundson PAGES: 27, DATE: 1956 COST: $ 4.00 ABST: A discussion of a model concerned with the distribution of weapon radial error and an illustration of its statistical application in war gaming. The density function and cumulative distribution function of the radial error are derived and graphed for one, two, and three dimensions. For each of these cases, formulas are given for the expectation, standard deviation, and median of the radial error. No abstract available. 28 pp. RM-1820: The Goodness-of-Fit Statistics of Kolmogorov and Smirnov. AUTH: H.P. Edmundson PAGES: 27, DATE: 1956 COST: $ 4.00 KEYS: Statistical analysis; Statistics ABST: An examination of the goodness-of-fit statistics of A. Kolmogorov and N. Smirnov. The theory and applications of these statistics are summarized and compared with the classical statistic for testing goodness of fit. (See also RM-1905, RM-1958.) 27 pp. RM-1833: Notes on Linear Programming--Part XXXVI: The Allocation of Aircraft to Routes--an Example of Linear Programming under Uncertain Demand. AUTH: A.R. Ferguson, G.B. Dantzig, G.B. Dantzig PAGES: 46, DATE: 1956 COST: $ 4.00 KEYS: Programming (mathematics) ABST: An application of linear programming to the problem of allocating aircraft to routes to maximize expected profits when there is uncertain demand. It is assumed that (1) the demand for each activity over the pertinent time period, while not known, can be estimated as a distribution of values and (2) each of these values has a specified probability of being the actual value. An application of linear programming to the problem of allocating aircraft to routes to maximize expected profits when there is uncertain demand. It is assumed that: (1) the demand for each activity over the pertinent time period, while not known, can be estimated as a distribution of values; and (2) each of these values has a specified probability of being the actual value. 46 pp. RM-1736: Notes on Linear Programming--Part XXXII: Solving the Transportation Problem. AUTH: L.R. Ford, D.R. Fulkerson, L.R. Ford, D.R. Fulkerson PAGES: 17, DATE: 1956 COST: $ 4.00 ABST: A description of a new computing procedure for the Hitchcock-Koopmans transportation problem and a step-by-step solution of an illustrative example. The procedure is based on Kuhn's combinatorial algorithm for the assignment problem and a simple labeling process for solving maximal flow problems in networks. No abstract available. 18 pp. RM-1798: Notes on Linear Programming--Part XXXIV: A Primal-Dual Algorithm for the Capacitated Hitchcock Problem. AUTH: L.R. Ford, D.R. Fulkerson, L.R. Ford, D.R. Fulkerson PAGES: 17, DATE: 1956 COST: $ 4.00 ABST: An algorithm for solving capacitated Hitchcock problems and a proof of convergence in a finite number of steps. The proposed algorithm is a generalization of a combinatorial method discovered by Kuhn for the optimal assignment problem. It uses as a subroutine the flow algorithm previously developed. No abstract available. 18 pp. RM-1737: Notes on Linear Programming--Part XXXIII: A Theorem on Flows in Networks. AUTH: D. Gale, O.G. Gale PAGES: 18, DATE: 1956 COST: $ 4.00 ABST: A study which obtains a condition for the existence of a flow from the origins to the destinations (connected by a network of edges of specified finite capacity) such that the flows into the destinations attain prescribed values. The existence theorem, which generalizes a well-known combinatorial theorem of P. Hall, is then applied to a particular example. RM-1676-AEC: A Catalog of Fallout Patterns. AUTH: S.M. Greenfield, R.R. Rapp, P.A. Walters, R.R. Rapp, P.A. Walters PAGES: 94, DATE: 1956 COST: $ 7.50 KEYS: Fallout; Nuclear weapons effects ABST: A method for estimating quickly the fallout from a massive nuclear attack. This method consists of 26 carefully computed fallout patterns, together with instructions for matching them approximately to a given yield and wind condition. An outline of the basic computational model is given, and possible sources of errors of estimates are discussed. A method for estimating quickly the fallout from a massive nuclear attack. This method consists of 26 carefully computed fallout patterns, together with instructions for matching them approximately to a given yield and wind condition. An outline of the basic computational model is given, and possible sources of errors of estimates are discussed. 96 pp. RM-1644: Notes on Linear Programming--Part XXX: A Class of Discrete-Type Minimization Problems. AUTH: O.A. Gross PAGES: 13, DATE: 1956 COST: $ 4.00 KEYS: Programming (mathematics) ABST: A proof that a minimization problem involving a finite set of convex functions is solvable in nonnegative integers by means of a simple algorithm. A criterion is established for testing whether or not a feasible solution is optimal. Special applications are included. No abstract available. 14 pp. RM-1755: Games with Payoff Discontinuities at Discrete Points. AUTH: O.A. Gross PAGES: 8, DATE: 1956 COST: $ 4.00 KEYS: Games ABST: A presentation of an indeterminate game G on the unit square S. It is assumed that G has a bounded rational continuous payoff at all except three points of S and that, of the three discontinuities, only one is nonremovable. A presentation of an indeterminate game [G] on the unit square [S]. It is assumed that [G] has a bounded rational continuous payoff at all except three points of [S] and that, of the three discontinuities, only one is nonremovable. 9 pp. RM-1807: A Method for Estimating Engine Failure Rates. AUTH: T.E. Harris PAGES: 26, DATE: 1956 COST: $ 4.00 KEYS: Engines; Reliability; Statistical analysis ABST: An application of a standard statistical method to the problem of estimating engine failure rates from observations on a group of engines. 27 pp. RM-1724: Some Physical Qualifications for Reliability Formulas. AUTH: W.J. Howard PAGES: 26, DATE: 1956 COST: $ 4.00 ABST: An extension of RM-1058, Chain Reliability: A Simple Failure Model for Complex Mechanisms, which analyzed the effect of complexity on the reliability of a chain. The present study determines formulas for reliability as a function of complexity, redundancy, and time for various stress-strength conditions. In addition, the merits of using redundancy at different levels of system subdivision are considered. No abstract available. 27 pp. RM-1652: Optimal Sequential Testing. AUTH: S.M. Johnson PAGES: 12, DATE: 1956 COST: $ 4.00 ABST: A discussion of the sequence in which components of a complicated machine should be tested and repaired in case of a breakdown in order to minimize the expected delay time. Some mathematical versions of the general problem and their solutions are presented. No abstract available. 13 pp. RM-1687: Communication Networks--I: Optimal Design and Utilization. AUTH: R.E. Kalaba, M.L. Juncosa, M.L. Juncosa PAGES: 22, DATE: 1956 COST: $ 4.00 KEYS: Communication networks; Communication systems; Programming (mathematics) ABST: Part of a broader investigation on communication networks in an attempt to determine the complex interactions among system capacities, users' demands, and economic factors. The present study, which considers system utilization and design, discusses a general communication system, optimal routing problems as linear programming problems, and optimal design problems in the same framework. Part of a broader investigation on communication networks in an attempt to determine the complex interactions among system capacities, users' demands, and economic factors. The present study, which considers system utilization and design, discusses a general communication system, optimal routing problems as linear programming problems, and optimal design problems in the same framework. 26 pp. RM-1664: A Brief Investigation of the Possibility of Increasing the Range of Aircraft by Dropping Unnecessary Parts in Flight. AUTH: T.F. Kirkwood PAGES: 28, DATE: 1956 COST: $ 4.00 KEYS: Airplanes ABST: An investigation of the increase in range obtained by designing an aircraft so that parts which have ceased to perform a useful function may be dropped in flight. A theoretical limiting case is studied, as well as more practical cases in which the landing gear is dropped after takeoff and non-lifting external fuel tanks are dropped when empty. An investigation of the increase in range obtained by designing an aircraft so that parts which have ceased to perform a useful function may be dropped in flight. A theoretical limiting case is studied, as well as more practical cases in which the landing gear is dropped after takeoff and non-lifting external fuel tanks are dropped when empty. 29 pp. RM-1612: Allocating MATS Equipment with the Aid of Linear Programming. AUTH: A.S. Manne PAGES: 34, DATE: 1956 COST: $ 4.00 KEYS: Airlift; Programming (mathematics) ABST: A study concerned with the planning of Military Air Transport Service airlift operations. In particular, a procedure is examined for allocating transport equipment in an efficient way. The method is illustrated by numerous examples and can be applied in a straightforward mechanical fashion. A 1956 study concerned with the planning of Military Air Transport Service airlift operations. In particular, a procedure is examined for allocating transport equipment in an efficient way. The method is illustrated by numerous examples and can be applied in a straightforward mechanical fashion. 35 pp. RM-1770: On the Detection of Stochastic Signals in Additive Normal Noise: Part I. AUTH: D. Middleton PAGES: 130, DATE: 1956 COST: $ 10.00 KEYS: Signal processing; Stochastic processes ABST: An examination of optimum and suboptimum detection of normal signals in additive normal noise backgrounds. General results for optimum receiver structure, error probabilities, and average risk are obtained for colored noise backgrounds. Threshold reception in white noise backgrounds is investigated. In addition, optimum detector structure for signal processes with rational intensity spectra is determined for the white-noise case. 131 pp. RM-1799: Notes on Linear Programming--Part XXXVII: Concerning Multicommodity Networks. AUTH: J.T. Robacker PAGES: 13, DATE: 1956 COST: $ 4.00 ABST: A generalization of the minimum-cut, maximum-flow theorem to multicommodity networks. The generalization is expressed as a decomposition theorem that is established for these networks. RM-1818: Equilibrium Points in Games with Vector Payoffs. AUTH: L.S. Shapley PAGES: 9, DATE: 1956 COST: $ 4.00 KEYS: Game theory ABST: An attempt to define and characterize the equilibrium-point solutions of games of a certain kind. It is assumed that the payoff of the game considered sometimes takes the form of a vector having components that represent amounts of different things which have unknown relative values. A definition and characterization of the equilibrium-point solutions of two-person games in which the payoff takes the form of a vector, the relative values of the components being unknown. (Also published as P-1212.) 10 pp. P-1212: Equilibrium Points in Games with Vector Payoffs. AUTH: L.S. Shapley PAGES: 9, DATE: 1956 COST: $ 4.00 KEYS: Game theory ABST: An attempt to define and characterize the equilibrium-point solutions of games with payoffs that sometimes take the form of a vector. It is assumed the vector has components that represent amounts of different things of which the relative values are unknown. A definition and characterization of the equilibrium-point solutions of two-person games in which the payoff takes the form of a vector, the relative values of the components being unknown. 9 pp. (Also published as RM-1818.) RM-1632: Expected Damage from Single and Multiple Bombs to Targets Distributed Uniformly Around a Circle. AUTH: C.V. Sturdevant PAGES: 21, DATE: 1956 COST: $ 4.00 ABST: Curves showing the expected damage from single and multiple bomb drops to equal-valued point targets (e.g., aircraft shelters) distributed uniformly around a circle. The damage function utilized is 1.0 (complete damage) when the bomb falls within its lethal radius of the individual target and 0 (zero) when it falls outside this distance. The expected damage has been empirically maximized by suitably selecting aim points for the one-bomb case only. No abstract available. 22 pp. RM-1858-PR: Relationships Between Program Elements and System Demand for Airframe Spare Parts. AUTH: T.A. Goldman PAGES: 88, DATE: 1957 COST: $ 7.50 ABST: The results of research on system-wide demand for spare parts by military aircraft. The relation of such demand to program elements is analyzed, and techniques are developed for forecasting future demands on the basis of past data. A new approach used in this study considers the relationships of substitution and interchangeability among parts, of part applicability within the weapons system, and of the differences between base-level and system-level demand for spare parts. In particular, the Worldwide Stock Balance and Consumption Reports are examined for B-47 airframe parts (primarily in Category I). Illus. RM-1866-PR: Strategic Air Power in World War II. AUTH: B. Brodie PAGES: 46, DATE: 1957 COST: $ 4.00 KEYS: Air power; Bombing; Germany; Japan; Military strategy; World war, KEYS: 1939-1945 ABST: Part of a broader investigation concerned with the general theory of air strategy in a nuclear age. Based on literature published by the U.S. Strategic Bombing Survey, the present study considers the Allied strategic bombing campaigns against Germany and Japan in World War II. The author concludes that these strategic successes were questionable in that they either came too late to have a decisive effect or they were imposed on an enemy already prostrated by other forms of war. 46 pp. RM-2080-PR: A Method for Evaluating Environmental Effects on Military Operations. AUTH: J.D. Sartor PAGES: 38, DATE: 1957 COST: $ 4.00 ABST: No abstract available. 38 pp. P-834: Application of Dynamic Programming to the Airplane Minimum Time-to-Climb Problem. AUTH: T.F. Cartaino, S.E. Dreyfus PAGES: 19, DATE: 1957 COST: $ 4.00 ABST: No abstract available. 19 pp. P-910: A Min-Max Solution of an Inventory Problem. AUTH: H.E. Scarf PAGES: 16, DATE: 1957 COST: $ 4.00 ABST: No abstract available. 16 pp. P-912: A Systematic Approach to Local Objective Forecast Studies. AUTH: J.D. Sartor PAGES: 23, DATE: 1957 COST: $ 4.00 KEYS: Meteorology ABST: A presentation of a systematic approach to the preparation of local objective forecast studies. The paper isolates the seasonal, daily, or other cyclic variations of the elements to be forecast, and determines the correlated (noncyclic) variables by using only synoptic data. In addition, it assembles several component studies into a logical forecast scheme. 23 pp. P-921: Upper Bounded Variables in Linear Programming. AUTH: G.B. Dantzig, S.M. Johnson PAGES: 13, DATE: 1957 COST: $ 4.00 ABST: A technique for bounding variables in a linear programming problem, together with several applications. These restraints can be applied without greatly increasing the computational effort. P-964: General Systems Approaches to Telecommunication Optimization. AUTH: R.E. Kalaba, M.L. Juncosa PAGES: 21, DATE: 1957 COST: $ 4.00 KEYS: Communication systems; Optimization; Programming (mathematics) ABST: An application of linear and dynamic programming to solve numerous communication system problems. Treatments for communication system extension problems and for equipment replacement policies are given, and various generalizations are indicated. 21 pp. P-980: Concepts, Origins, and Use of Linear Programming. AUTH: G.B. Dantzig PAGES: 18, DATE: 1957 COST: $ 4.00 ABST: No abstract available. 18 pp. P-982: Bounds on the Expectation of a Convex Function of a Random Variable. AUTH: H.P. Edmundson PAGES: 6, DATE: 1957 COST: $ 4.00 ABST: No abstract available. 6 pp. P-989: Sequential Production Planning Over Time at Minimum Cost. AUTH: S.M. Johnson PAGES: 8, DATE: 1957 COST: $ 4.00 ABST: No abstract available. 8 pp. P-1017: Generalized Analysis of Aerial Campaigns Against Strategic Targets. AUTH: R. Schamberg PAGES: 39, DATE: 1957 COST: $ 4.00 ABST: A technique for determining directly the outcome of optimal aerial bombing or reconnaissance campaigns against strategic targets without the usual examination of variations in attack strategy. P-1042: Scientific Aids to Decisionmaking: A Perspective. AUTH: J.R. Goldstein PAGES: 12, DATE: 1957 COST: $ 4.00 KEYS: Decision-making ABST: A discussion of the historical use of the committee in decisionmaking. It is suggested that the scientific method is better for this purpose, because it defines the problem properly, considers real objectives, provides a framework for solving problems of broad scope, and evaluates solutions on the basis of carefully drawn criteria. 12 pp. P-1047: Soviet Trade and Aid: Trickle or Torrent? AUTH: H. Heymann PAGES: 12, DATE: 1957 COST: $ 4.00 KEYS: Economics--Foreign; International trade and finance; United states--Economic KEYS: assistance; Soviet Union--Economics ABST: A consideration of the relationship between the growth of the Soviet economy and participation by the USSR during the midfifties in foreign trade and technical assistance programs. The author finds that the scale and economic significance of the Soviet effort generally had been overstated but notes that the ingeniously designed program had reaped large political rewards, out of proportion to its magnitude. 12 pp. P-1077: The Small Sample Distribution. AUTH: A.W. Marshall PAGES: 6, DATE: 1957 COST: $ 4.00 KEYS: Statistical analysis ABST: A discussion of asymptotic distribution. (Published in [The Annals of Mathematical Statistics], March 1958.) 6 pp. RM-1911-PR: Problems of Nuclear Sharing. AUTH: W.W. Kaufmann PAGES: 44, DATE: 1957 COST: $ 4.00 ABST: An attempt to establish the plausibility of certain developments that might result from the U.S. sharing nuclear weapons systems tactically and strategically with the major NATO powers. The author concludes that nuclear sharing should not be considered in the context of whether or not the U.S. wants other nations to have these weapons, but rather within the framework of when and under what institutional and political conditions they acquire an effective nuclear capability. RM-1976: Notes on Linear Programming--Part XLIII: A Feasibility Algorithm for One-Way Substitution in Process Analysis. AUTH: K.J. Arrow, S.M. Johnson, S.M. Johnson PAGES: 14, DATE: 1957 COST: $ 4.00 ABST: A proof that an algorithm for the most efficient assignment of machines to tasks solves an equivalent linear-programming problem. The study assumes that with a certain number of machines (not all of the same capability) with which to do a certain number of tasks (not all of the same difficulty), it is better to use a more capable machine for a more difficult task. No abstract available. 15 pp. P-1015: On Gradient Methods for Approaching Constrained Maxima. AUTH: K.J. Arrow, L. Hurwicz, T.A. Marschak PAGES: 21, DATE: 1957 COST: $ 4.00 ABST: A summary of the authors' previous work on gradient methods. The possibility is discussed of convergence in the large when gradient methods are applied to linear programming problems. In addition, computational difficulties encountered in applying the authors' methods to linear programming problems are examined. No abstract available. 21 pp. RM-1747: On the Computational Solution of Dynamic-Programming Processes--III: On the Optimal Use of Guided Missiles Against a Fixed Target System--Maximum Expected Damage. AUTH: R.E. Bellman, S.E. Dreyfus, S.E. Dreyfus PAGES: 13, DATE: 1957 COST: $ 4.00 ABST: An application of dynamic-programming techniques to the problem of determining the use of guided missiles against a fixed target system. The criterion of maximum expected damage is used, and the case of 100 missiles and 20 targets of varying values is given as an example. No abstract available. 14 pp. RM-1748: On the Computational Solution of Dynamic-Programming Processes--IV: On the Optimal Use of Guided Missiles Against a Fixed Target System--Maximum Probability of Success. AUTH: R.E. Bellman, S.E. Dreyfus, S.E. Dreyfus PAGES: 13, DATE: 1957 COST: $ 4.00 ABST: An application of dynamic-programming techniques to the problem of determining the use of guided missiles against a fixed target system. It is assumed that the purpose is to maximize the probability of achieving a damage greater than or equal to a given fixed level. No abstract available. 14 pp. RM-1749: On the Computational Solution of Dynamic-Programming Processes--V: A Smoothing Problem. AUTH: R.E. Bellman, S.E. Dreyfus PAGES: 15, DATE: 1957 COST: $ 4.00 ABST: A study of a particular case of the general problem of balancing cost of undersupply against cost of oversupply. The problem is typical of those arising in production smoothing. A computational solution is given. RM-1750-PR: Computational Solutions of Dynamic-Programming Processes--VI: On the Optimal-Trajectory Problem. AUTH: R.E. Bellman, S.E. Dreyfus PAGES: 13, DATE: 1957 COST: $ 4.00 ABST: An application of dynamic programming theory to the solution of trajectory problems for interceptors. After a discussion of the principles involved, a specific problem is solved. Illus. RM-1752: On the Computational Solution of Dynamic-Programming Processes--VIII: A Bottleneck Situation Involving Interdependent Industries. AUTH: R.E. Bellman, S.E. Dreyfus PAGES: 15, DATE: 1957 COST: $ 4.00 ABST: An examination of the computational solution of a maximization problem arising in the study of the use of interdependent industries. Assuming proportional costs and returns, it is shown that the dimensionality of the problem can always be reduced by one, and that all the transformations occurring can be taken to be "shrinking transformations." These transformations improve greatly the efficiency of the method. 16 pp. RM-1859-PR: Notes on Linear Programming: Part XXXIX--Slightly Intertwined Linear Programming Matrices. AUTH: R.E. Bellman PAGES: 11, DATE: 1957 COST: $ 4.00 NOTE: See condensed version P-918. ABST: The use of the functional equation approach of dynamic programming to treat a linear programming problem. This problem involves a slightly intertwined matrix, i.e., one which is almost block diagonal. RM-1888: On the Formulation of Dynamic-Programming Problems--I. AUTH: R.E. Bellman, S.E. Dreyfus PAGES: 15, DATE: 1957 COST: $ 4.00 ABST: A presentation of a wide variety of complicated multidimensional computational problems that can be treated by dynamic programming theory. Part I considers a logistics problem which involves the purchasing and servicing of numerous items. Part II shows how target-selection problems arising in the attack on a target complex by weapons of several different types or by successive waves of weapons of the same type may be treated. Part III discusses the solution of the optimal-inventory problem with delivery lags of arbitrary length. 17 pp. RM-1889: On the Computational Solution of Dynamic-Programming Processes--X: The Flyaway-Kit Problem. AUTH: R.E. Bellman, S.E. Dreyfus PAGES: 12, DATE: 1957 COST: $ 4.00 ABST: A study of the flyaway-kit problem, a special case of the cargo-loading problem. A kit that minimizes the expected cost due to shortage of a spare part is computed subject to restrictions on the weight and size of the kit. No abstract available. 13 pp. RM-1898: On the Formulation of Dynamic-Programming Processes--IV: On the Allocation of Bombers and Decoys. AUTH: R.E. Bellman, S.E. Dreyfus PAGES: 10, DATE: 1957 COST: $ 4.00 ABST: An extension of RM-1800, Concerning the Allocation of Decoys To Minimize Bomber Losses, which described the allocation of decoys to bomber strikes to saturate the defense and decrease losses. The present study shows that the type of problem treated in RM-1800 can be solved quickly by dynamic-programming processes. Problems are considered (1) where the quantities of bombers and decoys, or live missiles and dummy missiles, are given, and (2) where the funds are available to purchase both types of weapons. 10 pp. RM-1901: On the Computational Solution of Dynamic-Programming Processes--IX: A Multistage Logistic-Procurement Model. AUTH: R.E. Bellman, S.E. Dreyfus PAGES: 8, DATE: 1957 COST: $ 4.00 ABST: An application of dynamic programming to multistage logistic problems. The optimal procurement of a replacement part, assuming stochastic demand, is analyzed to determine an initial-order quantity and a replacement schedule that minimize expected cost. Cost factors include purchase cost, storage cost, and outage penalty. 9 pp. P-918: Notes on Matrix Theory--XIII: Slightly Intertwined Linear Programming Matrices. AUTH: R.E. Bellman PAGES: 5, DATE: 1957 COST: $ 4.00 ABST: The use of the functional equation approach of dynamic programming to treat a linear programming problem. This problem involves a slightly intertwined matrix, i.e., one which is almost block diagonal. P-1038: Dynamic Programming and the Variational Solution of the Thomas-Fermi Equation. AUTH: R.E. Bellman PAGES: 8, DATE: 1957 COST: $ 4.00 ABST: A numerical technique for integrating nonlinear differential equations satisfying two-point boundary conditions which arise from variational problems. The theory of dynamic programming is applied to the minimization problem considered, and two approaches are given. However, the computational results are not presented. P-1066: A Markovian Decision Process. AUTH: R.E. Bellman PAGES: 13, DATE: 1957 COST: $ 4.00 ABST: A discussion of the asymptotic behavior of the sequence <> generated by the nonlinear recurrence relation <>. This problem arises in connection with an equipment replacement problem treated by S. E. Dreyfus in P-1045, A Note on an Industrial Replacement Process. P-1081: Functional Equations in the Theory of Dynamic Programming--VIII: The Variation of Green's Functions--One-Dimensional Case. AUTH: R.E. Bellman PAGES: 6, DATE: 1957 COST: $ 4.00 ABST: A study of the functional equation technique of dynamic programming to determine the dependence of the Green's function of the equation u· + q(x)u = f(x), u(a) = u(1) = 0 upon the parameter a. P-1086: Multi-Dimensional Maximization and Dynamic Programming. AUTH: R.E. Bellman PAGES: 17, DATE: 1957 COST: $ 4.00 ABST: A discussion of various difficulties arising in multi-dimensional maximization problems and some of the special types of problems which can be treated by dynamic programming techniques. In addition, linear programming is considered. P-1101: Terminal Control, Time-Lags, and Dynamic Programming. AUTH: R.E. Bellman PAGES: 5, DATE: 1957 COST: $ 4.00 ABST: A discussion of terminal control problems for linear processes. By a preliminary transformation, numerous problems can be treated by means of the functional equation approach of dynamic programming in terms of functions of many fewer dimensions. In particular, problems of this nature involving time-lags and other hereditary effects can now be treated by the functional equation technique. P-1113: Random Walk, Scattering, and Invariant Imbedding --I: One-Dimensional Discrete Case. AUTH: R.E. Bellman, R.E. Kalaba PAGES: 8, DATE: 1957 COST: $ 4.00 ABST: A method of treating problems involving random walk processes, based upon the principle of invariant imbedding. Since scattering processes are often formulated in terms of random walk, a new method of treating scattering processes is used. In subsequent papers the same methodology will be applied to corresponding problems for multi-dimensional regions and to continuous versions. P-1133: Dynamic Programming, Nonlinear Variational Processes, and Successive Approximations. AUTH: R.E. Bellman PAGES: 7, DATE: 1957 COST: $ 4.00 ABST: An attempt to show that dynamic programming, combined with successive approximations and digital computers, aids in solving various classes of nonlinear variational problems. The problem considered is that of determining the minimum of a functional of the form <>, over all forcing functions <> subject to certain relations. P-1147: Dynamic Programming and Mean Square Deviation. AUTH: R.E. Bellman PAGES: 12, DATE: 1957 COST: $ 4.00 ABST: An application of the functional equation technique of dynamic programming to the treatment of some quadratic variational problems and linear equations. The author attempts (1) to determine the minimum value of the quadratic deviation <>, where f(x) is a given function of <>, a given sequence of real functions; (2) to minimize the quadratic form <> over all real <> , where <> and <> are given real sequences; and (3) to discuss the problem of solving the linear system Ax = b, under the assumption that A is positive definite. P-1148: Some New Techniques in the Dynamic-Programming Solution of Variational Problems. AUTH: R.E. Bellman PAGES: 21, DATE: 1957 COST: $ 4.00 ABST: An attempt to overcome some difficulties in solving a large class of variational problems in which the underlying equations and the criterion function are linear, although the restraints on the forcing functions may be nonlinear. It is indicated how the method of successive approximations may be combined with the techniques mentioned to reduce general variational problems, in which the equations and criterion function are nonlinear, to sequences of problems which can be solved numerically by sequences of functions of one variable. P-1150: Dynamic Programming and the Variation of Green's Functions. AUTH: R.E. Bellman, H.A. Osborn PAGES: 8, DATE: 1957 COST: $ 4.00 ABST: An application of the functional equation technique of dynamic programming to the study of quadratic functionals whose Euler variational equations are linear self-adjoint partial differential equations of the second order. A first consequence is the classical Hadamard variational formula for the Green's function of a region. Some extensions are indicated. P-1155: Dynamic Programming and the Computational Solution of Feedback Design Control Problems. AUTH: R.E. Bellman PAGES: 24, DATE: 1957 COST: $ 4.00 ABST: An attempt to indicate how a certain class of control processes can be reduced to problems involving sequences of functions of one variable in a number of cases, and sequences of functions of two variables in others. The results of this paper may serve as a guide to a systematic study of nonlinear control processes, with or without time-lags and other types of hereditary behavior, by way of the method of successive approximations. P-1175: Dynamic Programming, Successive Approximations, and Variational Problems of Combinatorial Nature. AUTH: R.E. Bellman PAGES: 7, DATE: 1957 COST: $ 4.00 ABST: An attempt to show that a combination of dynamic programming and the classical method of successive approximations permits a systematic study of various classes of combinatorial problems arising in scheduling, communication, and network theory. Examples are the Hitchcock-Koopmans transportation problem, an allocation problem, and the traveling-salesman problem. P-1223: On Weighted PCM and Mean Square Deviation. AUTH: R.E. Bellman, R.E. Kalaba PAGES: 9, DATE: 1957 COST: $ 4.00 ABST: A proof that the functional equation technique of dynamic programming can be used advantageously in analyzing weighted pulse-code modulation (WPCM) communication systems. WPCM differs from normal PCM in that the amplitude of the transmitted pulses representing the binary digits in a pulse-code group is made to depend on the size of the group and on the power of two represented by the individual pulses. P-1227: Dynamic-Programming Approach to Optimal Inventory Processes with Delay in Delivery. AUTH: R.E. Bellman PAGES: 10, DATE: 1957 COST: $ 4.00 ABST: A proof that a class of inventory processes with time lags can be treated in terms of sequences of functions of one variable, regardless of the length of the delay in delivery. A type of transformation is used which was applied previously in the study of engineering control processes. The usual dynamic-programming approach to inventory processes with delays in delivery leads to functions of many variables. This multi-dimensionality prevents the straightforward use of digital computers. P-1239: Invariant Imbedding, Wave Propagation, and the WKB Approximation. AUTH: R.E. Bellman, R.E. Kalaba PAGES: 6, DATE: 1957 COST: $ 4.00 ABST: An attempt to indicate how wave propagation may be considered in terms of an over-all physical process as a sequence of local processes. The results are based on an algorithm that, in general, can yield divergent series. In addition, the paper shows that wave propagation can be discussed in terms of reflection and refraction at infinitesimally separated interfaces and that the convergence of the Bremmer series can be established under a simple assumption concerning the slowly varying nature of the local wave number. RM-1877: Optimal Employment of Tactical Air Forces in Theater Air Tasks: A Game-Theoretic Analysis. AUTH: L.D. Berkovitz, M. Dresher, M. Dresher PAGES: 23, DATE: 1957 COST: $ 4.00 KEYS: Game theory ABST: A description, in terms of a two-sided war game, of the optimal allocation of tactical aircraft among three air tasks-counter air, air defense, and support of ground operations--on each strike of a multistrike campaign. The mathematical model assumes that counter-air missions destroy enemy aircraft, air-defense missions reduce the enemy's counter-air operations, and support of ground operations contributes to the accomplishment of the theater mission, or payoff, of the tactical forces. A dscription, in terms of a two-sided war game, of the optimal allocation of tactical aircraft among three air tasks--counter air, air defense, and support of ground operations--on each strike of a multistrike campaign. 24 pp. RM-1853: Cargo Density and Airlift. AUTH: R.E. Bickner PAGES: 71, DATE: 1957 COST: $ 7.50 KEYS: Airlift; Transport airplanes ABST: A presentation of (1) the results of RAND studies concerned with variations in the density of air cargo and (2) the effects of these variations on aircraft design, aircraft capacity estimates, airlift operations, and airlift costs. It is shown that air cargo varies in density and is seldom equal to the average generally computed. A presentation of the results of previous RAND studies concerned with variations in the density of air cargo and the effects of these variations on aircraft design, aircraft capacity estimates, airlift operations, and airlift costs. The Memorandum presents methods of comparing costs of airlifting different commodities, which take into account the densities of the commodities and the characteristics of the transporting aircraft. Attention is drawn to implications of the fact that air cargo varies in density and rarely, if ever, adheres to the average values that are usually computed. 71 pp. RM-1864: Notes on Linear Programming--Part XXXVIII: Note on B. Klein's "Direct Use of Extremal Principles in Solving Certain Problems Involving Inequalities.". AUTH: G.B. Dantzig PAGES: 11, DATE: 1957 COST: $ 4.00 ABST: A discussion of B. Klein's proposal that ordinary methods of the differential calculus be used to minimize a function z of n variables xÑ, xÒ,..., x[subscript n], where the latter are subject to inequality constraints instead of the usual equality constraints. The present study considers whether this method may be constructively used for determining the optimum. No abstract available. 15 pp. P-1028: On the Status of Multistage Linear Programming Problems. AUTH: G.B. Dantzig PAGES: 34, DATE: 1957 COST: $ 4.00 ABST: A survey of the kinds of structures encountered and the methods proposed for solving multistage linear programming problems. The single and multicommodity warehouse problem is used to illustrate some basic ideas. In addition, the study discusses the possibility of solving a dynamic problem from a steady-state problem, the need for solving large-scale systems, and the methods for solving block triangular systems. No abstract available. 13 pp. P-1192: A New Approach to the Kolmogorov-Smirnov Distributions. AUTH: D.A. Darling PAGES: 28, DATE: 1957 COST: $ 4.00 KEYS: Markov processes; Statistical analysis ABST: A theory for calculating the Kolmogorov-Smirnov distributions, which is based on a combination of (1) the observation that the empirical distribution function of a sample of data is merely a scaled and normalized Poisson process and (2) certain analytical methods developed for calculating the distribution of certain additive functionals of Markov processes. The Smirnov distribution of the one-sided deviation is determined, together with the error terms in asymptotic distribution of this statistic and the von Mises w criterion. A theory for calculating the Kolmogorov-Smirnov distributions, which is based on a combination of (1) the observation that the empirical distribution function of a sample of data is merely a scaled and normalized Poisson process, and (2) certain analytical methods developed for calculating the distribution of certain additive functionals of Markov processes. (Published in [Teoriia Veroiatnostei], Vol. 5, No. 4, 1960.) 28 pp. Bibliog. P-1140: A Commentary on Fire Research. AUTH: J.C. DeHaven PAGES: 13, DATE: 1957 COST: $ 4.00 ABST: An account of the Mass Fire Study Group Conference, jointly sponsored by the National Academy of Sciences and The University of California at Los Angeles, May 26-28, 1957. Research is suggested based on the description of hostile fires presented by the practical fire fighters. In addition, the application of operations research to problems of fire fighting is discussed. P-1039: A Generalized Equipment Replacement Study. AUTH: S.E. Dreyfus PAGES: 18, DATE: 1957 COST: $ 4.00 ABST: A study of the functional equation technique of dynamic programming to determine the optimal age of replacement of durable machinery. The paper discusses Bellman's analytic solution of a simplified model, a computation scheme applicable to more realistic models, and various dynamic programming formulations applicable in the field of equipment replacement. No abstract available. 18 pp. P-1045: A Note on an Industrial Replacement Process. AUTH: S.E. Dreyfus PAGES: 8, DATE: 1957 COST: $ 4.00 KEYS: Industry ABST: An application of the functional equation technique of dynamic programming to an industrial replacement process occurring in the tire manufacturing industry. A problem posed by M. W. Sasieni, and analyzed as a Markov chain process, is reconsidered from the viewpoint of dynamic programming. 8 pp. P-1083: Dynamic Programming Solution of Allocation Problems. AUTH: S.E. Dreyfus PAGES: 13, DATE: 1957 COST: $ 4.00 ABST: A discussion of the solution of allocation problems by means of the functional equation technique of dynamic programming. Dynamic programming is applied to static problems where allocation of a resource or resources is made to a variety of independent activities at a particular time. The formulation and computational solution of a simplified model is considered and then generalized to a more complex model. Numerical results are attained for the second model by use of the Lagrange multiplier approach. RM-1905: The Moments of Two Limiting Distributions of Kolmogorov. AUTH: H.P. Edmundson PAGES: 12, DATE: 1957 COST: $ 4.00 KEYS: Statistical analysis; Statistics ABST: A derivation of a general expression for the [i]th moment of two limiting distributions due to A. Kolmogorov. The dispersions of these two distributions are compared. (See also RM-1820, RM-1958.) 10 pp. Ref. RM-1958: The Moments of Two Distribution-Free Statistics of Smirnov. AUTH: H.P. Edmundson PAGES: 11, DATE: 1957 COST: $ 4.00 KEYS: Statistical analysis; Statistics ABST: A derivation of a general expression for the [i]th moment of two distribution-free statistics due to N. Smirnov. (See also RM-1820, RM-1905.) 9 pp. Ref. RM-1993: Logistics Laboratory Problem I After Two (Simulated) Years. AUTH: S. Enke PAGES: 26, DATE: 1957 COST: $ 4.00 ABST: An examination of the first two simulated years of Laboratory Problem I of RAND's Logistics Systems Laboratory, conducted to test an experimental set of logistics policies and procedures (Logistics System 2) for operational feasibility and to compare the performance of this system with another set of policies (Logistics System 1) based on recent and current Air Force practice. The two logistic systems in the laboratory have "flown" the same number of flying hours. Results to date show that LS-2 has fewer AOCP's, about the same AOCM's, and more ANFE's than LS-1, and that LS-2 is considerably less costly than LS-1. No abstract available. 29 pp. RM-1977: Notes on Linear Programming--Part XL: Network Flow and Systems of Representatives. AUTH: L.R. Ford, D.R. Fulkerson, L.R. Ford, D.R. Fulkerson PAGES: 19, DATE: 1957 COST: $ 4.00 ABST: Part of a broader investigation concerned with the maximal logistic flow in a railroad network and in the military interdiction of that flow. The present study extends a theorem of Hall, which gives necessary and sufficient conditions for the existence of a system of distinct representatives. The network-flow theory is then applied to generate necessary and sufficient conditions for (1) the existence of a system of restricted representatives and (2) the existence of a common system of restricted representatives for two different collections of subsets of the fundamental set. No abstract available. 19 pp. RM-1981: Notes on Linear Programming--Part XLI: Constructing Maximal Dynamic Flows from Static Flows. AUTH: L.R. Ford, D.R. Fulkerson, L.R. Ford, D.R. Fulkerson PAGES: 36, DATE: 1957 COST: $ 4.00 ABST: An outline of a method for constructing maximal dynamic flow from static flow and a presentation of a simple proof of maximality. It is assumed that for a given network of nodes and arcs (e.g., a railway system) each arc has associated with it two positive integers. These integers consist of a commodity-flow capacity and a commodity-traversal time. No abstract available. 39 pp. P-1079: Construction of Maximal Dynamic Flows in Networks. AUTH: L.R. Ford, D.R. Fulkerson, L.R. Ford, D.R. Fulkerson PAGES: 12, DATE: 1957 COST: $ 4.00 ABST: A description of an algorithm for solving the problem of finding a maximal dynamic flow through a network. A network is considered in which each link has associated with it two positive integers. It is assumed that some node of the network is a source for the commodity, another a sink, and the remaining may either transship the commodity immediately on receipt or hold for later shipment. P-1231: A Linear Programming Model of the Gaseous-Diffusion Isotope-Separation Process. AUTH: D.M. Fort PAGES: 24, DATE: 1957 COST: $ 4.00 ABST: An attempt to show how the gaseous-diffusion process for separating uranium isotopes may be treated as a linear-programming model. The model is developed by the theoretical or engineering approach, as opposed to empirical methods based on statistical analysis of observations. The model may be useful in the economic analysis of complicated systems involving various feedbacks between gaseous diffusion plant, nuclear reactors, and other facilities involved in the production of nuclear materials and nuclear power. P-1063: A Tactical Air Game. AUTH: D.R. Fulkerson, S.M. Johnson, S.M. Johnson PAGES: 20, DATE: 1957 COST: $ 4.00 KEYS: Aerial combat--Tactics; Combat models; Games ABST: A formulation of a discrete, linear model of a tactical air war as a multimove game. The symmetric case in which the attrition rates are the same for both sides is solved for both finite and infinite campaigns. A formulation of a discrete, linear model of a tactical air war as a multimove game. The symmetric case in which the attrition rates are the same for both sides is solved for both finite and infinite campaigns. 20 pp. P-1010: Continuous Production and Emergent Demand. AUTH: T.A. Goldman PAGES: 12, DATE: 1957 COST: $ 4.00 ABST: An examination of a model of the real and monetary costs involved in supplying spare parts from current production. The model leads to a cost function for each part individually depending on its production characteristics, its demand-probability function, and certain policy variables. By choosing appropriate values for the policy variables, the cost function for each part can be minimized independently of the others. No abstract available. 12 pp. P-1193: A Concept of Stability in Manpower Planning. AUTH: W. Gorham, H.E. Scarf, H.E. Scarf PAGES: 21, DATE: 1957 COST: $ 4.00 ABST: An attempt to predict future skill composition by devising a method for computing stable skill distributions for an extremely simple model. The solutions of this model are then compared with the solutions of somewhat more realistic ones. A subsequent paper will describe how the technique considered should be combined with information concerning effectiveness in such a way as to offer insight into good retention goals. P-1020: The Random Functions of Cosmic-Ray Cascades. AUTH: T.E. Harris PAGES: 4, DATE: 1957 COST: $ 4.00 ABST: A presentation of some theorems concerned with the stochastic processes arising in the theory of the soft component of cosmic radiation, as formulated by Bhabha and Heitler and by Carlson and Oppenheimer. Limit theorems are given, and the relation to a certain Markov process is indicated. No abstract available. 4 pp. P-1053: The Prospects of a Unified Theory of Organizations. AUTH: O. Helmer-Hirschberg, O. Helmer PAGES: 11, DATE: 1957 COST: $ 4.00 KEYS: Organization--Theory ABST: A suggestion that a unified theory of organizations be achieved by establishing the relationship in terminology between game theory and organization theory and by using an engineering approach to the psychological problems involved. A suggestion that a unified theory of organizations be achieved by establishing the relationship in terminology between game theory and organization theory and by using an engineering approach to the psychological problems involved. 11 pp. RM-1926-RC: NATO Deterrent Vs. Shield. AUTH: M.W. Hoag PAGES: 32, DATE: 1957 COST: $ 4.00 KEYS: Deterrence (Strategy); North Atlantic Treaty Organization; Strategic KEYS: warfare; Tactical warfare ABST: A discussion of the argument within NATO for supplementing strategic air forces with strong tactical forces for total war. The disadvantages are that tactical forces do not contribute greatly toward deterring or fighting total war, their cost imposes military sacrifices elsewhere, better air defenses may be more effective, and our European allies may have little incentive to supply tactical forces. However, in the case of a sharply limited war in Europe, tactical forces have renewed utility, with strategic air forces complementing tactical forces as the necessary enforcer of weapon limitations. 32 pp. P-1035: What Is a System?. AUTH: M.W. Hoag PAGES: 6, DATE: 1957 COST: $ 4.00 ABST: An attempt to define a "system" as a set of interrelated actions about which policy decisions are made. The difference between the administrator and analyst's-approach in defining a system is discussed, and several examples are given to illustrate this variance. 6 pp. P-1166: Game Theory. AUTH: H. Kahn, I. Mann, I. Mann PAGES: 65, DATE: 1957 COST: $ 7.50 KEYS: Game theory ABST: A section of a proposed book on military planning in an uncertain world. The present paper discusses game theory, defined as the study of any conflict situation. In particular, conflict situations are investigated where there are two or more participants who do not have identical objectives. Two-person, nonzero-sum games and [n]-person games are examined, together with other theorems and examples. 65 pp. P-1167: War Gaming. AUTH: H. Kahn, I. Mann, I. Mann PAGES: 14, DATE: 1957 COST: $ 4.00 KEYS: Games; Operations research; United states--Military planning; War KEYS: games ABST: A draft chapter of a proposed book on military planning in an uncertain world. The levels of war gaming discussed are (1) the informal game, an attempt to determine the enemy's reactions; (2) rule games, designed to abstract from the real world a fairly definite set of rules which all players must observe; (3) the formal minimum rule game which investigates the sensible rules of play; and (4) realistic war games where maneuvers and training exercises are tested in a realistic environment or in realistic contexts. 14 pp. P-1163: On Nonlinear Differential Equations, the Maximum Operation, and Monotone Convergence. AUTH: R.E. Kalaba PAGES: 98, DATE: 1957 COST: $ 7.50 ABST: A proof that the solutions to certain classes of nonlinear ordinary and partial differential equations may be represented in terms of the maximum operation applied to the solutions of associated linear equations. This, in effect, affords a new approach to the quasi-linearization of nonlinear differential equations. The representation readily yields uniform lower bounds for solutions, and, in the case of stochastic nonlinear differential equations, leads to representations for the distribution functions of the solutions. In addition, a technique is provided for constructing monotone sequences of functions which converge quadratically to the solution of the nonlinear equation, which is of value in machine computation. P-1232: A Note on Preventative Sampling. AUTH: R.E. Kalaba PAGES: 6, DATE: 1957 COST: $ 4.00 KEYS: Optimization; Programming (mathematics); Statistical analysis ABST: A proof that certain optimization problems of preventative sampling may be handled advantageously using the functional equation technique of dynamic programming. (Published in [Operations Research], May-June 1958.) 6 pp. Ref. RM-1890: A Briefing on a Method of Estimating Spare Part Essentiality. AUTH: H.W. Karr, H.W. Carr PAGES: 42, DATE: 1957 COST: $ 4.00 ABST: A presentation of a set of essentiality categories with examples which seem applicable to all tactical fighter-bombers. The author discusses (1) the ways in which essentiality factors can be used, (2) various elements to be considered in estimating essentiality factors, (3) an experiment with psychometric scaling techniques, and (4) a rationale for assigning essentiality or shortage penalty factors to particular categories of items. No abstract available. 44 pp. P-1107: The Graphical Integration of the One-Parameter Model with Terrain Effects. AUTH: J.B. Knox PAGES: 35, DATE: 1957 COST: $ 4.00 KEYS: Atmosphere; Meteorology ABST: A development of the theory of the oneparameter model of the atmosphere so that the dynamic equation at the p*-level (that of nondivergence over flat terrain) includes the effects of terrain and may be readily integrated by graphical procedures. The model makes possible the quantitative forecasting of the movement of trough systems pertaining to the North American mountain barrier. 35 pp. P-1108: A Physical Basis for Forecasting the Pressure and Horizontal Wind Fields in the Lower Stratosphere. AUTH: J.B. Knox PAGES: 14, DATE: 1957 COST: $ 4.00 KEYS: Atmosphere; Meteorology ABST: A re-examination of the theory of the one-parameter model of the atmosphere. It is shown that a second level of nondivergence exists in regions of 100 mb to 50 mb. In addition, the possibility of using the one-parameter model to forecast the horizontal wind field is discussed. 14 pp. RM-1924: First Tooling-Up Exercise for Logistics Systems Laboratory (October-November, 1956). AUTH: LogisticsDepartment PAGES: 45, DATE: 1957 COST: $ 4.00 KEYS: Airframes; Logistics; Spares ABST: A description of PROLOG I, an exercise designed to evaluate better procurement and distribution methods for airframe spare parts. The experiment attempted to determine whether its results, if applied to a reasonably complex simulation of the logistics system, were better than the methods used by the Air Force. PROLOG I is of historical interest in recording the beginnings of RAND's Logistics Systems Laboratory. (See also RM-1961.) 45 pp. RM-1961: Second Tooling-Up Exercise of Logistics Systems Laboratory (January-February, 1957). AUTH: LogisticsDepartment PAGES: 112, DATE: 1957 COST: $ 10.00 ABST: A supplement to RM-1924, First Tooling-up Exercise of Logistics Systems Laboratory (October-November, 1956). The present study attempts to determine whether a revised logistics system, incorporating changes proposed by RAND and by the Air Force which relate to provisioning, distribution, and data processing of airframe parts, will give equal or greater support at lower cost. The simulation techniques used in this second exercise (PROLOG II) will have a role in the first Laboratory Problem (LP-I), including the setting up of the two logistics systems on the laboratory floor, the use of time compression, and the calculation of system costs. No abstract available. 112 pp. P-1201: Sequential Decision Problems with a Limited Memory. AUTH: M.B. Marcus PAGES: 14, DATE: 1957 COST: $ 4.00 ABST: A study based on the idea of sequential decision problems with a limited memory, taken from Herbert Robbins' paper, A Sequential Decision Problem with a Finite Memory. In these problems a random identically distributed sequence of Bernoulli trials occurs with a fixed probability p; p is unknown. An experimenter tries to predict, prior to the happening of each event, what the event will be. To aid his prediction the experimenter knows the outcome of the preceding r events and the guesses he made concerning them. He attempts to optimize the proportion of times he guesses correctly over an infinite number of guesses. P-1228: The Utility of a Communication Channel and Applications to Suboptimal Information-Handling Procedures. AUTH: M.B. Marcus PAGES: 15, DATE: 1957 COST: $ 4.00 ABST: A study of the functional-equation technique of dynamic programming to analyze (1) some extensions of the Kelly-Bellman-Kalaba model of communication and (2) a null-zone reception system. The role of suboptimum systems is emphasized. P-1180-RC: Criteria of Efficiency in Government Expenditures. AUTH: R.N. McKean PAGES: 12, DATE: 1957 COST: $ 4.00 KEYS: Accounting and budgets; Government ABST: A discussion of the criteria problems involved in choosing efficient government programs. The inevitability of breaking problems into administratively manageable subproblems and the consequent danger of applying inconsistent criteria are explained. Common criteria errors and how they can be guarded against are discussed. A discussion of the criteria problems involved in choosing efficient government programs. The inevitability of breaking problems into administratively manageable subproblems and the consequent danger of applying inconsistent criteria are explained. Common criteria errors and how they can be guarded against are discussed. 12 pp. P-1182: Concepts of Cost for Use in Studies of Effectiveness. AUTH: D. Novick PAGES: 14, DATE: 1957 COST: $ 4.00 KEYS: Cost analysis; Weapon systems--Procurement ABST: A paper primarily concerned with weapon system cost. The author discusses the fixed-budget case, the fixed-effectiveness case, the role that cost and weapons systems effectiveness plays in the total weapon systems analysis picture, the importance of cost as a measure of effectiveness, and the accuracy in cost measurements. (Presented before the Operations Research Society of America at San Francisco, California, September 27, 1957.) 14 pp. P-1197: Federal Spending for National Security. AUTH: D. Novick PAGES: 16, DATE: 1957 COST: $ 4.00 KEYS: Accounting and budgets; Government ABST: A 1957 discussion of seven factors expected to influence current and future trends in federal spending for national security purposes: (1) external political, military, or economic pressures; (2) the possibility of a mutual inspection system leading toward weapons control; (3) possible decisions to use international forces in place of national ones; (4) changing technology that results in more effective weapons; (5) domestic demands for economy in government; (6) an inflation or deflation in the price level within the United States; and (7) the continuing impact of budget and procurement decisions made in earlier years. 16 pp. RM-2021: Notes on Linear Programming--Part XLII: Linear Programming and Structural Design. AUTH: W. Prager PAGES: 51, DATE: 1957 COST: $ 7.50 ABST: A discussion of (1) "limit analysis," which provides the structural engineer with an estimate of the load-carrying capacities of structures made of ductile materials, and (2) "limit design," which guides the structural engineer toward an economic design of structures made of ductile materials and carrying specified loads. From the mathematical viewpoint, these problems can be reduced to problems in linear programming. Methods for their solution are presented, together with a sketch of the historical development of limit analysis and design. No abstract available. 54 pp. P-1122: Linear Programming and Structural Design--I: Limit Analysis. AUTH: W. Prager PAGES: 17, DATE: 1957 COST: $ 4.00 ABST: A discussion of limit analysis, which provides the structural engineer with a realistic estimate of the load-carrying capacities of structures made of ductile materials. The problem of limit analysis is one of linear programming, and a method of solution (essentially the simplex method with prices) is determined. P-1123: Linear Programming and Structural Design--II: Limit Design. AUTH: W. Prager PAGES: 27, DATE: 1957 COST: $ 4.00 ABST: A discussion of limit design, which guides the structural engineer toward an economic design of structures that are made of ductile materials and have to carry specified loads. The problem can be reduced to one in linear programming, and a method of solution is discussed that has been found efficient for structures of moderate complexity. In addition, a sketch of the historical development of limit analysis and design is given. P-1019: Dispersion in the Upper Atmosphere. AUTH: R.R. Rapp, J.G. Edinger, J.D. Edinger PAGES: 18, DATE: 1957 COST: $ 4.00 KEYS: Atmosphere; Meteorology ABST: An analysis of transosonde balloon data to estimate the dispersion on a large scale in the upper atmosphere. An expression for the autocorrelation function is inferred from synoptic experience and is applied to autocorrelation values computed from the balloon data. Taylor's theorem is applied to this function to compute dispersion out to ten days. A comparison is made with direct computation at two days. 18 pp. RM-1917-1: The Game Monopologs. AUTH: J.R. Renshaw, A. Heuston, A. Heuston PAGES: 37, DATE: 1957 COST: $ 4.00 KEYS: Games; Logistics ABST: A discussion of the inventory management game, Monopologs, which simulates a part of the Air Force supply system. The study describes the game's evolution and philosophy, its rules, a sample run using the demand pattern generated for the original version of the game, and two methods by which the player can generate his own demand pattern as the game proceeds. 40 pp. RM-1830: Air Force Provisioning Policies: An Anaylsis. AUTH: W.A. Steger PAGES: 40, DATE: 1957 COST: $ 4.00 ABST: A review of present Air Force policies for initial provisioning of spare parts. The present system is described, together with the reasons leading to its development. It is shown that (1) spares delivered during the first few years of a weapon considerably exceed expected demands, (2) expected demand is generally overestimated as a precaution, and (3) under current policy and uncertainty a large percentage of initial provisioning purchases represent life-of-type procurement, which is more costly than necessary for adequate protection against stock-outs of spare parts. No abstract available. 41 pp. P-1219: The Use of Gaming and Simulation Devices in Business. AUTH: W.A. Steger PAGES: 6, DATE: 1957 COST: $ 4.00 ABST: A discourse on the use of gaming and simulation devices used in business to bring humans and machines together so that decision-making processes can be analyzed. Paper war games, RAND's Logistics Systems Laboratory, and top-management-decision gaming are given as examples. It is concluded that although the application of these devices to primarily economic situations is only in an embryonic stage, the results to date appear very promising. P-1185: A Method of Computing the Inherent Accuracy with Which a Time Delay Can Be Estimated. AUTH: P. Swerling PAGES: 21, DATE: 1957 COST: $ 4.00 ABST: An approach to the problem of calculating the limits of accuracy with which a time delay between transmission and reception of a waveform can be estimated. After a summary of requisite results from the theory of statistical estimation, certain functions are evaluated which are necessary for applying estimation theory to the case of time-delay estimation; the advantages of this method are discussed. No abstract available. 21 pp. P-1206: Optimum Linear Estimation for Random Processes as the Limit of Estimates Based on Sampled Data. AUTH: P. Swerling PAGES: 24, DATE: 1957 COST: $ 4.00 ABST: An analysis of a generalized form of the problem of optimum linear filtering and prediction for random processes. It is shown that, under very general conditions, the optimum linear estimation based on the received signal, observed continuously for a finite interval <>, is the limit of optimum linear estimation in cases where the conventional generalized Wiener-Hopf integral equation technique has not been shown to yield a solution. P-1160: Statistical Decision Theory as a Guide to Information Processing. AUTH: H.M. Wagner PAGES: 28, DATE: 1957 COST: $ 4.00 KEYS: Data processing; Decision-making; Statistics ABST: A suggestion that the statistical-decision-theory approach be applied to data processing problems concerned with decisionmaking in the face of uncertainty. The decision-theory technique automatically weighs the different economic considerations involved in taking action and gathering data. In addition, several drawbacks to this approach are considered. (Published in [The Journal of Industrial Engineering], January-February 1959.) 28 pp. P-1059: Chemical Equilibrium in Complex Mixtures. AUTH: W.B. White, S.M. Johnson, G.B. Dantzig, S.M. Johnson, G.B. Dantzig PAGES: 15, DATE: 1957 COST: $ 4.00 ABST: A method for determining the equilibrium composition of complex mixtures. Based on the minimization of free energy, this method states the problem with simplicity. Specific computation procedures shown are one using a steepest descent technique applied to a quadratic fit, and the other using linear programming. R-322-RC: Report on a Study of Non-Military Defense. AUTH: TheRandCorporation PAGES: 53, DATE: 1958 COST: $ 7.50 KEYS: Civil defense; Defense; Deterrence (Strategy); Fallout ABST: A report on non-military defense which considers such problems as population shelters, long-term fallout, economic recuperation, possible non-military defense programs, and interactions with other aspects of national defense. The study was initiated in the belief that non-military defense measures, if they could be made effective in protecting the civilian population, economy, and institutions of the United States, might make two significant contributions to the national defense. First, they might alleviate the catastrophe of a nuclear attack and, if military victory were attained, provide a reasonable chance that the United States as a nation could survive. Second, they might increase U.S. freedom of action in conducting peacetime foreign policy and in implementing a broad deterrence strategy. A report on nonmilitary defense that considers such problems as population shelters, long-term fallout, economic recuperation, possible nonmilitary defense programs, and interactions with other aspects of national defense. The study was initiated in the belief that nonmilitary defense measures, if they could be made effective in protecting the civilian population, economy, and institutions of the United States, might make two significant contributions to the national defense. First, they might alleviate the catastrophe of a nuclear attack and, if military victory were attained, they might provide a reasonable chance that the United States as a nation could survive. Second, they might increase U.S. freedom of action in conducting peacetime foreign policy and in implementing a broad deterrence strategy. 53 pp. RM-2086-PR: BASELOGS: A Base Logistics Management Game. AUTH: L. Gainen, R.A. Levine, W.H. McGlothlin PAGES: 22, DATE: 1958 COST: $ 4.00 KEYS: Computer simulation; Games; Logistics ABST: A description of Baselogs, a game which demonstrates the interactions between logistics and operations on a fighter-interceptor airbase of the ADC type. The player assumes the composite role of director of finance at USAF and command level, as well as director of base-level operations, supply, and maintenance at a simulated ADC-type base. The game may be used as a demonstration tool and, in addition, may be valuable in further research on maintenance-operations interactions. 22 pp. RM-2137-PR: Optimal Employment of Tactical Air Forces in Theater Air Tasks: II, A Game-Theoretic Analysis. AUTH: L.D. Berkovitz, M. Dresher PAGES: 19, DATE: 1958 COST: $ 4.00 KEYS: Combat models; Games ABST: A problem concerned with allocating aircraft among three different air tasks--counterair, air defense, and support of ground operations--in a multistrike campaign as a two-sided war game. Previous studies assumed that in any strike of the campaign each plane allocated to air defense prevents one attacking plane from fulfilling its counterair mission. This Memorandum removes this assumption and derives the optimal strategies as a function of the air defense kill potential. P-929: A Failure Model for Equipments Undergoing Complex Operation. AUTH: D.S. Stoller PAGES: 8, DATE: 1958 COST: $ 4.00 ABST: No abstract available. 8 pp. P-1250: Economics and Military Operations Research. AUTH: C.J. Hitch PAGES: 25, DATE: 1958 COST: $ 4.00 KEYS: Decision-making; Economics--Domestic; Operations research ABST: An examination of some of the relations between operations research and economics. Operations research is defined as the use of systematic quantitative analysis to aid in the making of military and management decisions. Economics is described as a logic of choice rather than as a study of "those things that can be brought into relation with the measuring rod of money." The author suggests that an alliance between economics and military or governmental operations research may result in a new branch of endeavor, namely, an economics of government expenditure. 25 pp. P-1298: Economic Prospects for Communist China. AUTH: R.H. Moorsteen PAGES: 58, DATE: 1958 COST: $ 7.50 KEYS: China; Economics--Foreign; Soviet Union--Economics ABST: A 1958 comparison of the accomplishments of the Soviet Union and the People's Republic of China (PRC) in developing heavy industry during the period of each country's First Five Year Plan. The record shows that the Chinese were performing as well as, or perhaps better than, the Russians at a comparable developmental stage. Chinese prospects for fulfilling the goals of the Second Five Year Plan in heavy industry--and for continuing its growth beyond the period of the Second Plan--depended on the ability of the PRC to direct a large share of the nation's output to industrial investment. 58 pp. P-1314: The Foundations and Advances in Game Theory. AUTH: H.M. Wagner PAGES: 33, DATE: 1958 COST: $ 4.00 KEYS: Game theory ABST: A commentary on R. Duncan Luce and Howard Raiffa, [Games and Decisions:] [Introduction and Critical Survey], in relation to the foundations and advances in game theory. Besides recommending this book to economists interested in behavioral models of conflicts, this paper discusses such topics as the game-theory model, utility axioms for stochastic events, utility and money, two-person games, [n]-person games, decision theory, and the future of game theory. 33 pp. P-1396: Some Statistical Methods of Potential Value in Radio Wave Propagation Investigations. AUTH: W.C. Hoffman PAGES: 36, DATE: 1958 COST: $ 4.00 ABST: A description of certain statistical theories and techniques which possess considerable potential value for radio propagation research. These include the Kolmogorov-Smirnov statistics for testing goodness-of-fit, the statistical theory of extreme values, and the compound Poisson distribution and certain related stochastic processes. P-1447: Dynamics of the Moscow-Peking Axis. AUTH: A.S. Whiting PAGES: 29, DATE: 1958 COST: $ 4.00 KEYS: China; Soviet Union--Foreign relations ABST: An examination of the developments in the alliance between the Soviet Union and Communist China. The paper discusses (1) the dependence of Peking upon Moscow during the Stalin period; (2) the increased leverage during the post-Stalin era when Peking intervened in Bloc affairs in 1956; and (3) the abandonment of this formula in November 1957, with a shift by Mao Tse-tung to a harsher line both on Bloc affairs and toward the noncommunist world. The change in Peking policy from 1956 to 1957 may have resulted from a reappraisal of Soviet strength, consequent from ICBM and artificial satellite developments in the latter half of 1957. 29 pp. P-1521: Reliability Estimating by the Use of Random Sampling Simulation. AUTH: S.I. Firstman PAGES: 29, DATE: 1958 COST: $ 4.00 ABST: The application of random sampling simulation to the problem of predicting system performance based upon component and "black-box" performance data. The validity of results and the unbiased nature of derived estimates are argued heuristically, and the requirements for input data are explained by the use of hypothetical examples. P-1578: An Economic Development of Strategic Significance in Communist China. AUTH: R.H. Moorsteen PAGES: 5, DATE: 1958 COST: $ 4.00 KEYS: China ABST: A discussion of the military implications of the Chinese Communist program, initiated toward the end of 1957, of building very small industrial enterprises to be located in towns, rural villages, or on collective farms. The small plant campaign could result in an unusual decentralization of future economic development and in the Chinese economy's becoming extraordinarily resilient under enemy attack, if it fulfills even a part of Chinese expectations. Furthermore, the new patterns of development, relying primarily on relatively unskilled labor, local building materials, and widely distributed natural resources, are well adapted to the work of economic recuperation in a post-attack period. 5 pp. RM-1788/PR: A Study of a Proposed Southern Early Warning Perimeter. AUTH: L.L. Giller PAGES: 141, DATE: 1958 COST: $ 10.00 ABST: A discussion of part of the problem of providing adequate warning of a surprise attack by enemy bombers on that portion of SAC based in the United States. The planned radar system is examined, and it is found that the radar coverage protecting southern SAC bases is inadequate. A program of additions to this portion of the warning perimeter is described, and estimates are provided of the cost and effectiveness of the suggested additions. P-1449: Costs and Outputs. AUTH: A.A. Alchian PAGES: 28, DATE: 1958 COST: $ 4.00 KEYS: Cost analysis; Production ABST: Propositions designed to eliminate some of the ambiguities and errors involved in the relationships between cost and output both in the long and short run. The suggested propositions are shown to be empirically valid in distinguishing between rate and quantity of output, the changes in technology as distinct from changes in technique, the use of calendar-time dates of output instead of technical fixity for distinguishing output operations, and the use of capital-value concepts instead of rates of costs. (Published in Baran, Scitovsky, and Shaw (eds.), [The] [Allocation of Resources], Stanford University Press, 1959.) (See also P-2448.) 28 pp. RM-1751: On the Computational Solution of Dynamic-Programming Processes--VII: Radar Nets. AUTH: R.E. Bellman, S.E. Dreyfus PAGES: 16, DATE: 1958 COST: $ 4.00 ABST: A problem concerned with constructing a radar warning line surrounding a set of air bases, such that the length of the perimeter of the configuration is minimum for a given protection level. No abstract available. 16 pp. RM-2189: Some Applications of Dynamic Programming to Communication and Information Theory. AUTH: R.E. Bellman, R.E. Kalaba PAGES: 42, DATE: 1958 COST: $ 4.00 ABST: A study which shows that the fundamental problem of determining the usefulness of a noisy communication channel in conveying information can be interpreted as a problem within the framework of multistage decision processes of stochastic type. As such, the problem may be treated by means of the functional-equation technique of dynamic programming. Part I of this research memorandum formulates several aspects of the general problem in terms of stochastic multistage decision processes. Part II examines communication processes involving the use of channels, the statistical properties of which are not completely known. 42 pp. RM-2245: On the Computational Solution of Dynamic-Programming Processes-XVI: Reliability of Multicomponent Devices. AUTH: R.E. Bellman, S.E. Dreyfus PAGES: 19, DATE: 1958 COST: $ 4.00 ABST: A proof that the functional-equation technique of dynamic programming may be used to treat a class of problems that arise in the construction of multicomponent devices. An attempt is made to determine the types of components and the quantities that should be used for constructing the most reliable device possible subject to given cost and weight constraints. A numerical example is given. 19 pp. RM-2288: Invariant Imbedding and Wave Propagation in Stochastic Media. AUTH: R.E. Bellman, R.E. Kalaba PAGES: 28, DATE: 1958 COST: $ 4.00 ABST: An application of the theory of invariant imbedding to problems of propagation in stochastic media. The particular example is discussed in which a plane wave is incident on a stratified slab which is characterized by stochastic wave numbers in each stratum. The distribution functions for the amplitude of the random reflected and transmitted waves can then be determined by Monte Carlo, or analytically under very special assumptions. The study illustrates the applicability of functional equations and principles of invariance to the study of various types of wave propagation; indicates the importance of functional equations in stochastic variables prior to the appearance of any expected values; and emphasizes that to determine the nonlinear aspects of the recurrence relations, the actual probability distribution of the random variables appearing must be examined. P-1194: On Communication Processes Involving Learning and Random Duration. AUTH: R.E. Bellman, R.E. Kalaba PAGES: 18, DATE: 1958 COST: $ 4.00 ABST: An application of the functional-equation technique to communications problems arising from incomplete information. Using techniques of dynamic programming, a communication-system model is described, and some effects of incomplete information are discussed. This paper is a first step toward a more general theory. 18 pp. P-1252: Invariant Imbedding and Neutron Transport Theory--II: Functional Equations. AUTH: R.E. Bellman, R.E. Kalaba, G.M. Wing PAGES: 30, DATE: 1958 COST: $ 4.00 ABST: A discussion of some one-dimensional fission processes with particular attention to questions of critical length and energy dependence of the products of fission. Various interconnections between the functions used in the invariant-imbedding approach and the classical approach are indicated. In addition, it is shown how one may pass from the consideration of certain linear two-point boundary-value problems to nonlinear (Riccation type) initial-value problems. The former are useful for theoretical considerations, the latter for numerical computations. 30 pp. P-1284: Combinatorial Processes and Dynamic Programming. AUTH: R.E. Bellman PAGES: 65, DATE: 1958 COST: $ 7.50 ABST: A discussion of the application of dynamic-programming techniques to a class of combinatorial problems. The essential difficulty of these problems appears in their apparent lack of complexity, as it is usually either a question of performing a finite set of arithmetic operations or of determining the largest of a finite set of numbers. Although no specific numerical results are presented, references to extensive computational studies of S. E. Dreyfus and the author are given. 65 pp. P-1331: Functional Equations in the Theory of Dynamic Programming--IX: Variational Analysis, Analytic Continuation, and Imbedding of Operators. AUTH: R.E. Bellman, S.R. Lehman PAGES: 5, DATE: 1958 COST: $ 4.00 ABST: An attempt to show how variational techniques can be applied to deduce properties (similar to those deduced from Green's function of various functional equations and properties of the resolvent operator) for complex and nonsymmetric operators. The study uses (1) a min-max variation and analytic continuation, if necessary, for complex operators and (2) an imbedding technique and analytic continuation, if required, for nonsymmetric operators. A nonsymmetric operator is imbedded within a family of symmetric operators associated with a variational problem. Once the variational problem is formulated, the functional-equation techniques of dynamic-programming theory are applied. 5 pp. P-1332: Functional Equations in the Theory of Dynamic Programming--X: Resolvents, Characteristic Functions, and Values. AUTH: R.E. Bellman, S.R. Lehman PAGES: 28, DATE: 1958 COST: $ 4.00 ABST: An application of the functional-equation technique of dynamic programming to the variational problem yielding the equation <>. With the introduction of the parameter <>, the resolvent operator is studied and the variational relations derived for the characteristic values and functions of the associated Sturm-Liouville equation. 28 pp. P-1333: Approximation in Policy Space, Linear, and Nonlinear Programming. AUTH: R.E. Bellman PAGES: 7, DATE: 1958 COST: $ 4.00 ABST: Part of a broader investigation concerned with the applicability of the technique of successive approximations to a variety of nonlinear and multidimensional problems arising in the theory of dynamic programming. The present paper indicates how the method of dynamic-programming theory, in the guise of approximation in policy space, can be used to yield monotone approximation for linear, quadratic, and nonlinear programming. 7 pp. P-1471: Invariant Imbedding and Wave Propagation in Stochastic Media. AUTH: R.E. Bellman, R.E. Kalaba PAGES: 24, DATE: 1958 COST: $ 4.00 ABST: An extension of previous results and techniques of the principle of invariant imbedding to include cases involving plane wave propagation in stochastic media. The approach considers the derivation of stochastic functional equations for reflection and transmission coefficients and the obtaining of expected values of appropriate functions of the random state variables. The particular example is discussed where a plane wave is incident on a stratified slab which is characterized by stochastic wave numbers in each stratum. P-1494: Functional Equations and Maximum Range. AUTH: R.E. Bellman PAGES: 7, DATE: 1958 COST: $ 4.00 ABST: An attempt to show how functional equations are used to determine (for various kinds of trajectories) the range, the maximum elevation, and similar quantities as functions of initial position and velocities. Previous studies have treated questions of this type by means of dynamic-programming theory. P-1529: Functional Equations, Wave Propagation, and Invariant Imbedding. AUTH: R.E. Bellman, R.E. Kalaba PAGES: 44, DATE: 1958 COST: $ 4.00 ABST: A proof that wave propagation in inhomogeneous media may be studied through the use of invariance principles similar to those used in radiative transfer and neutron transport theory. A wave- localization principle is proved. The analytical techniques derived furnish a new approach to some significant problems in mathematical physics, while the physical concepts provide new insight into the analytic structure of the solutions of the one-dimensional wave equation. P-1551: On an Application of Dynamic Programming to the Synthesis of Logical Systems. AUTH: R.E. Bellman, J.H. Holland, R.E. Kalaba PAGES: 16, DATE: 1958 COST: $ 4.00 ABST: An application of dynamic programming to problems arising in the synthesis of logical systems. In a number of fields a system in one state must be optimally converted into another state (e.g., in mathematical economics, in the theory of control processes, in network theory, and in trajectory processes). The present study considers a type of question occurring in the design of computers and switching circuits. The problem is treated in general terms, and a special example is given to illustrate the methods. P-1151: A Multimove Infinite Game with Linear Payoff. AUTH: L.D. Berkovitz, M. Dresher, M. Dresher PAGES: 52, DATE: 1958 COST: $ 7.50 KEYS: Game theory ABST: An analysis of a multimove infinite game with linear-payoff function. The game is symmetric in every respect except for the initial conditions of the two players, which are different. On each move, each player allocates his resources to tasks of attacking, defending, and scoring. His resources for the next move are diminished by the amount that his opponent's attack exceeds his own defense, while his score cumulates from move to move. The game value and the optimal strategies for the players are derived. It is shown that one player has a pure optimal strategy and that the other player must randomize. An analysis of a multimove infinite game with linear-payoff function. The game is symmetric in every respect except for the initial conditions of the two players, which are different. On each move, each player allocates his resources to tasks of attacking, defending, and scoring. His resources for the next move are diminished by the amount that his opponent's attack exceeds his own defense, while his score cumulates from move to move. The game value and the optimal strategies for the players are derived. It is shown that one player has a pure optimal strategy and that the other player must randomize. 52 pp. P-1533: A Multimove Allocation Game. AUTH: L.D. Berkovitz, M. Dresher, M. Dresher PAGES: 32, DATE: 1958 COST: $ 4.00 KEYS: Game theory; Games ABST: An analysis, as a multimove two-person game, of the problem of allocating two types of resources (bombers and fighters) among three independent tasks (attack, defend, and score). Optimal tactics are derived: (1) during the last moves of the game both players allocate all their resources, regardless of the size of their resources; and (2) during the early moves of the game, both players may need to randomize, or only one player may need to randomize, depending on the size of their resources. An analysis, as a multimove two-person game, of the problem of allocating two types of resources (bombers and fighters) among three independent tasks (attack, defend, and score). Optimal tactics are derived: (1) during the last moves of the game both players allocate all their resources, regardless of the size of their resources; and (2) during the early moves of the game, both players may need to randomize, or only one player may need to randomize, depending on the size of their resources. 32 pp. RM-2218: The Anatomy of Deterrence. AUTH: B. Brodie PAGES: 35, DATE: 1958 COST: $ 4.00 KEYS: Deterrence (Strategy); Military strategy; Nuclear warfare ABST: Another in a series of studies concerned with the general theory of air strategy in a nuclear age. The present study deals with some of the peculiar and historically novel requirements of a deterrence posture. The argument presented is that modern deterrence is like traditional deterrence in some respects, but differs in that today deterrence of total war is considered a policy that must go permanently unchallenged. A deterrence strategy diverges significantly from a strategy which emphasizes ability to win if war comes. (Also published as P-1405.) 35 pp. P-1539: Supersonic Transports. AUTH: T.F. Cartaino, R.B. Johnston, T.F. Kirkwood, R.B. Johnston, T.F. Kirkwood PAGES: 37, DATE: 1958 COST: $ 4.00 KEYS: Airlift ABST: A 1958 review of past predictions concerning supersonic transports. The technical state of the art of the early transport aircraft is compared with that of aircraft which could be operational about 1970. The advanced aircraft are evaluated within the context of typical airlift missions. Th- economics and operating characteristics of advanced supersonic transports are discussed, together with the implications of extra-economic factors. One of the associated technical problems, that of possible alternative fuels, is given special attention. 37 pp. RM-2220: Implementing Logistics Policies in Laboratory Problem I (LP-I). AUTH: A. Clark, R.M. Paulson, A.J. Clark, R.M. Paulson PAGES: 95, DATE: 1958 COST: $ 7.50 ABST: A description of two provisioning and inventory management policies developed by RAND's Logistics Department and tested in Laboratory Problem I (LP-I). These policies were incorporated into an operable model system designated as Logistics System 2 (LS-2) and were pitted against an analogous model, Logistics System 1 (LS-1), representing then- current Air Force procedures. The two models were run simultaneously for a period representing 14 quarters of real-world operation. The framework of this operation consisted of the simulated supply and maintenance activity connected with phasing in and supporting an aircraft used by the Air Defense Command. No abstract available. 94 pp. RM-2297: A Dynamic, Single-Item, Multi-Echelon Inventory Model. AUTH: A. Clark, A.J. Clark PAGES: 43, DATE: 1958 COST: $ 4.00 ABST: A mathematical model constructed as a computational aid for planners attempting to establish least-cost order and supply policies within a complex and dynamic structure. The model is a dynamic, single-item, multi-echelon inventory model, which integrates stockage policies for individual activities to minimize inventory costs for the logistics system as a whole. A typical Air Force supply system is used as its frame of reference, in which many bases stock a particular item, a depot replenishes base stocks, and a factory and a repair facility resupply the depot with new and repaired items. The main decisions to be made at any given time are how much to ship to each base, how much to repair, and how much to procure from the factory. The dynamic element in the problem is accentuated by bases phasing into and out of operation at different times and experiencing changing failure patterns while in operation. No abstract available. 43 pp. RM-2209: Notes on Linear Programming-Part XLVII: Solving Linear Programs in Integers. AUTH: G.B. Dantzig PAGES: 12, DATE: 1958 COST: $ 4.00 ABST: The development of a variant to a recent result of Gomory (Princeton). In solving linear programs in integers, Gomory showed how to add linear inequality constraints to a linear-programming problem automatically in such a way that the extreme points of the resulting convex contain only integral solutions in the neighborhood of the minimum. The present study gives an alternative method for generating additional constraints in a way easy to justify and apply. It is not known, however, whether these conditions will lead to a solution in a finite number of iterations as is true for the stronger Gomory conditions. Anyone considering their practical use should therefore weigh the ease of generation against the extra number of iterations required for convergence. No abstract available. 12 pp. P-1448: An Equivalent Linear-Programming Problem. AUTH: G.B. Dantzig, S.M. Johnson, S.M. Johnson PAGES: 8, DATE: 1958 COST: $ 4.00 ABST: The development of an equivalent formulation for a standard linear-programming problem. For the case where the number of variables is twice the number of equations m, the equivalent problem has the same size but has the inverses of the first and second m columns of the matrix of coefficients. P-1459: Solving Two-Move Games with Perfect Information. AUTH: G.B. Dantzig PAGES: 7, DATE: 1958 COST: $ 4.00 KEYS: Games; Programming (mathematics) ABST: A study of a two-move game with perfect information, such as a move and countermove situation between two firms or economies. This leads to the problem of finding a global minimum of a concave function over a convex domain and the distressing possibility of local minima at every extreme point. It is shown, however, that the global minimum can be obtained by solving a linear-programming system, with side conditions that at least one of certain pairs of variables vanish. The latter problem can be shown to be equivalent to solving a linear-programming problem with some integer-valued variables. A study of a two-move game with perfect information, such as a move and countermove situation between two firms or economies. This leads to the problem of finding a global minimum of a concave function over a convex domain with the distressing possibility of local minima at every extreme point. It is shown, however, that the global minimum can be obtained by solving a linear-programming system, with side conditions that at least one of certain pairs of variables vanish. The latter problem can be shown to be equivalent to solving a linear-programming problem with some integer-valued variables. 7 pp. P-1532: The Dual of a Transportation Problem Is Not a Transportation Problem. AUTH: G.B. Dantzig PAGES: 7, DATE: 1958 COST: $ 4.00 ABST: A proof that the dual of the classical transportation problem-after elimination of the variables unrestricted in sign-cannot by row operations be reduced to transportation format, nor can it be so reduced by augmenting the system with k additional variables and equations. The dual of the transportation problem possesses the unimodular property that every subdeterminant has value 0, 1, or -1. Therefore, extreme point solutions have integer values if the constant terms are integer valued. The question is undetermined whether unimodular systems exist which are more general than those derived from transportation (distribution) problems. RM-2170-RC: Attitudes of the French Parliament and Government Toward Atomic Weapons. AUTH: C. DelaMalene, C. Melnik, R. Manheim, R. Manheim PAGES: 80, DATE: 1958 COST: $ 7.50 KEYS: France; Nuclear weapons ABST: A discussion of the attitudes of the French government and parliament toward atomic weapons since their discovery and use. Part I deals with the historic development of these attitudes (e.g., those ranging from the total absence of nuclearmindedness to the growth of the atomic weapon issue in the minds of civilians and military alike). Part II describes the causes of the lag in nuclear-mindedness: the "European" controversy, the French parliamentary situation, atomic neutralism, the rules of the French political "game," feelings of incapacity, fear of public opinion, and the changes implied by an atomic arsenal. (See also RM-2954-RC.) 89 pp. P-1372-RC: The Relation of Salary to the Supply of Scientists and Engineers. AUTH: J.C. DeHaven PAGES: 27, DATE: 1958 COST: $ 4.00 ABST: A model which demonstrates how the pecuniary and nonpecuniary factors of total income may operate on the margin to determine the numbers of people in different occupations. The net present income values at age 18 for several occupations--building-construction workers, chemists, and chemical engineers--are calculated using actual income and cost data to show the relevant pecuniary factors which may influence young people in their choices of careers. The implications for three meanings of "shortage" are discussed in terms of the numbers of people who may choose scientific occupations. In addition, an estimate is made of the future trend of income for chemical engineers in respect to other occupations. No abstract available. 27 pp. P-1254: An Electronics Engineer's View of Operations Research. AUTH: J. Digby, J.F. Digby PAGES: 11, DATE: 1958 COST: $ 4.00 ABST: An address delivered before the National Conference on Aeronautical Electronics at Dayton, Ohio, May 13, 1958. The general nature of operations research is described, and some suggested applications relating to future problems of electronic systems are discussed. No abstract available. 11 pp. RM-2134: On the Computational Solution of Dynamic-Programming Processes--XV: An Industrial Replacement Process. AUTH: S.E. Dreyfus PAGES: 11, DATE: 1958 COST: $ 4.00 ABST: A discussion of an industrial replacement problem which involves two identical parts of a single machine. This problem, which arose in the tire-manufacturing industry, has been studied by M. W. Sasieni who arrived at a replacement policy shown to be nonoptimal. The present memorandum applies the functional-equation technique of dynamic programming to the problem. Numerical examples are considered; optimal replacement policies are determined. No abstract available. 11 pp. P-1029: Dynamic Programming: Methods and Application. AUTH: S.E. Dreyfus PAGES: 13, DATE: 1958 COST: $ 4.00 ABST: A study of dynamic programming, defined as a mathematical technique applicable to multistage decision problems. It is shown how a functional equation for finite processes may be solved recurrently and the optimal policy determined. Applications are examined in the fields of mathematics, logistics, economics, military planning, and physics. No abstract available. 13 pp. P-1369: Introduction to Dynamic Programming. AUTH: S.E. Dreyfus PAGES: 13, DATE: 1958 COST: $ 4.00 ABST: A discussion of the conceptual framework of dynamic programming and an indication of some of the types of processes that can be treated. The functional-equation method of formulating multistage-decision-process problems is explained. In addition, several classes of problems to which this technique has proved applicable are given to illustrate some analytic and computational devices for resolving these problems. No abstract available. 13 pp. P-1527: Dynamic-Programming Algorithms and Formulations. AUTH: S.E. Dreyfus PAGES: 15, DATE: 1958 COST: $ 4.00 ABST: A discussion of four algorithms for the solution of dynamic-programming processes. The areas of applicability of each are indicated, and the solution of a particular problem by the use of each algorithm is considered. P-1473: The Distribution of Radial Error and Its Statistical Application in War Gaming. AUTH: H.P. Edmundson PAGES: 28, DATE: 1958 COST: $ 4.00 ABST: A discussion of the assumptions and theorems concerning the distribution of weapon radial error and a demonstration of its statistical application in war gaming. The density function and cumulative distribution function of the radial error are derived and graphed for one, two, and three dimensions. For each of these cases, formulas are given for the expectation, standard deviation, and median of the radial error. P-1474: The Goodness-of-Fit Statistics of Kolmogorov and Smirnov. AUTH: H.P. Edmundson PAGES: 21, DATE: 1958 COST: $ 4.00 ABST: An examination of the goodness-of-fit statistics of A. Kolmogorov and N. Smirnov. This paper summarizes the theory and applications of these statistics and compares them with the classical x statistic for testing goodness of fit. P-1475: The Moments of Two Limiting Distributions of Kolmogorov. AUTH: H.P. Edmundson PAGES: 13, DATE: 1958 COST: $ 4.00 ABST: A derivation of a general expression for the ith moment of two limiting distributions due to A. Kolmogorov. The dispersions of these two distributions are then compared. No abstract available. 13 pp. P-1476: The Moments of Two Distribution-Free Statistics of Smirnov. AUTH: H.P. Edmundson PAGES: 12, DATE: 1958 COST: $ 4.00 ABST: A derivation of a general expression for the ith moment of two distribution-free statistics due to N. Smirnov. P-1492: The Progress Curve Computer. AUTH: D.M.4. Eisemann, D.M. Eisemann PAGES: 5, DATE: 1958 COST: $ 4.00 KEYS: Curves, Logarithmic; Airplanes--Costs--Mathematical models ABST: A discussion of the progress-curve computer, a device that determines the average cost, unit cost, and total cost for all quantities of output from 1 to 1000. The computer consists of a logarithmic grid on which a family of curves is superimposed. Any specific point on a curve may be assigned any value on the ordinate, and all other points on the curve automatically assume their proper values. An example illustrates how the computer works. Its applications to other uses are considered. (Published in [Operations Research], January-February, 1959.) 5 pp. P-1379: Consensus of Subjective Probabilities: The Pari-Mutuel Method. AUTH: E. Eisenberg, D. Gale, D. Gale PAGES: 9, DATE: 1958 COST: $ 4.00 KEYS: Probability ABST: A discussion of the pari-mutuel system of betting on horse races in which the final track odds are in some sense a consensus of the "subjective odds" of the individual bettors weighted by the amounts in their bets. The authors formulate the properties which this consensus must possess and prove that there always exists a unique set of odds having the required properties. (Published in [The Annals of Mathematical Statistics], March 1959.) 8 pp. RM-1962: Stockage Policies for Medium- and Low-Cost Parts. AUTH: A.R. Ferguson, L. Fisher, L. Fisher PAGES: 158, DATE: 1958 COST: $ 15.00 ABST: A method for determining base and depot stock levels in the face of the dynamic and uncertain environment with which the Air Force supply system has to deal. The method examines the major variables which must be considered to achieve economical and effective provisioning and distribution under such circumstances. The study indicates what stockage rules should include, how the dynamics of weapon-system or other program phase-in or phase-out can be taken into account, how to free management to manage better the more costly and critical items, what further research is needed, and how the application of these as well as other supply policies can be improved. No abstract available. 159 pp. P-1262: Air Force Logistics: From Research to Policy. AUTH: A.R. Ferguson PAGES: 15, DATE: 1958 COST: $ 4.00 ABST: An attempt to show that getting simple operations-research "solutions" to problems is really only the first step in getting a set of decision rules into practical use. Some decision rules are presented for setting stock levels for an Air Force inventory in those cases where a minimum of management per line item is appropriate. In particular, some problems of modifying and elaborating the decision rules for practical implementation are discussed. As the rules cover items which are consumed but not repaired at the stockage point in question, the paper considers how much to stock of any line items for which the decision has already been made that they be brought into the inventory. No abstract available. 15 pp. RM-2149: Monte Carlo Models for Estimating Reliability: An Exploratory Analysis. AUTH: S.I. Firstman PAGES: 42, DATE: 1958 COST: $ 4.00 KEYS: Monte carlo method; Reliability ABST: An analysis of the problem of a priori reliability estimating by means of the Monte Carlo method. The Monte Carlo model considered is used to predict system malfunctions that do not occur through component failure but occur because the entire system performs outside the bounds set by its specifications. It uses the stochastic properties of component performance to evaluate system output. The study demonstrates the usefulness of the method, the validity of the results, the unbiased nature of derived estimates, and the requirements for input data. 42 pp. P-1114: A Suggested Computation for Maximal Multi-Commodity Network Flows. AUTH: L.R. Ford, D.R. Fulkerson, L.R. Ford, D.R. Fulkerson PAGES: 10, DATE: 1958 COST: $ 4.00 ABST: A computation which uses the structure of one formulation of the multi-commodity problem within the framework of a simplex computation to determine maximal multi-commodity flows in networks. For this particular formulation, the number of variables is too large to be dealt with explicitly. The suggested computation treats nonbasic variables implicitly by replacing the pricing operation of the simplex method with several applications of a combinational algorithm for finding a shortest chain joining a pair of points in a network. No abstract available. 10 pp. RM-2159: Notes on Linear Programming--Part XLV: A Network-Flow Feasibility Theorem and Combinatorial Applications. AUTH: D.R. Fulkerson PAGES: 30, DATE: 1958 COST: $ 4.00 ABST: An establishment of necessary and sufficient conditions for the existence of a flow in a network (e.g., a railway network) satisfying prescribed bounds on the net flow leaving certain nodes and entering other nodes. These conditions are applied to the study of combinatorial problems concerning matrices of zeros and ones, subgraphs of a directed graph, and systems of distinct representatives. No abstract available. 31 pp. RM-2178: Notes on Linear Programming-Part XLVI: Bounds on the Primal-Dual Computation for Transportation Problems. AUTH: D.R. Fulkerson PAGES: 16, DATE: 1958 COST: $ 4.00 ABST: One of a series of studies concerned with optimal transportation flow through a network (e.g., through a railway network). Theoretical bounds on the number of labelings required to solve either a transshipment problem or a Hitchcock-Koopmans problem by the primal-dual method are established. These bounds depend on the amount K to be sent through the network and the number N of nodes, but not on the cost function. For the transshipment problem, a bound is K(N + 1). For the Hitchcock-Koopmans problem with m sources and n sinks, this may be sharpened to K(min(m,n) + 1). No abstract available. 16 pp. P-1401: Increasing the Capacity of a Network: The Parametric Budget Problem. AUTH: D.R. Fulkerson PAGES: 24, DATE: 1958 COST: $ 4.00 ABST: A study concerned with allocating a budget of resources among the links of a network to increase its flow capacity relative to given sources and sinks. On the assumption that the cost of increasing each link capacity is linear, a labeling algorithm is described that permits rapid calculation of optimal allocations for all budgets. P-1216: A Note on Polynomial and Separable Games. AUTH: D. Gale, O.A. Gross, O.A. Gross PAGES: 16, DATE: 1958 COST: $ 4.00 KEYS: Game theory ABST: A proof that given a pair of infinite metric spaces and a pair of respective finite mixed strategies on them, a separable game exists with bounded continuous payoff on their Cartesian product such that the given strategies constitute the unique solution of the game. If the spaces are identical, corresponding to any given finite mixture, a symmetric polynomial-like game can be obtained with bounded (skew-symmetric) continuous payoff so that the given strategy is the only optimal one. If the spaces are bounded subspaces of Euclidean n-space with sufficiently many cluster points in their closures, the payoff can be a polynomial and have the desired property. A proof that given a pair of infinite metric spaces and a pair of respective finite mixed strategies on them, a separable game exists with bounded continuous payoff on their Cartesian product such that the given strategies constitute the unique solution of the game. If the spaces are identical, corresponding to any given finite mixture, a symmetric polynomial-like game can be obtained with bounded (skew-symmetric) continuous payoff so that the given strategy is the only optimal one. If the spaces are bounded subspaces of Euclidean [n]-space with sufficiently many cluster points in their closures, the payoff can be a polynomial and have the desired property. 16 pp. RM-2152: Notes on Linear Programming--Part XLIV: Transient Flows in Networks. AUTH: D. Gale PAGES: 17, DATE: 1958 COST: $ 4.00 ABST: A study concerned with flows in two-terminal dynamic networks as defined by Ford and Fulkerson (RM-1981). These authors have shown how to construct for each positive integer k a flow <> that maximizes the amount <> shipped from source to sink in k time periods. Their method leads to different functions <> for different values of k. The present research memorandum shows that the problem can be solved by a single flow <> when k maximizes the cumulative amount shipped from source to sink. The conclusion holds even when the capacities and transit times in the network are allowed to vary with time. The results of this study may be applied in analyzing logistics problems involving railway networks. No abstract available. 18 pp. RM-2088: A Priori Demand Prediction: A Case Study of B-52 Airframe Parts. AUTH: T.A. Goldman PAGES: 39, DATE: 1958 COST: $ 4.00 ABST: A study which deals with predicting the demand for airframe parts in the absence of consumption data to determine whether the level of demand is related to physical and operational characteristics of parts. In particular, an attempt is made to predict the demand for B-52 airframe spare parts with the help of B-47 consumption experience. The results of these tests are then compared with the reported consumption of the same parts during the early phase-in of the B-52 weapon system. In addition, some of the theoretical foundations for the concept of service-life factors are discussed, together with the relationship of these to the demand predictions in the present study. No abstract available. 42 pp. RM-2144: Factors Affecting the Experience Composition of Airmen in USAF Job Categories: A Mathematical Approach. AUTH: W. Gorham PAGES: 45, DATE: 1958 COST: $ 4.00 ABST: A method for measuring the relative importance of the factors which shape the experience mix or composition of the airmen in an Air Force job category. Factors considered are the length of the enlistment period, eligibility for re-enlistment, re-enlistment, retirement, retraining, attrition, force size, and input mix (between recruits and retrainees). The sensitivity of the experience mix to each of these factors except force size is demonstrated by the use of a steady-state model. To show the impact of changing force size on experience composition, an inventory model is used. Prior to the quantitative treatment of the determinants, each is discussed generally in terms of its effect on the average experience level of the force. No abstract available. 46 pp. RM-2265: A Class of Function-Space Games. AUTH: O.A. Gross PAGES: 11, DATE: 1958 COST: $ 4.00 KEYS: Game theory ABST: A solution to two classes of two-person zero-sum games over function space, arising from a mine- laying and search problem. Any game in either class shares, with all other games in the two classes, a common pure optimal strategy for the maximizer. The games of the first class have saddle points in pure strategies of special character. The second class consists of subgames of the first, obtained by restricting the minimizer's strategies to characteristic functions. In general, these games require mixed strategies for the minimizer, and the value of a game of the first class is strictly less than the value of its subgame in the second class. A solution to two classes of two-person zero-sum games over function space, arising from a mine-laying and search problem. Any game in either class shares, with all other games in the two classes, a common pure optimal strategy for the maximizer. The games of the first class have saddle points in pure strategies of special character. The second class consists of subgames of the first, obtained by restricting the minimizer's strategies to characteristic functions. In general, these games require mixed strategies for the minimizer, and the value of a game of the first class is strictly less than the value of its subgame in the second class. 11 pp. RM-2279: An Optimal-Inventory Model. AUTH: O.A. Gross PAGES: 25, DATE: 1958 COST: $ 4.00 ABST: An attempt to determine what inventory-ordering policy maintains the inventory as low as possible at all times. A situation is considered where there is an empty inventory of two different items and where a buyer has the option at any time of ordering either of two specified kinds of packages-of different composition of the two items but of equal total amount-subject to the constraint that no item is allowed to be depleted for a positive length of time. The second part of this study discusses a proposed solution to a problem involving discrete replenishment, by tankers of specified type, of several kinds of continuously depleting petroleum products at three different port facilities. No abstract available. 25 pp. P-1513: On the Epistemology of the Inexact Sciences [By] Olaf Helmer [And] Nicholas Rescher ... AUTH: O. Helmer-Hirschberg, N. Rescher, O. Helmer, N.H. Rescher PAGES: 66, DATE: 1958 COST: $ 7.50 KEYS: Social sciences--Methodology; Research--Psychological aspects ABST: An outline of a new epistemological approach to the inexact sciences, which include applied physical sciences such as engineering or medicine as well as most of the social sciences. The purpose of all sciences is to explain past events and to predict future events in an objective manner. In the exact sciences explanation and prediction have the same logical structure. However, in the inexact sciences specifically predictive instrumentalities in these fields and various mehtodological innovations must be considered. Among these are the systematic use of expert judgment and pseudoexperimentation, involving simulation processes and operational gaming. P-1269: Future Prospects for Soviet Economic Aid. AUTH: H. Heymann PAGES: 17, DATE: 1958 COST: $ 4.00 KEYS: Economics--Foreign; International trade and finance; United states--Economic KEYS: assistance; Soviet Union--Economics ABST: A summary and full text of a talk given at the 12th Annual Conference of the Middle East Institute in Washington, D.C., January 31, 1958, and published in the transcript of that meeting. Such aspects of Middle East development are considered as (1) the size of current Soviet trade and aid effort, (2) the Soviet role in machinery exports, (3) the future of Soviet industrial exports to the underdeveloped countries, (4) the fact that Soviet aid is not a quantitative but a qualitative threat, and (5) future Soviet opportunities in the field of civil aviation. A 1958 discussion of the meaning, scope, and likely future course of the Soviet policy of expanded trade and economic assistance to underdeveloped countries. While the Soviet economic aid effort was less than it appeared to be, the finesse of implementation made the aid offensive a startlingly successful gambit in the influence-building contest between the two great powers. 17 pp. P-1528: Statistical Methods in Radio-Wave Propagation. AUTH: W.C. Hoffman PAGES: 15, DATE: 1958 COST: $ 4.00 ABST: The text of an address presented to the International Scientific Radio Union at University Park, Pennsylvania, October 21, 1958, and published in the proceedings of the meeting. Current knowledge of the application of statistical methods to radio-wave propagation is reviewed. Contributions of individual workers are mentioned. Outstanding problems in the field are also indicated. No abstract available. 15 pp. P-1560-RC: The Distribution of a Drug in the Body. AUTH: J.A. Jacquez, R.E. Bellman, R.E. Kalaba PAGES: 22, DATE: 1958 COST: $ 4.00 KEYS: Drugs; Physiology ABST: A continuation of P-1550, Some Mathematical Aspects of Chemotherapy-I: One-organ Models, which considers a model of the distribution of a compound within the plasma flowing through a capillary bed and within the extracellular space and intracellular space. The model includes the possibility of the reaction of the drug with a component of the intracellular space. The present paper extends the model to include the effects of the major tissues of the body and circulation. An attempt is made to show the relationship of this general problem to feedback problems, input-output analysis, and transportation problems arising in economic and engineering control processes. An extension of the model discussed in P-1550, to include the effects of the major tissues of the body and circulation. An attempt is made to show the relationship of this general problem to feedback problems, input-output analysis, and transportation problems arising in economic and engineering control processes. 22 pp. P-1526: Sequencing N Jobs on Two Machines with Arbitrary Time Lags: Alternate Proof and Discussion of General Case. AUTH: S.M. Johnson PAGES: 10, DATE: 1958 COST: $ 4.00 ABST: An alternate proof of a result of L. G. Mitten in solving the problem of sequencing n jobs through two machines with arbitrary time lags, assuming similarity of the job sequences for both machines. The more difficult general problem is discussed and partially solved. No abstract available. 10 pp. P-1548: A Simulation Model of Air Force Maintenance Operations. AUTH: R.A. Levine, R.B. Rainey, R.B. Rainey PAGES: 10, DATE: 1958 COST: $ 4.00 KEYS: Logistics--Mathematical models; Maintenance; Operations research ABST: A description of a model which simulates aircraft maintenance and operations at the air base level. The model is of the random sampling or Monte Carlo type programmed for the IBM 704 computer. Using the model to make predictions, it is possible to eliminate certain field testing and to select key estimates of mission regimes and maintenance organizations to be subjected to confirmation through actual field testing. The model is highly useful for making planning recommendations in situations new to the Air Force and has proved advantageous in RAND's maintenance research efforts. P-1375: Use of Mathematical Models for Logistical Planning. AUTH: J.D. Little PAGES: 17, DATE: 1958 COST: $ 4.00 ABST: A study that defines machine models and explains their uses in logistic planning and experimentation. As examples, a description is given of "Laboratory Project 1" (a man-machine model) and of the Missile Support Model (a machine model used in "Laboratory Project 2"). The paper discusses the purpose of these models, the general procedure used in creating the models, the trouble areas found in this creative period, the results obtained from the running of the models, the trouble areas found in the running of the models, and other possible uses of models. No abstract available. 17 pp. RM-2287: Notes on Linear Programming-Part XLVIII: Inequalities for Stochastic Linear Programming Problems. AUTH: A. Madansky PAGES: 19, DATE: 1958 COST: $ 4.00 ABST: A consideration of a linear-programming problem in which the "right-hand side" is a random vector whose expected value is known and where the expected value of the objective function is minimized. The conditions are studied under which an approximate solution (found by replacing the "right-hand side" by its expected value and solving the resulting linear programming problem) is satisfactory. In particular, conditions are given for the equality of the expected value of the objective function for the optimal solution and the value of the objective function for the approximate solution. Bounds on these values are also given. The relation is discussed between this problem and a related problem where an observation is made on the "right-hand side" and where the non- stochastic linear programming problem based on this observation is solved. No abstract available. 19 pp. P-1236: The Fitting of Straight Lines When Both Variables Are Subject to Error. AUTH: A. Madansky PAGES: 66, DATE: 1958 COST: $ 7.50 KEYS: Numerical methods and approximations; Statistical analysis ABST: A study of the problem where X and Y are related by Y = ¯ + ¾X, where ¯ and ¾ are unknown, and where X and Ynd Ynd Ynd Ynd Y are observed with error (i.e., x = X + u and y = Y + v). It is assumed that Eu = Ev = 0, and that the errors (u and v) are uncorrelated with the true values (X and Y). Solutions are described to the problem of obtaining consistent estimates of ¯ and ¾ from a sample of (x,y)'s, when various assumptions are made about properties of the errors and the true values other than those mentioned, and when various kinds of additional information are given which aid in constructing these consi The title of this paper describes its content. (Published in the [Journal of the American Statistical Association], March 1959.) 63 pp. Ref. P-1289: A Note on "Efficient Estimation and Local Identification in Latent Class Analysis.". AUTH: A. Madansky PAGES: 3, DATE: 1958 COST: $ 4.00 KEYS: Statistical analysis ABST: A commentary on R. B. McHugh, "Efficient Estimation and Local Identification in Latent Class Analysis," which appeared in [Psychometrika], No. 21, 1956. The method in which McHugh obtains information functions is discussed, together with the conditions under which his estimator is consistent. 3 pp. Ref. P-1355: On the Maximum Likelihood Estimate of the Correlation Coefficient. AUTH: A. Madansky PAGES: 7, DATE: 1958 COST: $ 4.00 KEYS: Numerical methods and approximations; Probability; Statistical analysis ABST: A study which determines the maximum likelihood estimate of the correlation coefficient for the bivariate normal distribution when the variances are known. 6 pp. Ref. P-1358: Least Squares Estimation in Finite Markov Processes. AUTH: A. Madansky PAGES: 12, DATE: 1958 COST: $ 4.00 KEYS: Markov processes; Probability ABST: A consistent estimate of the transitional probability matrix of a finite Markov process in the case when at each point in time only the proportions of the sample in each state are known. It is shown that this estimate is asymptotically more efficient, in a sense defined in this paper, than previously considered estimates for this matrix. (Published in [Psychometrika], June 1959.) 12 pp. P-1418: Bounds on the Expectation of a Convex Function of a Multivariate Random Variable. AUTH: A. Madansky PAGES: 13, DATE: 1958 COST: $ 4.00 ABST: A derivation of the upper and lower bounds on the expectation of a convex function of a vector-valued random variable by examining the boundary of an appropriate multivariate moment space. The bounds obtained are also improved. P-1538: Determinantal Methods in Latent Class Analysis. AUTH: A. Madansky PAGES: 31, DATE: 1958 COST: $ 4.00 KEYS: Matrices--Theory; Statistical analysis ABST: Some extensions of the existing determinantal methods for solving the accounting equations in latent class analysis. These extensions cover more cases than previous methods, produce new sufficient conditions for identifiability of the latent class model, and show the necessity of various sufficient conditions for identifiability. Implications to the identifiability problem are discussed. (Published in [Psychometrika], June 1960.) 29 pp. Ref. P-1174: Experimentation by Simulation and Monte Carlo. AUTH: A.W. Marshall PAGES: 14, DATE: 1958 COST: $ 4.00 KEYS: Computer simulation; Experimental design; Monte carlo method; Operations KEYS: research ABST: A discussion of simulation and Monte Carlo as modes of analysis of particular interest in problems of operations analysis involving many variables. After defining these terms, the author considers (1) Monte Carlo design when simulation aspects are not emphasized, and (2) simulation design with Monte Carlo aspects. 14 pp. P-1348: Some Finite Population Unbiased Ratio and Regression Estimators. AUTH: M.R. Mickey PAGES: 39, DATE: 1958 COST: $ 4.00 KEYS: Numerical methods and approximations; Regression (statistics); Stochastic KEYS: processes ABST: A presentation of a class of ratio- and regression-type estimators such that the estimators are unbiased for random sampling, without replacement, from a finite population. Nonnegative unbiased estimators of estimator variance are provided for a subclass. Similar results are given for the case of generalized procedures of sampling without replacement. Efficiency is compared with comparable estimation-sample-selection methods for this case. (Published in the [Journal of the American Statistical Association], September 1959.) 37 pp. Ref. P-1376: A Method for Determining Supply Quantity for the Case of Poisson Distribution of Demand. AUTH: M.R. Mickey PAGES: 15, DATE: 1958 COST: $ 4.00 ABST: A study of the problem of determining the number of units of an item to be supplied against a future demand, on the basis of the past record of demand for that item. A method is described for the case of Poisson distribution of demand and known relation between the expected demand for the experience and the future periods. No abstract available. 15 pp. RM-2124: A Comparison of Random and Periodic Data Sampling for the Detection of Signals in Noise. AUTH: D. Middleton PAGES: 51, DATE: 1958 COST: $ 7.50 KEYS: Probability; Radar; Signal processing; Stochastic processes ABST: An analysis, by means of probability theory, of the effect of using random rather than periodic sampling in radar detection systems. In the specific examples examined, it is found that periodic sampling gives the better performance. 51 pp. RM-2146: The Economics of Invention: A Survey of the Literature. AUTH: R.R. Nelson PAGES: 59, DATE: 1958 COST: $ 7.50 KEYS: Innovation; Research and development; Technology ABST: A selective summary of the literature on the economics of invention. Both growing social demand and new scientific knowledge are examined as factors stimulating inventive effort. The comparative importance of the private inventor and the research and development laboratory are appraised. The study stresses the great uncertainties which still surround any inventive effort seeking a significant advance, and investigates how this uncertainty affects management practices in industrial-research laboratories. The general analysis is supported by a number of case studies. A selective summary of the literature on the economics of invention. Both growing social demand and new scientific knowledge are examined as factors stimulating inventive effort. The comparative importance of the private inventor and the research and development laboratory are appraised. The study stresses the great uncertainties which still surround any inventive effort seeking a significant advance, and investigates how this uncertainty affects management practices in industrial-research laboratories. The general analysis is supported by a number of case studies. 59 pp. RM-2233: Experimental Design, Test, and Evaluation of an F-100D Flyaway Kit. AUTH: B. Okun PAGES: 107, DATE: 1958 COST: $ 10.00 ABST: One of a series of studies dealing with the flyaway kit problem. The present memorandum describes and analyzes the results of an F-100D flyaway kit test, designed to compare the effectiveness of six alternative "paper" flyaway kits and to evaluate the merits of the RAND flyaway kit method. Consumption data were collected for a 30-day period from two F-100D squadrons stationed in West Germany, and were then compared with the contents of each kit. A kit's effectiveness was measured in terms of its ability to satisfy the squadrons' demands for spare parts. No abstract available. 106 pp. P-1515: On the Foundations of Dynamic Programming. AUTH: H.A. Osborn PAGES: 12, DATE: 1958 COST: $ 4.00 ABST: A proof that Bellman's formalism in the calculus of variations furnishes an approximation which converges to the value of the slope function at any given point of the field of extremals. RM-2085: Savings from Procurement Deferral with Interim Contractor Support: The Case of High-Value Airframe Spares. AUTH: J.W. Petersen, J.W. Peterson PAGES: 119, DATE: 1958 COST: $ 10.00 ABST: An evaluation of the deferred spares procurement concept, a system in which major spares buys are delayed or deferred until later in the program, after support experience is obtained. This study identifies and quantifies the savings and cost elements that would be involved in operating a deferred procurement system, and it considers the impact on supply effectiveness. The investigation is based on an analysis of a sample of high-value airframe spares chosen from three current aircraft models, the B-47, B-52, and F-100. No abstract available. 119 pp. RM-2117: Simulated Wars in LP-I. AUTH: R.M. Rauner PAGES: 42, DATE: 1958 COST: $ 4.00 KEYS: Logistics; War games ABST: A study of the simulation of war in RAND's Logistics Systems Laboratory, which presents some of the results obtained in Laboratory Problem I (LP-I). LP-I attempted to compare the performance of two logistics systems through a substantial part of a weapon-system life cycle. Two wars were simulated, the first occurring without warning and the second preceded by a five-day period of warning and preparation. In both wars the Air Materiel Area, the factory, and the ground transportation system were assumed to have been destroyed. Some bases of the Strategic Air Command were assumed to have been destroyed, and their tenant Air Defense Command aircraft lost. 40 pp. P-1299: Meteorological Aspects of Infrared Operations. AUTH: J.D. Sartor PAGES: 16, DATE: 1958 COST: $ 4.00 KEYS: Clouds; Meteorology ABST: A discussion of the use of meteorological information and its limitations in infrared applications. Data on high-level clouds are presented, with some indication of their effect on infrared transmission. 16 pp. P-1385: Re-Interpretation of the Solution Concept for "Non-Cooperative" Games. AUTH: T.C. Schelling PAGES: 17, DATE: 1958 COST: $ 4.00 KEYS: Games ABST: A discussion of coordination-game theory, suggesting that the "solution in the strict sense" of a tacit non-zero-sum game is to be understood largely by reference to its signalling qualities. Since other sources of signals may be present even in the purely mathematical formulation of the game, the particular qualities of the "solution in the strict sense" are but one of many potential determinants of a "rational solution." It is an empirical question-not a matter of deduction a priori- of what signals can be appreciated. A theory is neither a good normative theory nor a good descriptive theory if players can consistently do better than the theory predicts by using rational process that the theory cannot recognize. A discussion of coordination-game theory, suggesting that the "solution in the strict sense" of a tacit nonzero-sum game is to be understood largely by reference to its signalling qualities. Since other sources of signals may be present even in the purely mathematical formulation of the game, the particular qualities of the "solution in the strict sense" are but one of many potential determinants of a "rational solution." It is an empirical question--not a matter of deduction a priori--of what signals can be appreciated. A theory is neither a good normative theory nor a good descriptive theory if players can consistently do better than the theory predicts by using rational process that the theory cannot recognize. 17 pp. P-1386: For the Abandonment of Symmetry in the Theory of Cooperative Games. AUTH: T.C. Schelling PAGES: 29, DATE: 1958 COST: $ 4.00 KEYS: Bargaining theory; Cooperative games; Game theory ABST: An argument that the pure "moveless" bargaining game (analyzed by Nash, Harsanyi, Luce, Raiffa, and others) may not exist or, if it does, is of a different character from that generally supposed. In addition, it is argued that symmetry in the solution of bargaining games cannot be supported on the notion of "rational expectations." The point of departure for this argument is the operational identification of irrational expectations. An argument that the pure "moveless" bargaining game (analyzed by Nash, Harsanyi, Luce, Raiffa, and others) may not exist or, if it does, is of a different character from that generally supposed. In addition, it is argued that symmetry in the solution of bargaining games cannot be supported on the notion of "rational expectations." The point of departure for this argument is the operational identification of irrational expectations. 29 pp. P-1392: The Solutions of a Symmetric Market Game. AUTH: L.S. Shapley PAGES: 30, DATE: 1958 COST: $ 4.00 KEYS: Competition; Game theory ABST: An attempt to determine solutions for a symmetrical market game in which the value of a coalition is assumed to be proportional to the number of buyers or sellers participating, whichever is smaller. A determination of von Neumann-Morgenstern solutions for a symmetrical market game in which the value of a coalition is assumed to be proportional to the number of buyers or sellers participating, whichever is smaller. 30 pp. RM-2300-RC: The Rocket Performance Computer. AUTH: E.H. Sharkey PAGES: 18, DATE: 1958 COST: $ 4.00 KEYS: Computers; Missiles ABST: An instruction book describing the operation of the Rocket Performance Computer. Enclosed with the publication, the computer aids in calculating rapidly approximate solutions to single-stage rocket performance problems. By iterative solutions, multistage performance can also be calculated. An instruction book describing the operation of the Rocket Performance Computer. The computer enclosed with the publication is an aid to the rapid calculation of approximate solutions to single-stage rocketperformance problems. By iterative solutions, multi-stage performance can also be calculated. 18 pp. P-1601: RAND, a Personal View of Its History. AUTH: R.D. Specht PAGES: 26, DATE: 1958 COST: |c$4.00 KEYS: RAND Corporation--History; Research--History; Research institutes--History RM-2131: Management Information for the Maintenance and Operation of the Strategic Missile Force. AUTH: D.S. Stoller, R.L. VanHorn, R.L. VanHorn PAGES: 61, DATE: 1958 COST: $ 7.50 KEYS: Antimissile defense; Management information systems ABST: An investigation of the planning- and operating-data requirements and information flow patterns for the strategic-missile force. The main function considered is the measurement and control of maintenance-operations interactions that determine launch capability. The study discusses decision areas, data requirements, desirable system characteristics, and one proposed system. The authors suggest that immediate consideration be given to testing the feasibility and desirability of the proposed system in an appropriate Air Force environment. No abstract available. 64 pp. P-1478: A Mathematical Study of Arbitrage. AUTH: J.J. Stone, H.M. Wagner, H.M. Wagner PAGES: 42, DATE: 1958 COST: $ 4.00 ABST: A study of the mathematical structure underlying nearly perfect exchange markets spatially or temporally separated. Such questions are investigated as the equilibrium conditions for a set of exchange rates and how arbitrage possibilities are discovered and if they exist. The analysis involves the combined use of an algebraic representation-conducive to deriving qualitative features characterizing a multiexchange market-and two linear-programming models. One model is used in establishing a desirable set of equilibrium exchange rates, and the other permits an efficient computational scheme for discovering arbitrage possibilities. P-1490: The Cross-Section Method: An Algorithm for Linear Programming. AUTH: J.J. Stone PAGES: 24, DATE: 1958 COST: $ 4.00 ABST: An algorithm that solves the linear-programming problem. This algorithm combines the usual phase one (obtaining feasibility) and phase two (obtaining optimality) of the simplex or dual methods into a single phase. The algorithm begins with either a single activity (column) or a constraint (equation) and proceeds to add either activities or constraints one at a time, solving the subproblems that arise for their optimal solutions. The final solution is attained after adding the last activity or constraint. The algorithm promises to be an efficient one and has several advantages arising from the information supplied about subproblems. P-1465: A New Look at Experience Rating. AUTH: H.M. Wagner PAGES: 20, DATE: 1958 COST: $ 4.00 ABST: An analysis of the recent developments in experience rating (provided under the Federal Unemployment Act of 1939) to evaluate suggested policy changes in the system's operation. The various arguments presented are that a potential lowering of taxes gives firms an incentive to stabilize their work force, "unstable" employers should bear more of the cost for unemployment compensation than "stable" employers, current financing is inadequate to meet possible rises in the unemployment rate, and undesirable interstate and interindustry inequities prevail. It is concluded that a diminution of experience-rating differentials, combined with a more direct cyclical scheme of varying over-all rates, will provide financial benefits outweighing those presently in effect. RM-2200: Cost and Performance Data from LP-I: The First Experiment in Simulation by the Logistics Systems Laboratory. AUTH: R.L. Winestone, R.L. Winestein PAGES: 119, DATE: 1958 COST: $ 10.00 ABST: A summary, in terms of cost and effectiveness of performance, of the results of Laboratory Problem I (LP-I), an experiment designed to test a promising set of logistic policies and procedures for the USAF. These policies and procedures were incorporated into an operable laboratory model system designated as Logistics System 2 (LS-2), which was pitted against an analogous model representing the actual policies and procedures of the Air Force as of mid-1956 (LS-1). The framework within which both systems operated was the simulated supply and maintenance activity connected with phasing in and supporting an aircraft employed by the Air Defense Command. No abstract available. 119 pp. RM-2282: On the Computational Solution of Dynamic-Programming Processes-XIV: Missile-Allocation Problems. AUTH: R.E. Bellman, S.E. Dreyfus, O.A. Gross, S.M. Johnson PAGES: 40, DATE: 1959 COST: $ 4.00 ABST: One of a series of studies that applies dynamic- programming techniques to the computational solution of mathematical problems involving multistage decision processes. This memorandum applies the dynamic-programming technique to problems involving the optimal allocation of attack against a target system and the optimal allocation of defense against this attack. In the case of two types of attackers (either manned aircraft and decoys, or missiles of different capabilities), the Lagrange-multiplier technique is applied to reduce the computational solution to one involving sequences of functions of one variable. Large-scale target allocations are resolved computationally in a reasonable period of time with the use of such computers as the RAND JOHNNIAC or the IBM 704. 40 pp. RM-2417-NASA: Public Opinion and Social Effects of Space Activity. AUTH: J.M. Goldsen PAGES: 16, DATE: 1959 COST: $ 4.00 KEYS: Education; Nasa; Propaganda; Social science; Space programs; Soviet KEYS: Union--Science ABST: A study that investigates American public reaction to Soviet success in the space race, the response of Congress in relation to public opinion, the objectives and programs of NASA's information activities, the impact of space activities on education and training, and some of the broad social and economic implications of the space era. 16 pp. RM-2473-FF: Systems Analysis and Education. AUTH: J.A. Kershaw, R.N. McKean PAGES: 70, DATE: 1959 COST: $ 7.50 KEYS: Education; System analysis NOTE: See also RM-3009-FF. ABST: A study to assess the possibilities of making quantitative comparisons of educational systems (that is, comparisons of specific systems with variants in which changes and innovations are incorporated). Only elementary and secondary schools are considered. Comparisons of this type to help administrators and others choose improved education systems will soon be feasible. However, it is necessary for more work to be done toward estimating the "input-output relationships" in education. P-132: Modification of the Monte Carlo. AUTH: H. Kahn PAGES: 18, DATE: 1959 COST: $ 4.00 KEYS: Monte carlo method ABST: Evaluates integrals and the solutions to integral equations by random sampling. The techniques available to the computer that can reduce the size of the sample required are emphasized. (Published in the [Proceedings of the Endicott Conference], November 1949.) 18 pp. P-1690: A Macro Analysis of Military Air Transportation. AUTH: W.A. Niskanen PAGES: 7, DATE: 1959 COST: $ 4.00 KEYS: Airlift ABST: A discussion of the use of various programming techniques to determine the nature and magnitude of the major military airlift missions and the best mix of airlift resources to perform these missions. The study examines the strong tradeoff between flying hours and fleet composition, the potential contribution of the commercial fleet in the context of planning for the military fleet, and the separation of mission requirements into discrete periods to permit evaluation of the imputed cost of airlift in different periods. 7 pp. P-1780: The Use of Man-Machine Simulation in the Design of Control Systems. AUTH: M.A. Geisler PAGES: 16, DATE: 1959 COST: $ 4.00 ABST: A discussion of control systems in the Air Force context. These are man-machine systems intended to assist the control organization in planning and directing the use of its resources so that the objectives of the organization can best be realized. Future control systems demand much of their designers in terms of flexibility, capability, and responsiveness. Such characteristics are essential for designing systems so far in advance of actual time of use. Simulation techniques, using man and machine methods, provide an effective means of helping the designer to develop system specifications for the range of uncertainties that can be identified at this time. They also provide concrete representations for developing the confidence of the consumer in the capability of the proposed system design. P-1793: A New Book on East German Trade. AUTH: H. Mendershausen PAGES: 5, DATE: 1959 COST: $ 4.00 KEYS: Germany (East); Economics--Foreign; International trade and finance ABST: A review of Erich Klinkmuller's new book on the foreign trade system of Soviet-occupied Germany ([Die Gegenwartige Aussenhandelsverflechtung der Sowjetischen Besatzungszone Deutschlands], Berlin, 1959). The book offers a statistical study of East German foreign economic relations, particularly with the Soviet Union and the Soviet Bloc. It discusses various theoretical and institutional aspects of these relations, such as the problems of planning foreign trade, the dichotomy of internal and foreign trade prices, the dominant role of the Soviet Union in East German economic policy, bilateralism, and economic coordination within the Bloc. The review concludes that this monograph is one of the best studies of the East German economy. 5 pp. P-1808: Simulation Techniques. AUTH: M.A. Geisler PAGES: 9, DATE: 1959 COST: $ 4.00 ABST: A talk presented before the International Air Transport Association at Paris, France, September 4, 1959, which discusses how the Air Force is attempting to substitute better management for larger resource expenditures. Simulation is shown as a powerful planning tool. Its design, construction, and use requires the application of many skills. Some of the complex requirements of this work are a knowledge of the real-world environment, mathematical training to design simulation models, accounting people and others to provide data for the model, computing people to program and compute with the models, and analysts to interpret the results and control the experiment. P-1826: A Structural Approach to Military Air Transportation. AUTH: W.A. Niskanen, R.B. Rainey PAGES: 14, DATE: 1959 COST: $ 4.00 KEYS: Airlift ABST: A 1959 discussion of the use of various operations research techniques to determine the nature and magnitude of the major military airlift missions and the best combination of aircraft and trained personnel to perform these missions. The approach used considers the strong tradeoff between flying hours and fleet composition, evaluates the potential contribution of the commercial fleet in the context of planning for the military fleet, and separates mission requirements into discrete periods to permit evaluation of the imputed cost of airlift in different periods. 14 pp. RM-2303-PR: A SAC Alert Concept for the Immediate Future. AUTH: R.A. Levine, R.B. Rainey PAGES: 34, DATE: 1959 COST: $ 4.00 ABST: Proposals that are expected to triple SAC's deterrent and retaliatory ability by modifying its alert and maintenance concepts. A maintenance policy is discussed that removes some maintenance impediments to a high state of alert and would provide SAC with a round-the-clock, seven-days-per-week maintenance policy. An alert policy is examined that helps minimize the effects of the remaining maintenance impediments, keeps all operationally ready airplanes not actually flying equipped with special weapons and fueled, and places as many airplanes as possible on alert status. The additional costs of these proposals would be small compared with the present total cost of operating the B-52 force, or compared with the value of the increase in effective aircraft. RM-2391-PR: Notes on Posture and Vulnerability of United States Air Forces in Europe. AUTH: J.W. Ellis, T.E. Greene PAGES: 58, DATE: 1959 COST: $ 7.50 ABST: A review of and commentary on previous RAND studies dealing with the preservation of a theater air capability in Western Europe in the early 1960's. In particular, the study examines USAFE combat systems, their vulnerability characteristics to enemy nuclear attack, and ways to reduce this vulnerability. Possible future developments in the problem of theater airpower are also discussed. P-1856-RC: Economic Welfare and the Allocation of Resources for Invention. AUTH: K.J. Arrow PAGES: 23, DATE: 1959 COST: $ 4.00 KEYS: Economics--Domestic; Innovation; Research and development; Technology ABST: A discourse on invention, defined broadly as the production of knowledge. From the viewpoint of welfare economics, determining optimal resource allocation for invention will depend on the technological characteristics of the invention process and on the nature of the market for knowledge. It is shown that the competitive system fails to achieve an optimal resource allocation in the case of invention because of increasing returns, inappropriability, and uncertainty. For an optimal allocation to invention, it is necessary for the government or some other agency not governed by profit-and-loss criteria to finance research and invention. A discourse on invention, defined broadly as the production of knowledge. From the viewpoint of welfare economics, determining optimal resource allocation for invention will depend on the technological characteristics of the invention process and on the nature of the market for knowledge. It is shown that the competitive system fails to achieve an optimal resource allocation in the case of invention because of increasing returns, inappropriability, and uncertainty. For an optimal allocation to invention, it is necessary for the government or some other agency not governed by profit-and-loss criteria to finance research and invention. 23 pp. RM-2396: On Control of Reactor Shutdown Involving Minimal Xenon Poisoning. AUTH: M. Ash, R.E. Bellman, R.E. Kalaba PAGES: 20, DATE: 1959 COST: $ 4.00 ABST: An application of the theory of dynamic programming to the control of reactor shutdown involving minimal xenon poisoning. After a high-flux thermal nuclear reactor is shut down, the con- centration of fission product xenon may rise for many hours as a result of the decay of fission product iodine into xenon-135. This results in reactor poisoning and may, with consequent loss of efficiency, postpone the time at which the reactor may be restarted. This poisoning may be minimized by carefully controlling the rate at which the neutron flux is decreased during the shut-down operation. The study shows how dynamic programming, assisted by high-speed digital computers with large memories, determines optimal control in this situation. RM-2451: A Model for Assessing the Effect of Maintenance on Missile Launch Probability. AUTH: E.E. Bean, W.H. McGlothlin, W.H. McGlothlin PAGES: 41, DATE: 1959 COST: $ 4.00 ABST: An analytical model designed as a tool to measure the effects of various operational modes and maintenance policies on ballistic-missile launch probability. The model is concerned with two elements of maintenance policy: operational mode and checkout frequency. The probability that the missile is alert when a launch order is given and will survive the countdown without failure is calculated as a function of these two variable elements of maintenance policy. Although the model itself cannot determine an optimal maintenance policy, the logistics planner is aided in selecting one that will produce the maximum probability of launch in a prescribed time period and in evaluating the effect of preferred policies on launch capability. No abstract available. 41 pp. P-1696: An Analytical Model for Developing Optimal Ballistic Missile Maintenance Procedures. AUTH: E.E. Bean, W.H. McGlothlin, W.H. McGlothlin PAGES: 23, DATE: 1959 COST: $ 4.00 ABST: An analytical model to determine the probability that the missile system is in an alert condition and that it will survive the countdown and launch phase with 0, 1, 2,..., n delays of known duration. Both of these aspects are examined for several sets of maintenance schedules and operational modes, allowing a determination of the set of conditions producing a maximum probability of a successful launch within a fixed period of time. When used in conjunction with vulnerability considerations, this model is a useful tool for obtaining the relationship between mode of operation, maintenance policy, and system effectiveness. RM-2319: On the Computational Solution of Dynamic Programming Processes-XI: A Feedback-Control Problem. AUTH: R.E. Bellman, S.E. Dreyfus PAGES: 13, DATE: 1959 COST: $ 4.00 ABST: A computational solution, by means of sequences of functions of one variable, to a problem typical of those arising in the design of feedback-control circuits. The usual functional-equation technique of dynamic programming is shown to lead to a computation involving sequences of functions of two variables. The specific problem considered is that of determining the function v(t) to minimize the functional <> and <>. Some numerical results are given. 13 pp. RM-2354: On the Application of Dynamic Programming to a Class of Implicit Variational Problems. AUTH: R.E. Bellman, J.M. Richardson PAGES: 18, DATE: 1959 COST: $ 4.00 ABST: An illustration of the applicability of the functional-equation technique of dynamic programming to the computational solution of implicit variational problems. Questions of this type arise in connection with the problem of landing a rocket on the moon, or on another planet, with minimum terminal velocity, and in connection with problems involving minimum miss-distance. 18 pp. P-1176: Functional Approximations and Dynamic Programming. AUTH: R.E. Bellman, S.E. Dreyfus PAGES: 12, DATE: 1959 COST: $ 4.00 ABST: Ways in which the theory of approximation can be used to increase the range of present-day computers. An attempt is made to trade additional computing time, which is expensive, for additional memory capacity, which does not exist. Although primary interest is in applying these techniques to the functional equations occurring in dynamic programming theory, the same methods are applicable to the classical functional equations of mathematical physics. 12 pp. P-1463: An Application of Dynamic Programming to the Determination of Optimal Satellite Trajectories. AUTH: R.E. Bellman, S.E. Dreyfus PAGES: 18, DATE: 1959 COST: $ 4.00 ABST: A discussion of a simplified satellite trajectory problem, corresponding to a flat earth assumption, first treated by Okhotsimskii and Eneev. A numerical solution based on the functional-equation technique of dynamic programming is presented, together with a proof of the fundamental result in the analytic solution. The same computational approach can be applied to more realistic trajectory problems. 18 pp. P-1550-RC: Some Mathematical Aspects of Chemotherapy-I: One-Organ Models. AUTH: R.E. Bellman, J.A. Jacquez, R.E. Kalaba PAGES: 27, DATE: 1959 COST: $ 4.00 KEYS: Chemotherapy; Mathematics; Physiology ABST: The first of a series of papers discussing the qualitative and quantitative aspects of chemotherapy, the treatment of disease through the use of chemical reagents that kill specific types of cells while leaving the patient relatively unpoisoned. Specifically, the series deals with the distribution of a compound in the organs of the body after its injection into the blood stream. The present study considers several simplified mathematical models in which the heart pumps blood to just one organ. It is hoped ultimately to find the characteristics of the most efficacious drugs to use and the manner of their injection. A discussion of models designed to study concentrations of a reagent injected into the blood stream of a relatively simple system consisting of the heart and one organ. Even at this level, there are formidable mathematical problems involving systems of linear and nonlinear parabolic differential equations with time lags in the boundary condition. 27 pp. P-1614: Invariant Imbedding, Random Walk, and Scattering-II: Discrete Versions. AUTH: R.E. Bellman, R.E. Kalaba PAGES: 19, DATE: 1959 COST: $ 4.00 ABST: An extension of P-113, Random Walk, Scattering, and Invariant Imbedding-I: One-dimensional Discrete Case, which applies the techniques of invariant imbedding to various random-walk processes and to questions of scattering theory. The present paper shows how the ideas presented in the earlier study enable multidimensional, time-dependent, and energy-dependent processes to be treated. A remarkable formal equivalence holds in all of these cases, with the result that the same equations occur repeatedly in different variables. Both new analytic and new computational approaches are achieved. Only the discrete versions of these processes are considered. 19 pp. P-1643: Functional Equations and Successive Approximations in Linear and Nonlinear Programming. AUTH: R.E. Bellman PAGES: 38, DATE: 1959 COST: $ 4.00 ABST: An illustration of the applicability of functional equations and successive approximations to various classes of multidimensional maximization problems. The advent of the modern digital computer makes it particularly appropriate that this synthesis of new and old be made. By suitably combining classical and modern devices, many challenging, complex, and significant problems can be solved. 38 pp. P-1699: A Mathematical Theory of Adaptive Control Processes. AUTH: R.E. Bellman, R.E. Kalaba PAGES: 5, DATE: 1959 COST: $ 4.00 ABST: The construction of a general mathematical framework, using the techniques of the theory of dynamic programming, for application to the study of adaptive control processes. 5 pp. P-1700: Invariant Imbedding and Neutron Transport in a Rod of Changing Length. AUTH: R.E. Bellman, R.E. Kalaba, G.M. Wing PAGES: 5, DATE: 1959 COST: $ 4.00 ABST: A study which uses the method of invariant imbedding to analyze a one-dimensional neutron transport process in which the length of a rod of fissionable material varies in a known way as a function of time. This step is preparatory to one in which Stefan-type problems will be studied through use of invariance principles. P-1766: What Is Dynamic Programming?. AUTH: R.E. Bellman PAGES: 27, DATE: 1959 COST: $ 4.00 ABST: A description of the theory of dynamic programming as the study of multistage decision processes. An attempt is made to explain a multistage process that is a natural extension of semigroups of operations and to illustrate this process by means of the familiar difference and differential equations. To indicate the range and versatility of the functional-equation approach to multistage decision processes, the study considers some maximization problems taken from calculus; some trajectory problems of the type that occur in the study of rockets, satellites, and space travel; a typical feedback control problem of the type current in modern electronic engineering; and an interesting class of multistage games, "games of survival." P-1778: Dynamic Programming and Feedback Control. AUTH: R.E. Bellman, R.E. Kalaba PAGES: 17, DATE: 1959 COST: $ 4.00 ABST: An application of the functional equation approach of dynamic programming to deterministic, stochastic, and adaptive control processes. The paper assumes that feedback control processes are multistage decision processes and that problems in the calculus of variations are continuous decision problems. Emphasis is on the development of methods well suited for high-speed digital computation. P-1804: Dynamic Programming and Classical Analysis. AUTH: R.E. Bellman PAGES: 22, DATE: 1959 COST: $ 4.00 ABST: A consideration of questions in analysis that arise naturally out of the functional-equation technique of dynamic programming. It is shown that this theory constitutes a natural extension of classical investigations and that the corresponding problems of classical analysis. Emphasis is on deterministic processes. P-1843: Functional Equations in the Theory of Dynamic Programming--XI: Limit Theorems. AUTH: R.E. Bellman PAGES: 7, DATE: 1959 COST: $ 4.00 ABST: A presentation of a limit theorem valid for a general class of Markovian decision processes. The result is of interest because of the simple conditions imposed and the rather simple argument used. R-336-RC: Research and the Ulcer Problem. AUTH: I.S. Blumenthal PAGES: 90, DATE: 1959 COST: $ 7.50 KEYS: Health--Research; Ulcers ABST: A report on one particular group of chronic diseases: the ulcerative disorders of the gastro-intestinal tract. The group includes peptic ulcer and ulcerative colitis. An attempt is made to answer questions concerning the social magnitude of the problem, the adequacy of current medical solutions, and the scope of certain research efforts in the ulcerative-disorder field. Money devoted to research in this area has been less than 1 per cent of the estimated economic loss to the nation because of these diseases. It is hoped that this analysis may be of interest to governmental agencies and private foundations supporting research in the biomedical field. A report on one particular group of chronic diseases: the ulcerative disorders of the gastrointestinal tract. The group includes peptic ulcer and ulcerative colitis. An attempt is made to answer questions concerning the social magnitude of the problem, the adequacy of current medical solutions, and the scope of certain research efforts in the ulcerative-disorder field. Money devoted to research in this area has been less than 1 percent of the estimated economic loss to the nation because of these diseases. It is hoped that this analysis may be of interest to governmental agencies and private foundations supporting research in the biomedical field. 90 pp. P-1623: Reliability, Quality Control, and Simulation. AUTH: A.S. Cahn PAGES: 15, DATE: 1959 COST: $ 4.00 KEYS: Computer simulation; Reliability ABST: An examination of the reliability, quality control, and simulation factors affecting an enterprise to determine the interrelationships among the various parameters and the cost and operational effectiveness of the given system. It is concluded that (1) finding the value of reliability or of quality control is complex; (2) simulation helps not only to indicate the complete relationship of reliability and quality control to the specific objectives of an enterprise, but also to obtain the probable reliability of a proposed system; (3) a useful simulation of any large complex enterprise must be carefully designed; and (4) one useful method for designing such a simulation is to use simultaneously a man-machine model and an all-machine model. 15 pp. P-1586: Random Simulation of an Air Base Inventory Control System for a Reparable Part. AUTH: H.S. Campbell PAGES: 25, DATE: 1959 COST: $ 4.00 ABST: A description of a random sampling simulation (or Monte Carlo) model of an inventory control system for a single commodity. The system represented is the spare parts supply function of an Air Force base. This model may serve as a computational aid for simulating the response of a complex inventory system under varying conditions of uncertainty. The variables considered are the base resupply time for both routine and priority requisitions, the degree of reliance placed on base maintenance, and the relationship between supply decision rules, or stockage policies, and the demand prediction technique used. No abstract available. 25 pp. P-1689: The Use of Numerical Simulation in the Development of Inventory Policy. AUTH: H.S. Campbell PAGES: 13, DATE: 1959 COST: $ 4.00 ABST: A discussion of the role of numerical simulation in the development of inventory policy. Numerical simulation is a computational program, reproducing the structure of a real-world organization, or of a simplified model of the organization. The advantages and disadvantages of analysis by simulation are described, as well as a random-sampling simulation model of an inventory system. This model is applied (1) to the effect on the costs of operating an inventory system when severe initial uncertainty exists concerning the mean demand rate or other demand characteristics and (2) to the effect of the inefficiencies resulting from the use of statistical estimates as the basis for setting stock levels. RM-2310-ARPA: A Survey of Current Research in Gaseous Electronics in the United States. AUTH: W.H. Culver, R. Geballe, P. Tamarkin, R. Geballe, P. Tamarkin PAGES: 103, DATE: 1959 COST: $ 10.00 KEYS: Atmosphere; Electronics; Geophysics; Wave mechanics ABST: A survey of current and projected research on gaseous electronics in various laboratories in the United States, with some comments on the relation of atomic and ionic impact phenomena to the propagation of electromagnetic waves in the upper atmosphere. A survey of current and projected research on gaseous electronics in various laboratories in the United States, with some comments on the relation of atomic and ionic impact phenomena to the propagation of electromagnetic waves in the upper atmosphere. 103 pp. (See also RM-2309.) RM-2321: On a Linear-Programming-Combinatorial Approach to the Traveling-Salesman Problem: Notes on Linear Programming and Extensions-Part 49. AUTH: G.B. Dantzig, D.R. Fulkerson, S.M. Johnson, D.R. Fulkerson, S.M. Johnson PAGES: 26, DATE: 1959 COST: $ 4.00 ABST: A demonstration that the linear-programming- combinatorial approach, wherein simplex multipliers are used in a combinatorial analysis of undominated tours at some stage of the linear-programming approach, affords a practical way of solving traveling-salesman problems. No abstract available. 26 pp. RM-2519: A Mathematical Model of the Human External Respiratory System. AUTH: G.B. Dantzig, J.C. DeHaven, I. Cooper, S.M. Johnson, E.C. DeLand, H.E. Kanter, C.F Sams PAGES: 109, DATE: 1959 COST: $ 10.00 KEYS: Computer simulation; Respiration NOTE: Also published as P-1811. See also P-2048 and P-2139. ABST: The results of a mathematical simulation of the external respiratory function to illustrate the thesis that important subsystems of the human body can be studied by mathematical programming techniques that have been used to program and control complex military and industrial systems. The model constructed shows the process occurring when air is breathed and mixed with venous blood in the lungs, which results in exhaled air and arterial blood. From the long-range viewpoint, such simulation may provide a powerful new tool for biological investigations. The results of a mathematical simulation of the external respiratory function to illustrate the thesis that important subsystems of the human body can be studied by mathematical programming techniques that have been used to program and control complex military and industrial systems. Two mathematical models were set up to represent the more important of the known interrelated physiological functions and chemical reactions involved in the human respiratory system. Model I uses a simplified concept of the hemoglobin molecule, and Model II is based on Linus Pauling's theory of the complex hemoglobin molecular structure. P-1345: On the Shortest Route Through a Network. AUTH: G.B. Dantzig PAGES: 8, DATE: 1959 COST: $ 4.00 ABST: A procedure for finding the shortest route from a given origin to all other nodes in the network or to a particular destination point when little effort is required to arrange distances in increasing order by nodes or to skip consideration of arcs into nodes whose shortest route to the origin has been determined earlier in the computation. It is shown that n(n-1)/2 comparisons are needed to obtain the shortest route from a given origin to all other nodes and less between two fixed nodes. No abstract available. 8 pp. P-1486: On the Significance of Solving Linear-Programming Problems with Some Integer Variables. AUTH: G.B. Dantzig PAGES: 28, DATE: 1959 COST: $ 4.00 ABST: A discussion of recent proposals by Gomory and others for solving linear programs involving integer-valued variables. Problems that can be reduced to this class, and thereby solved, are reviewed. It is significant that the reduction can be made for problems involving multiple dichotomies and k-fold alternatives. These problems include those with discrete variables, nonlinear separable minimizing functions, conditional constraints, global minimum of general concave functions, and combinatorial problems such as the fixed-charge problem, traveling-salesman problem, orthogonal latin-square problems, and map-coloring problems. No abstract available. 28 pp. P-1502: A Machine-Job Scheduling Model. AUTH: G.B. Dantzig PAGES: 12, DATE: 1959 COST: $ 4.00 ABST: A discussion of a device proposed by Fulkerson and Ford for maximal multi-commodity network flows. A machine-job scheduling model is formulated that avoids the usual in-process inventories and that has fewer equations. The activities are the possible sequence, for each job, of machine steps and interspersed delays which greatly multiply the number of activities. However, a compact network representation of the set of possible activities is developed which permits the generating of just the activity to enter the basis on each iteration without explicitly generating the others. This is accomplished by using one of the efficient procedures that now exist for computing the shortest route through a network. No abstract available. 12 pp. P-1545: Computing Tetraethyl Lead Requirements in the Linear Programming Format. AUTH: G.B. Dantzig, T.K. Kawarantani, R.J. Ullman, T.K. Kawarantani, R.J. Ullman PAGES: 13, DATE: 1959 COST: $ 4.00 ABST: A discussion of some types of non-linearities that are difficult to incorporate into a linear programming model. One of these occurs in the scheduling of refinery operations where linear programming methods are widely used. The specific problem is one of determining simultaneously the quantities of various components of gasoline and tetraethyl lead to blend to form regular or premium type gasolines. It is believed that the general approach can be used for other non-linear situations. Linearization is accomplished by viewing the lead requirements of a blend first as a known general function of two variables, each of which is a linear function of the quantities in the blend. The general function is approximated by a convex linear combination of a mesh of representative points. No abstract available. 13 pp. P-1646: New Directions in Mathematical Programming. AUTH: G.B. Dantzig PAGES: 12, DATE: 1959 COST: $ 4.00 ABST: An introductory talk for the RAND Mathematical Programming Symposium, held at Santa Monica, California, March 16-20, 1959. The paper reviews the practical and theoretical developments of linear programming during the past 12 years and discusses the current extensions of this tool into areas of special structures, discrete programming, network theory, nonlinear programming, and uncertainty. No abstract available. 12 pp. P-1664: General Convex Objective Forms. AUTH: G.B. Dantzig PAGES: 19, DATE: 1959 COST: $ 4.00 ABST: A study concerned with the minimization of a general convex objective form subject to linear inequality restrictions. An alternative procedure is developed that has points in common with those given in P-1544 on the decomposition principle for linear programs. The general convex objective form, however, leads to an infinite algorithm and requires a special proof of convergence. The special devices used in the proof can also be applied to show convergence of the simplex algorithm for infinite programs. No abstract available. 19 pp. P-1625-RC: Some Economic Features of Public Education. AUTH: J.C. DeHaven PAGES: 16, DATE: 1959 COST: $ 4.00 KEYS: Alternative schools; Education ABST: A talk presented on March 11, 1959, to the Council of Directors and Supervisors of the Los Angeles City Board of Education. Granting the case for a minimum compulsory education for everyone and public financial support for this minimum education, the desirability of the sole operation of the school system by public entities is questioned. Public financial support of private schools and the freedom of choice of schools by students within the system could bring about an improvement in the quality and productivity of both public and private schools. This improvement could be achieved through the reinstitution of the merit and differential pay system for teachers, ensuring that the skilled, competent people would remain in the school system and that the best young people would be attracted to education as a career. A talk presented on March 11, 1959, to the Council of Directors and Supervisors of the Los Angeles City Board of Education. Granting the case for a minimum compulsory education for everyone and public financial support for this minimum education, the desirability of the sole operation of the school system by public entities is questioned. Public financial support of private schools and the freedom of choice of schools by students within the system could bring about an improvement in the quality and productivity of both public and private schools. This improvement could be achieved through the reinstitution of the merit and differential pay system for teachers, ensuring that the skilled, competent people would remain in the school system and that the best young people would be attracted to education as a career. 16 pp. P-1833: The Simple Mathematics of Maximization. AUTH: A.C. Enthoven PAGES: 70, DATE: 1959 COST: $ 7.50 KEYS: Economics--Domestic; United states--Military planning ABST: An economic approach to the problem of military choice (namely, that of allocating a fixed budget among alternative strategic weapon systems, or of finding the maximum of some relevant measure of strategic airpower, given the limitation of a fixed budget). The complexity of military choice is discussed in terms of criterion selection, values, and intangibles, and in terms of risk and uncertainty about nature, technology, and enemy reactions. As no simple formal model of choice is sufficient for a satisfactory analysis of most real military problems, this paper formulates part of the problems of choice in economic terms, that is, in terms of discovering the most effective uses of limited resources. 70 pp. P-1638: The Application of Random Sampling Simulation to Reliability Estimating. AUTH: S.I. Firstman PAGES: 27, DATE: 1959 COST: $ 4.00 KEYS: Forecasting; Monte carlo method; Reliability ABST: A discussion of the applicability of random sampling simulation to the problem of predicting "drift" failures. Drift failures are defined as system malfunctions occurring because the entire system, with its many interdependencies, performs at a level outside design limits. In particular, the study applies the Monte Carlo method to the problem of predicting system performance based on component performance data and subsystem or "black-box" performance data. The technique permits the integration into one model of all known stresses--environmental and operational--and other events affecting the system operation. Therefore, for a properly designed and executed Monte Carlo experiment at any level of aggregation, the derived performance estimates will be unbiased estimates of the actual system performance. 27 pp. P-1678: An Approximating Algorithm for an Optimum Aim-Points Problem. AUTH: S.I. Firstman PAGES: 28, DATE: 1959 COST: $ 4.00 ABST: An algorithm that will yield approximate solutions in integers for the problem of assigning missiles to aim points so as to maximize the resultant expected target destruction. The target complex is such that a weapon aimed at one target can destroy another, or a weapon aimed between several targets can destroy more than one. A precise statement of the algorithm and an example of its use are given. P-1839: Ballistic-Missile Payload Allocation. AUTH: S.I. Firstman PAGES: 22, DATE: 1959 COST: $ 4.00 KEYS: Ballistic missiles; Uncertainty ABST: A method for determining for a ballistic missile the optimum division of weight allocation to warhead, guidance, and penetration aids when the weight-effectiveness relationships of the individual elements are known for an attack against a defended point target. The use of this method shows the influence of the estimate uncertainties on the optimal payload division and may be helpful in design compromise procedures. A method for determining for a ballistic missile the optimum division of weight allocation to warhead, guidance, and penetration aids when the weight-effectiveness relationships of the individual elements are known for an attack against a defended point target. The use of this method shows the influence of the estimate uncertainties on the optimal payload division and may be helpful in design compromise procedures. 22 pp. P-1857: Optimum Search Routines for Automatic Fault Location. AUTH: S.I. Firstman, B. Gluss PAGES: 18, DATE: 1959 COST: $ 4.00 ABST: A study concerned with automatic equipment that is being developed to diagnose malfunctions in equipment and to locate faulty parts. For use as an adjunct to the usual engineering-logic method of programming for fault location, this paper develops search rules, founded on probabilistic concepts, that show the preferred order of conducting tests to find the fault in the shortest time. A two-step search process is used, finding first the faulty module, and then the faulty component within the module. No abstract available. 18 pp. P-1415: A First Experiment in Logistics System Simulation. AUTH: M.A. Geisler PAGES: 50, DATE: 1959 COST: $ 4.00 KEYS: Logistics; Models ABST: An overall picture of Laboratory Problem I (LP-I), which tested a series of proposed changes to the Air Force supply system. Such aspects are discussed as the experimental design of LP-I, various policies, the preparations for the Laboratory run, the operation of LP-I, peacetime results, the LP-I war, and Laboratory management experience. The experiment indicated that the logistics system containing the newer supply policies was better and that this type of simulation developed many more insights into the operation of proposed policies than traditional analytical techniques provide normally. (Published in the [Naval] [Research Logistics Quarterly], March 1960.) 50 pp. P-1615: Communications and Control Requirements in the Air Force Logistics System. AUTH: M.A. Geisler PAGES: 19, DATE: 1959 COST: $ 4.00 ABST: A discussion of the role of the communications and control system in Air Force logistics as one of the tools available to Air Force management in attaining its goals for future weapon systems. The operational setting within which communications and control systems must be developed is examined. The present status and future outlook of these systems are presented, and the use of simulation is described as a research tool for studying communications and control systems. No abstract available. 19 pp. P-1634: Integration of Modeling and Simulation in Organizational Studies. AUTH: M.A. Geisler PAGES: 17, DATE: 1959 COST: $ 4.00 ABST: A study of military logistics in which a Monte Carlo model is used to formulate a hypothesis about the characteristics of a logistics organization that will significantly reduce the cost of logistics support with no loss in support effectiveness. This hypothesis is developed so that the resulting organization, policies, and information system can be tested in a realistic man-machine simulation and compared with an alternative system. The simulation produces data showing the feasibility and desirability of the proposed organization. An analytical representation of the simulation is constructed to establish the range of parameter values over which the advantages of the proposed system persist. The paper emphasizes the relative roles that can be played by machine models and man-machine simulation in research directed toward designing preferred and compatible organizational structures, policies, and integrated information flows and communications design. No abstract available. 17 pp. RM-2301: The Deterrence and Strategy of Total War, 1959-1961--a Method of Analysis. AUTH: H. Goldhamer, A.W. Marshall, N.C. Leites PAGES: xvii, 195, DATE: 1959 COST: $ 15.00 KEYS: Deterrence (Strategy); United States--Military policy RM-2309-ARPA: Availability of Upper Atmospheric and Other Selected Data from the IGY. AUTH: S.M. Greenfield PAGES: 57, DATE: 1959 COST: $ 7.50 KEYS: International Geophysical Year, 1957-1958 ABST: A survey of the United States IGY data-collecting activities pertaining to the geophysics of the upper atmosphere. Our data centers and programs in the ionosphere, aurora, cosmic rays, solar activity, and geomagnetism are described. The IGY rocket and satellite program is discussed, and the need for more extensive data analysis by the United States is indicated. (See also RM-2310.) 57 pp. RM-2320: A Mechanical Proof of the Min-Max Theorem. AUTH: O.A. Gross PAGES: 19, DATE: 1959 COST: $ 4.00 KEYS: Game theory ABST: A description of a machine that solves finite games. The study considers the components of the device to obtain a novel mechanical "proof" of the min-max theorem for finite games based on the laws of statics. A description of a machine that solves finite games. The study considers the components of the device to obtain a novel mechanical "proof" of the minmax theorem for finite games based on the laws of statistics. 19 pp. P-1751: Computing and Education. AUTH: F.J. Gruenberger, F. Gruenberger PAGES: 9, DATE: 1959 COST: $ 4.00 KEYS: Computers; Higher education; Training ABST: A discussion of such aspects of the relation between computers and educators as (1) the role of a computing center on a university campus and (2) some conjectures as to the proper method of training computer programmers. A discussion of such aspects of the relation between computers and educators as (1) the role of a computing center on a university campus and (2) some conjectures as to the proper method of training computer programmers. 9 pp. P-1563: A Mathematical Model for Multiplication by Binary Fission. AUTH: T.E. Harris PAGES: 35, DATE: 1959 COST: $ 4.00 ABST: An explanation of the use of the "point of regeneration" in the mathematical treatment of the multiplication of biological cells by binary fission. No abstract available. 35 pp. P-1666: A Lower Bound for the Critical Probability in a Certain Percolation Process. AUTH: T.E. Harris PAGES: 20, DATE: 1959 COST: $ 4.00 ABST: A study that considers the lattice in the Cartesian plane consisting of all points (x, y) such that either x or y is an integer (positive, negative, or zero). The sides of the unit squares are called links. Each link is designated "active" with probability p or "passive" with probability 1 - p, independently of all other links. It is shown that if <>, then the probability is 0 that there is a connected infinite set of active links. No abstract available. 20 pp. P-1627: Approximation Techniques in Dynamic Programming. AUTH: C. Hastings, C. Hastings PAGES: 15, DATE: 1959 COST: $ 4.00 ABST: A paper concerned with the numerical solution of the functional equation <> over the interval (0,1), as part of a study on numerical methods in dynamic programming. The ideas that led to the solution are also discussed. No abstract available. 15 pp. P-1685: The Aggregation of Servicing Facilities in Queueing Processes. AUTH: J.W. Hooper, D.S. Stoller, D.S. Stoller PAGES: 11, DATE: 1959 COST: $ 4.00 ABST: A paper concerned with the problem of finding the conditions under which individual service facilities should be aggregated to perform a certain workload in an optimal way, on the basis of whether personnel should work as individuals or teams. This is a problem of widespread application to the many production or repair activities characterized by a stochastic flow of workload units through a service facility. The problem does not yield to intuitive reasoning, since the decision depends on the value of the parameters of the distributions involved as well as on the efficiency of the team. The basic model used is the standard queueing model with an infinite population of units whose arrival at the service facilities and whose servicing are characterized by a Poisson distribution. P-1807: Tables of the Binomial Probability Distribution <> for Large N and Small P. AUTH: D.S. Hopp, J. Warshaw, M. Warshaw PAGES: 90, DATE: 1959 COST: $ 7.50 ABST: The title of this paper describes its contents. P-1741: Peaceful Atomic-Energy Programs in Soviet Bloc Nations. AUTH: A.M. Jonas PAGES: 33, DATE: 1959 COST: $ 4.00 KEYS: China; Communist countries; Soviet Union--Science ABST: A 1959 study concerned with the peaceful sharing of atomic energy in the previous four years by the Soviet Union with certain nations of the Soviet Bloc. Progress varied from country to country according to the degree of economic and political stability, the level of industrialization, and other factors. These nations remained closely dependent on technical assistance from the Soviet Union, although all of them wanted their own atomic-power stations eventually. Developments in East Germany, Czechoslovakia, Poland, Communist China, Hungary, Romania, and Bulgaria are reviewed. 33 pp. RM-2415: The Flight Operations Planner. AUTH: W.M. Jones, M.F. Shapiro, N.Z. Shapiro PAGES: 98, DATE: 1959 COST: $ 7.50 KEYS: Computer simulation; Operations research ABST: A study that examines the problems involved in planning the operations of large numbers of high- performance aircraft and that describes the role of the Flight Operations Planner (FLIOP). FLIOP is a digital computer program designed to reduce significantly the amount of time and effort necessary in calculating detailed flight plans for individual aircraft. By using FLIOP, the human planner can concentrate more on the general objectives considered and still retain the assurance that the final result is feasible. Although the B-47 and KC-97 aircraft are used for illustrative purposes, the techniques described are equally applicable to the various models of the B-52, B-58, B-66, KC-135, KB-50, F-101, C-124, C-130, and C-133, and can be applied to any fixed-wing-type aircraft. P-1723: Machine Analysis Methods for Network Vulnerability Problems. AUTH: M.L. Juncosa PAGES: 25, DATE: 1959 COST: $ 4.00 ABST: A review of some optimization problems involving communication networks that are usually of such size as to require a high-speed computer for solution. Some parallelisms and translations between different problems are also illustrated. P-1809: Some Aspects of Adaptive Control Processes. AUTH: R.E. Kalaba PAGES: 18, DATE: 1959 COST: $ 4.00 ABST: A study of adaptive control processes that shows how the functional-equation technique of dynamic programming can be used in their analytical and computational treatment. Several adaptive control processes pertaining to a system governed by an inhomogeneous Van der Pol equation are discussed, one of which involves optimal control of the system with an objective that is only partially known to the controller. RM-2374: The Base Maintenance-Operations Model Used in RAND Logistics Research. AUTH: R.A. Levine, R.B. Rainey, R.B. Rainey PAGES: 48, DATE: 1959 COST: $ 4.00 KEYS: Bases; Logistics; Logistics--Mathematical models; Maintenance; Operations KEYS: research ABST: A description of the model that RAND's Logistics Department uses in studying the interaction of aircraft operations and base-level logistics, particularly direct maintenance. This model (1) improves on past methods of estimating the effects of Air Force maintenance and operations policies, (2) simulates the random nature of real-world maintenance and operations events by using Air Force data on fixed numbers and probability distributions, and (3) produces data from which credible short-range predictions of the behavior of random phenomena become possible. These predictions result in reasonably accurate estimates of the effects of proper manning and of the immediate effects of policy changes. No abstract available. 48 pp. P-1423: Use of Tolerance Limits in Missile Evaluation. AUTH: A. Madansky PAGES: 15, DATE: 1959 COST: $ 4.00 ABST: A presentation of a use of tolerance limits in reliability analysis. Tolerance limits for normal and exponential distributions are given, as well as nonparametric tolerance limits. The latter are compared with the parametric limits, and further properties of the parametric limits are discussed. No abstract available. 15 pp. P-1596: Some Results and Problems in Stochastic Linear Programming. AUTH: A. Madansky PAGES: 20, DATE: 1959 COST: $ 4.00 ABST: A description of the results and problems in the ordinary "here-and-now" and "wait-and-see" stochastic linear-programming problems. A general formulation of the "here-and-now" problem is presented, and an approach for solving a special kind of "here-and-now" problem is suggested. No abstract available. 20 pp. P-1644: Partitioning Methods in Latent Class Analysis. AUTH: A. Madansky PAGES: 31, DATE: 1959 COST: $ 4.00 KEYS: Matrices--Theory; Numerical methods and approximations; Statistical KEYS: analysis ABST: A method for obtaining estimates of the parameters of the latent-class model based on first classifying individuals into "latent classes." Properties of the estimates and implications to the identifiability problem are discussed. An example is given of the use of the partitioning method as contrasted with the determinantal method. 29 pp. Ref. RM-2414: Dependence of East Germany on Western Imports. AUTH: H. Mendershausen PAGES: 59, DATE: 1959 COST: $ 7.50 KEYS: Germany (East); International trade and finance ABST: An attempt to determine the impact of a Western trade embargo against East Germany and the Soviet Bloc, an event that might be provoked by Soviet-backed East German measures against Berlin. The study discusses both the dependence of East Germany on trade with the West and the vulnerability of East Germany to allied economic countermeasures. The impact of such an embargo may depend in part on the forcefulness of Western responses in political and military fields in which economic countermeasures do not serve as substitutes. The outcome of a Bloc-wide embargo is dubious and must be weighed against the political difficulties of bringing it about. 59 pp. P-1642: A Comparison of Random and Periodic Data Sampling for the Detection of Signals in Noise. AUTH: D. Middleton PAGES: 31, DATE: 1959 COST: $ 4.00 ABST: An analysis, by means of probability theory, of the effect of using random rather than periodic data sampling in radar detection systems. In the specific examples examined, it is found that periodic sampling gives the better performance. No abstract available. 31 pp. P-1739: Review of Choh-Ming Li's Economic Development of Communist China (Berkeley, 1959). AUTH: R.H. Moorsteen PAGES: 7, DATE: 1959 COST: $ 4.00 KEYS: China ABST: A review of the book Economic Development of Communist China by Professor Li. The study is an economic analysis of the growth of the Chinese economy from 1952 to 1957 and ranges over almost every major aspect of Communist China's economy (namely, agricultural and industrial output, transportation, national product, investment, budget revenues and expenditures, and international trade). Individual topics on which Professor Li's discussion seems questionable are examined, and the need for finer focus and greater penetration is emphasized. However, the reviewer feels that this book is by far the best to appear on the subject and that one of its most valuable aspects is its extensive collection of economic statistics. P-1779: What Do We Mean by "Research and Development"?. AUTH: D. Novick PAGES: 50, DATE: 1959 COST: $ 4.00 KEYS: Research and development ABST: Suggestions as to how to effectively allocate resources to research and development. A real research effort-one basic in its approach-must be undertaken, and it must be directed toward long-range research. The nation must decide on its objectives and policy in order to establish meaningful classifications of research activities and measurements of the factors in their rate of growth and to determine the allocation of national resources being made to these varying and distinctive types of specialized activities. Suggestions as to how to effectively allocate resources to research and development. A real research effort--one basic in its approach--must be undertaken, and it must be directed toward long-range research. The nation must decide on its objectives and policy in order to establish meaningful classifications of research activities and measurements of the factors in their rate of growth and to determine the allocation of national resources being made to these varying and distinctive types of specialized activities. 50 pp. P-1803: The Federal Budget as an Indicator of Government Intentions and the Implications of Intentions. AUTH: D. Novick PAGES: 24, DATE: 1959 COST: $ 4.00 KEYS: Accounting and budgets; Government ABST: An examination of the budget structure as it existed in the 1950s from the standpoint of how well it indicated intentions of the government and the implications of these intentions. It is shown that this purpose of the budget is essentially synonymous with that aspect of the budgetary process associated with making major resource allocation decisions. In such a context, the budget structure was found deficient in several major respects. These deficiencies provide the basis for various suggestions on how the budget format might be improved. 24 pp. P-1725: Experimental Design, Test, and Evaluation of an F-100D Flyaway Kit. AUTH: B. Okun PAGES: 62, DATE: 1959 COST: $ 7.50 ABST: Part of a broader investigation concerned with flyaway kits, or sets of spare parts that enable squadrons to maintain their own airplanes for a given time period when cut off from outside supply and maintenance. Former RAND studies (RM-1490 and RM-2062) dealt with flyaway-kit tests for the B-47 and F-86H. The present paper describes the history and results of a subsequent kit test for the F-100D. It is hoped that from the F-100D results, even better flyaway kits will emerge. P-1824: The Mutual Attraction of Cloud Droplets in the Electrostatic Field of the Atmosphere. AUTH: J.D. Sartor PAGES: 20, DATE: 1959 COST: $ 4.00 KEYS: Clouds; Meteorology ABST: A discussion of the coalescence of cloud droplets that is necessary for the formulation of rain at temperatures above freezing. Upon colliding, larger water drops are commonly observed to rebound without coalescing unless electrostatic fields are present. This paper uses a theoretical solution by Dr. M. H. Davis for the force and field between two equal conducting spheres in a uniform field to compute the forces and fields between neighboring cloud droplets. The results explain the observed electrostatic coalescence. 20 pp. P-1829: Dynamic Similarity and the Modeling of Cloud Droplets. AUTH: J.D. Sartor PAGES: 6, DATE: 1959 COST: $ 4.00 KEYS: Clouds; Meteorology ABST: An investigation of the requirements for the laboratory modeling of the motion of cloud droplets, using the principles of dynamic similarity and the concepts of induced mass and hydrostatic buoyancy. It is concluded that cloud droplets can be successfully modeled in the laboratory as long as the Reynolds number is small with respect to 18 and that the results can be compared with Hocking's theoretical results when the Reynolds number is less than one. 6 pp. P-1716: Randomization of Threats and Promises. AUTH: T.C. Schelling PAGES: 13, DATE: 1959 COST: $ 4.00 KEYS: Game theory ABST: An investigation of randomization in non-zero-sum games. In its role of making indivisible objects divisible, or incommensurate objects homogeneous, randomization is relevant to threats and promises. In the illustrations given, a rationale is found for a "fractional threat." The paper also considers whether the tactic of "unconditional commitment" is one that in certain cases can advantageously be made less than certain. An investigation of randomization in nonzero-sum games. In its role of making indivisible objects divisible, or incommensurate objects homogeneous, randomization is relevant to threats and promises. In the illustrations given, a rationale is found for a "fractional threat." The paper also considers whether the tactic of "unconditional commitment" is one that in certain cases can advantageously be made less than certain. 13 pp. RM-2338: On Network Flow Functions: Notes on Linear Programming and Extensions-Part 50. AUTH: L.S. Shapley PAGES: 26, DATE: 1959 COST: $ 4.00 ABST: An investigation of the capacity of a network as a function of the capacities of its individual arcs. The case of two variable arcs is examined. It is found that in each pair of arcs they either con- sistently help each other or consistently hinder each other. Interaction types are computed for a number of special cases. No abstract available. 26 pp. P-1665: A Discussion of Several Concepts Used in the Optimization of Control Systems by Dynamic Programming. AUTH: F.T. Smith PAGES: 54, DATE: 1959 COST: $ 7.50 ABST: The application of dynamic-programming techniques to the optimization of control systems. The concepts of the state of a controlled element and the transition matrix are used to describe the behavior of the controlled element. The paper discusses various types of performance indexes or error criteria used to measure controlled element performance. The examples given involve the optimization of a simple linear sampled data servo system and an application to a controlled element, the behavior of which is described by the Van der Pol equation. No abstract available. 54 pp. P-1672: Measuring the Reliability of Equipments in Operating Environments. AUTH: D.S. Stoller PAGES: 8, DATE: 1959 COST: $ 4.00 ABST: A discussion of some of the concepts and problems applicable to the measurement of reliability. This term is described as encompassing a probability, an aggregate, an environment, a set of criteria, and a time interval. The interdependence of these reliability factors on operations, maintenance, and supply actions related to the equipments is examined from the viewpoint of designing a reliability measurement system. No abstract available. 8 pp. RM-2455: Misslogs: A Game of Missile Logistics. AUTH: B.J. Voosen, D.D. Corona, D.D. Corona PAGES: 14, DATE: 1959 COST: $ 4.00 KEYS: Games; Logistics; Missiles ABST: A description of a simple logistics management game, called Misslogs. The game was developed to illustrate the interactions among operations, supply, maintenance, and personnel in a ballistic-missile squadron. Like its forerunners, Monopologs and Baselogs, the game is an educational device. It is designed for logisticians involved in the support of missile programs. The game does not duplicate all the logistics problems of a missile-alert operation. However, it gives the player, who must work within a limited budget, a clear-cut view of the tradeoffs he can make to achieve maximum readiness. 21 pp. RM-2418: The Base Repair Cycle for the F-102 Fire Control System. AUTH: A. Weifenbach PAGES: 78, DATE: 1959 COST: $ 7.50 ABST: Data on the base repair cycle for the case of the F-102 fire-control system from Project FULL HOUSE and an attempt to indicate the supply implications. Several factors analyzed are the length of the base repair cycle and the percentages of malfunctions repaired at the base, requiring spare boxes and requiring parts in base repair. These malfunctions are classified into groups in which the boxes are sent to the depot for repair, are replaced with spares and sent to radar mockup for repair, are repaired and reinstalled in the same aircraft, and are repaired in aircraft or in field maintenance shops, not in mockup. In addition to furnishing inputs for other RAND research, this study may prove useful as a fund of basic information for Air Force logistics specialists interested in data of maintenance-operation interactions. No abstract available. 78 pp. RM-2413: War Gaming Methodology. AUTH: M.G. Weiner PAGES: 112, DATE: 1959 COST: $ 10.00 KEYS: Games; Logistics; War games ABST: A description of the methodology of the Project SIERRA war games, including air, sea, ground, and logistic factors, as well as political and economic aspects. This Memorandum is intended for use as a reference by small staffs studying limited war by means of war-gaming techniques. The author discusses (1) background material on the general nature and usefulness of war games, (2) the preparations needed for war-game exercises, (3) gaming, (4) the functions of the player and control teams and the procedures of play, and (5) game evaluation. As only war-gaming methods are considered, the results of the Project SIERRA limited-war studies are not included. 108 pp. P-1772: The Small World. AUTH: J.D. Williams PAGES: 24, DATE: 1959 COST: $ 4.00 KEYS: Mathematics; Social science ABST: Part of a broader investigation concerned with the place of mathematics in the changing society, prepared in response to an invitation from the National Council of Teachers of Mathematics. The Paper discusses the implications of certain striking features of our times, external and internal to our society, such as the rate of change of technology and population growth. The fact is emphasized that we have a lot of thinking to do and not much time to do it in and that it would be wise to make decisions and choices deliberately while there are real alternatives, rather than by default when there are none. 24 pp. (Published in The Saturday Evening Post, August 6, 1960. Also published in the second series of Adventures of the Mind, published by Alfred A. Knopf, New York, 1961, $6.50.) B-144: Command and Support Systems: Introduction. AUTH: J.D. Williams PAGES: 9, DATE: 1959 COST: $ 4.00 KEYS: Mathematics; Social science P-1583: Gains from Trade, Materials Supplies, and Economic Development. AUTH: C. Wolf PAGES: 20, DATE: 1959 COST: |c$7.50 KEYS: Economics--Foreign; United states--Economic assistance ABST: An assessment of the feasibility of the objectives of U.S. economic assistance to underdeveloped countries from the standpoint of their connection with economic development, defined in terms of secularly rising national income. The connection between economic development on the one hand, and, successively, U.S. terms of trade, volume of trade, and materials supplies on the other, is shown to be too uncertain for these to be practical objectives of development aid. Aid directed toward maximizing development will not necessarily maximize trade gains and materials supplies. Maximum development may even reduce U.S. gains from trade with, and U.S. materials supplies from, the underdeveloped countries. 20 pp. RM-2388: The Simplex Method for Quadratic Programming: Notes on Linear Programming and Extensions-Part 51. AUTH: P.S. Wolfe PAGES: 43, DATE: 1959 COST: $ 4.00 ABST: A computational procedure for finding the minimum of a quadratic function of variables subject to linear inequality constraints. The procedure is analogous to the simplex method for linear programming, being based on the Barankin-Dorfman procedure for this problem. A usable computational procedure for quadratic programming can be applied to the solution of elaborate nonlinear programming problems that economic models often present and to such problems as regression, efficient production, the "portfolio"problem, and convex programming. No abstract available. 43 pp. P-1205: The Simplex Method for Quadratic Programming. AUTH: P.S. Wolfe PAGES: 35, DATE: 1959 COST: $ 4.00 ABST: A computational procedure for finding the minimum of a quadratic function of variables subject to linear inequality constraints. The procedure is analogous to the simplex method for linear programming and is based on the Barankin-Dorfman procedure for this problem. No abstract available. 35 pp. P-1842: Linear Programming in a Markov Chain. AUTH: P.S. Wolfe, G.B. Dantzig, G.B. Dantzig PAGES: 19, DATE: 1959 COST: $ 4.00 ABST: A study of an infinite Markov process with a finite number of states in which the transition probabilities for each state range independently over sets which are either finite or are convex polyhedra. A finite computational procedure is given for choosing those transition probabilities which minimize appropriate functions of the resulting equilibrium probabilities. R-351: The RAND Symposium on Mathematical Programming: Linear Programming and Recent Extensions-Proceedings of a Conference, March 16-20, 1959. AUTH: P.S. Wolfe PAGES: 142, DATE: 1959 COST: $ 10.00 KEYS: Programming (mathematics) ABST: The proceedings of the Symposium on Mathematical Programming, held at Santa Monica, California, March 16-20, 1959, and sponsored by RAND. The Symposium emphasized extensions of linear programming into areas of nonlinear programming, integer programming, programming under uncertainty, network theory, and special multistage dynamic structures. Each of these areas has seen important breakthroughs in the last two years, heralding rapid development in the application of these mathematical tools to practical problems. The proceedings consist of summaries of fifty-three papers. Fifty-seven papers devoted to linear programming and its extensions were presented at the symposium held in March 1959. The papers can be grouped in the following categories: formulation and applications, economic models and dynamic programming, general linear programming, special structures, discrete programming, network theory, nonlinear programming, and programming under uncertainty. 142 pp. Book-040150: Linear Programming and Extensions. AUTH: G.B. Dantzig PAGES: 632, DATE: 1963 COST: $ 25.00 KEYS: Combinatorial analysis; Communication networks; Matrices--Theory; KEYS: Programming (mathematics) ABST: A basic text in linear programming, the solution of systems of linear equalities. The subjects covered include the concepts, origins and formulations of linear programs, and the simplex method of solution as applied to the price concept, matrix games, and transportation problems. Also included is the background, on convex sets and linear spaces, necessary to forward the discussion on such topics as duality, variants of the simplex method, and the extensions of linear programming to convex programs, to programming under uncertainty, and to certain network, topological, and combinatorial problems that may be couched in the form of linear inequalities with integer-valued variables. (Published by Princeton University Press, 1963. Available only from booksellers or the publisher.) 632 pp. Book-080950: Water Supply: Economics, Technology, and Policy. AUTH: J. Hirshleifer, J.C. Dehaven, J.W. Milliman PAGES: 378, DATE: 1960 COST: $ 25.00 KEYS: Economics--Domestic; Law; Technology; Water ABST: A critical examination of current and proposed water management schemes. Improvement in allocation of existing water supplies and development of additional sources are contrasted as ways of meeting water demands. Two case studies of crucial water-supply decisions, the Cannonville Project in New York City and the Feather River Project in Southern California, are analyzed to illustrate and define the technical, economic, and legal aspects of the problem. 378 pp. (Published by The University of Chicago Press, 1960, 1969, $7.50. Available only from booksellers or the publisher.) Book-080965: The Economics of Defense in the Nuclear Age. AUTH: C.J. Hitch, R.N. Mckean PAGES: 442, DATE: 1960 COST: $ 25.00 KEYS: Defense; Economics--Domestic ABST: A discussion of the contribution of analysis to military policy planning in the nuclear age in terms of the most efficient allocation of available resources. Economic problems are considered at each of three levels: the quantity of national resources available, now and in the future; the proportion of these resources allocated to national security purposes; and the efficiency with which the resources so allocated are used by the defense departments. Alternative policies existing at each level are also considered. (Published by Harvard University Press, 1960; paperback edition published by Atheneum, 1965. Available only from booksellers or the publishers.) 442 pp. BOOK-110520: Strategic Surrender: The Politics of Victory and Defeat. AUTH: P. Kecskemeti PAGES: 297, DATE: 1964 COST: $ 20.00 KEYS: Military strategy; Nuclear warfare; War--Termination; World war, KEYS: 1939-1945 ABST: A study of strategic surrender as a problem in political theory within the context of the transition from war to peace when one side is completely victorious. Such a transition sometimes involves strategic surrender, i.e., the orderly capitulation of the loser's remaining forces, sometimes not. It is the theorist's task to specify the general conditions that determine whether or not the termination of hostilities will involve surrender. The author presents his theoretical analysis in the historical context of World War II. Four major cases of strategic surrender are examined to show the interaction of strategic constraints and of political objectives and beliefs of the belligerents in shaping the conclusion of hostilities: the French (June 1940), the Italian (September 1943), the German (May 1945), and the Japanese (August 1945). In each case, the author outlines the capitulation and interprets the major decisions of the protagonists. Interpretation leads to evaluation, and the study is frankly critical of the surrender policy of the Western Allies in World War II. This paperback reprint of the original 1958 edition includes a note (added to the second printing, 1959), spelling out the implications of a controversial paragraph in Chap. 8 regarding "surrender without fighting." (Published by Atheneum, 1964. Available only from booksellers or the publisher.) 297 pp. Bibliog. R-0358: Automatic Checkout Equipment: Employment and Design Considerations. AUTH: S.I. Firstman, M. Kamins, B.J. Voosen PAGES: 84, DATE: 1960 COST: $ 7.50 KEYS: Airplanes; Automatic checkout equipment; Maintenance; Test methods ABST: Electronically controlled equipment can perform some maintenance tests with more rapidity and precision than possible with manual techniques. Machine-programmed logic, coupled with test capability, can often readily solve problems made difficult by complex chains of interconnected black boxes. This report is intended to aid test and checkout design by presenting the capabilities and limitations of the various design concepts and of test, measurement, and decision methods. It also discusses alternative ways to satisfy specific kinds of operational and test requirements of weapon systems. 84 pp. R-0362-RC: International Political Implications of Activities in Outer Space: A Report of a Conference, October 22-23, 1959. AUTH: J.M. Goldsen PAGES: 216, DATE: 1960 COST: $ 20.00 KEYS: Political science; Propaganda; Space technology; United states--Foreign KEYS: relations ABST: A report of the Conference on International Political Implications of Activities in Outer Space, held on October 22 and 23, 1959, at Washington, D.C. Part I presents a transcript of the conference covering the technological environment of outer space and its prospects, the political and military background and short-run outlook, some problems of the near future and possible approaches, and the future from 1984 and beyond. Part II consists of conference papers dealing with public opinion and the development of space technology, the international implications of outer space activities, outer space and international politics, and the natural history of man's emergence into space. 216 pp. RM-727-PR: An Experimental Application of the Delphi Method to the Use of Experts. AUTH: N.C. Dalkey, O. Helmer PAGES: 24, DATE: 1962 COST: $ 4.00 KEYS: Delphi method; Targets ABST: An abridgement and revision of RM-727. 24 pp. RM-2317-PR: On One-Dimensional Neutron Multiplication. AUTH: T.E. Harris PAGES: 33, DATE: 1960 COST: $ 4.00 NOTE: See also RM-2693. ABST: A Discussion of a model (related to one used earlier in RM-2288, Invariant Imbedding and Wave Propagation in Stochastic Media) to investigate the probability distribution of the total number of neutrons produced by an initial trigger neutron. Emphasis is given to the case in which the length of the fissionable body is exactly critical. The model is a simplified one that examines only one-dimensional motion of the neutrons in a nuclear chain reaction. The results of this work may be suggestive to nuclear physicists and weapon designers in studies of critical size or of situations in which a stray neutron may excite a chain reaction. RM-2508-PR: The Measurement of Missile Reliability in Pre-Launch Operating Environments. AUTH: D.S. Stoller PAGES: 34, DATE: 1960 COST: $ 4.00 NOTE: See RM-2131 for earlier results of the study. ABST: A discussion of some of the basic concepts, measurement techniques, uses of data, and data-system implications involved in measuring missile reliability during the pre-launch phase of operations. A feasible reliability-measurement policy is outlined, and the ues of a weapon-centered missile status log to obtain reliability data is explained. The study provides a basis for critical reliability planning information required in both force-employment analysis and support-requirement calculations. It is a product of continuing work designed to improve the maintenance and operations of both manned aircraft and missile systems at the base level. Tables. RM-2713-AFOSR: Procedures for the Determination of Distributional Classes. AUTH: K.E. Harper PAGES: 24, DATE: 1961 COST: $ 4.00 KEYS: Grammar; Linguistics; Translating and interpreting NOTE: See also: RM-2712, RM-2714. ABST: The second in a series of publications dealing with transformation and word classification. This Memorandum describes typical procedures to be used in the automatic analysis of a Russian physics text and discusses some of the problems involved. Data derived from semiautomatic analysis are also presented. (See also RM-2712, RM-2714.) 24 pp. RM-2842-PR: Factory Subsystem and System Test for Agena Satellite. AUTH: S.I. Firstman, K.H. Meyer PAGES: 68, DATE: 1961 COST: $ 7.50 KEYS: Checkout equipment; Cost analysis; Satellite vehicles; System analysis NOTE: See also: RM-3006-PR. ABST: An analysis of the procedures and equipment used for the Agena-B factory test activities. The study attempts to reduce the total elapsed time that each vehicle spends in subsystem and system test facilities and to determine consequent cost and operational benefits. One approach used deals with improving existing operations, while the other considers in gross terms a potential, fully automatic, test facility. 68 pp. (See also RM-3006-PR.) RM-2849-AFT: Electromagnetic Radiation from a Nuclear Explosion in Space. AUTH: W.J. Karzas, R. Latter PAGES: 40, DATE: 1961 COST: $ 4.00 KEYS: Detection; Electromagnetic radiation; Nuclear explosions ABST: A mechanism of radiating a high-frequency radio signal based on the emission of gamma rays from a nuclear explosion in space. The gamma rays from a nuclear explosion in space Compton-scatter electrons near the surface of the device or in a surrounding material shield. The scattered electrons leave the surface and are accelerated back toward it by the positively charged matter. Provided they are asymmetrically distributed the accelerating electrons radiate an electromagnetic signal. The electron motions are analyzed, the electromagnetic signal is estimated, and its detectability is examined. 40 pp. RM-2856-ARPA: Detection of Ionization Effects from Nuclear Explosions in Space. AUTH: R. Latter, R.E. Lelevier PAGES: 68, DATE: 1961 COST: $ 7.50 KEYS: Atmosphere; Detection; Nuclear explosions; Radiation; Radio ABST: An estimation of the limits of detectability of absorption effects due to atmospheric ionization by nuclear explosions in space. Ionization effects produced by x-rays, gamma rays, and beta rays are considered separately. Estimates are made of the distances at which the effects of these radiations will produce a given level of absorption (1 db) from a one-kiloton fission explosion using an operating frequency of 30 mc/sec. The memorandum also discusses the problems of identifying space explosions by this means. 68 pp. RM: The Electromagnetic Signal Due to the Exclusion of the Earth's Magnetic Field by Nuclear Explosions. AUTH: W.J. Karzas, R. Latter PAGES: 18, DATE: 1961 COST: $ 4.00 KEYS: Electromagnetic signals; Magnetic fields; Nuclear explosions ABST: A description of two possible mechanisms by which the earth's magnetic field might be excluded from a large region about a nuclear explosion. First, the Compton-recoil electrons generated by explosion gamma rays interact with the earth's magnetic field, producing a "back" field. Approximate calculations presented indicate that this mechanism does not exclude the field. The other possibility is that the field is excluded because of the blast-wave motion of heated (conducting) air. It is shown that this mechanism is effective and its magnitude is crudely estimated. 18 pp. RM-2971-NASA: Foreign Participation in Communication Satellite Systems: The Implications of the Federal Communications Act. AUTH: M.L. Schwartz PAGES: 58, DATE: 1961 COST: $ 7.50 KEYS: Communication satellites; International relations; Law ABST: Discusses the problems of foreign participation in a communication satellite system from the standpoints of policy formulation and agreement negotiation. This Memorandum assesses the legal eligibility of foreign nations to share in the ownership or control of a U.S.-licensed communication satellite operation. 58 pp. RM-3003-PR: Managing Shop Workloads. AUTH: T.C. Smith PAGES: 35, DATE: 1962 COST: $ 4.00 KEYS: Bases; Logistics; Maintenance ABST: An outline of a tentative system (based on AFM 66-1, [Organization and Field Maintenance]) for summarizing, monitoring, and controlling the flow of work through base repair shops or work centers. The system attempts to maximize shop support of both mission-oriented requirements and the base master-repair program. It not only assumes that all flight-line requirements are to be met first and other requirements last, but also recognizes and establishes the need for centralized cognizance and control over the total workload of each shop. The system was formulated during a preliminary survey of maintenance-management activities at Oxnard Air Force Base. 35 pp. RM-3012-PR: A Differential Game Without Pure Strategy Solutions on an Open Set. AUTH: L.D. Berkovitz PAGES: 34, DATE: 1962 COST: $ 4.00 KEYS: Games ABST: An investigation concerned with the theoretical aspects of developing a satisfactory theory of differential games. The general name "differential game" is applied to conflicts in which the state of a system is influenced by choices made continuously by each of two antagonists. One player seeks to maximize a payoff while the other seeks to minimize it. Examples of differential games occur in models of tactical air warfare and in problems of interception and pursuit. 34 pp. RM-3022-JPL: Quarterly Technical Progress Report-6: Studies of the Physical Properties of the Moon and Planets. AUTH: PlanetarySciencesDepartment PAGES: 15, DATE: 1961 COST: $ 4.00 KEYS: Astronomy; Planetary sciences NOTE: See also: RM-2661, RM-2711, RM-2769, RM-2817, RM-2900. ABST: A progress report covering Rand studies (from October 1-December 31, 1961) on the physical properties of the moon and planets. Such topics are discussed as light scattering and radiative transfer, planetary atmospheres, planetary experiments, and lunar and planetary geology and magnetic fields. 15 pp. (See also RM-2661, RM-2711, RM-2769, RM-2817, RM-2900.) RM-3060-RC: Technological Aspects of Contemporary and Future Civil Aircraft for the World's Less-Developed Areas. AUTH: T.F. Cartaino PAGES: 85, DATE: 1962 COST: $ 7.50 KEYS: Air transportation; Airplanes; Technology ABST: An examination of the 1962 status of, and future possibilities for, aircraft technology in the less-developed areas of the world. The Memorandum describes the aviation environment encountered in such areas, delineates the special aircraft-design considerations relevant to them, and discusses engineering solutions devised to meet the special requirements of these areas. A representative sample of existing aircraft appropriate to operations in less-developed areas is presented, and the major state-of-the-art possibilities that are possible for this class of aircraft by 1975 are forecast. 85 pp. RM-3088-PR: On the Perturbed Motion of a Lunar Satellite. AUTH: H.B. Schechter PAGES: 39, DATE: 1962 COST: $ 4.00 KEYS: Astronomy; Moon; Planetary sciences; Satellite vehicles ABST: A discussion of Pontecoulant's solution of the three-body problem of the lunar theory. This solution is applied to the motion of a lunar satellite perturbed by the earth to obtain an estimate of the changes caused in the radial coordinate. It is found that the maximum decrease in nominal perilunar radius depends on the ratio of the angular velocities of the perturbing body and the satellite, and on an eccentricity parameter. For a satellite with an orbital period approximately one-fifteenth that of the moon and with an eccentricity parameter of 0.2, this decrease amounts to about 3 percent of the perilunar radius. 39 pp. RM-3106-PR: Some Summary Views on Soviet-American Cooperation on Space Activities. AUTH: J.M. Goldsen PAGES: 13, DATE: 1962 COST: $ 4.00 KEYS: International relations; Space programs; Soviet Union--Space ABST: A brief summary of the author's views on space cooperation with the Soviet Union. The objectives to be sought through bilateral U.S.-S.U. cooperation and the criteria of essential significance in shaping each country's position are reviewed. Examples are given of cooperative activities which might be proposed by the United States, ranging from on-the-ground agreements through coordinated but separate national programs, jointly staffed ground laboratories, and in-flight programs. RM-3112-PR: Soviet National Income and Product, 1956-1958. AUTH: N. Nimitz PAGES: 189, DATE: 1962 COST: $ 15.00 KEYS: Economics--Foreign; Income; Soviet Union--Economics ABST: Estimates of the national income and product of the USSR at current actual prices for 1956-1958, and at current adjusted prices (ruble factor cost) for 1949-1958. Over the period 1956-1958, the share of gross investment rose from 26 to 28 percent (or from 30 to 32 percent at adjusted prices), while the share going to consumption remained constant at about 56 percent (50 percent at adjusted prices). Per capita consumption, roughly deflated to constant prices, increased at an average rate of 6 percent a year, compared with 9 percent for 1953-1955. The share of outlays explicitly designated to defense declined from 7.3 to 5.9 percent of total gross national product (or from 8.5 to 6.8 percent at adjusted prices). Since, however, the prices of military goods may have fallen significantly (unlike the prices of civilian goods and services, which were comparatively stable), real defense outlays probably increased rather than declined. 189 pp. RM-3153/PR: Bomber Range Performance at Mach 2.3 and 3.0. AUTH: C.M. Weber PAGES: 31, DATE: 1962 COST: $ 4.00 KEYS: Bombers ABST: A comparison of range performance of supersonic bombers with aluminum and steel airframes, designed for cruise Mach numbers of 2.3 and 3.0, respectively. The performance differences and some design changes that might negate them are indicated. RM-3208-ARPA: The Vietnamese Strategic Hamlets: A Preliminary Report. AUTH: J.C. Donnell, G.C. Hickey PAGES: 38, DATE: 1962 COST: $ 4.00 KEYS: Counterinsurgency; Economics--Foreign; Military strategy; Social KEYS: science; South vietnam; Southeast asia ABST: A discussion of the social, economic, administrative, and political aspects of the strategic hamlets, a key part of the South Vietnam program known as "Operation Sunrise." No effort is made to evaluate the direct military worth of the hamlets. Some suggestions are made for improving the hamlet system. 38 pp. RM-3212-PR: Reactions of Hemoglobin and Steady States in the Human Respiratory System: An Investigation Using Mathematical Models and an Electronic Computer. AUTH: J.C. Dehaven, E.C. Deland PAGES: 193, DATE: 1962 COST: $ 15.00 KEYS: Blood; Computer simulation; Health--Research; Respiration ABST: A report on results of mathematical experiments performed with a detailed model of the human external respiratory subsystem. An earlier study (RM-2519, "A Mathematical Model of the Human External Respiratory System") discusses the mathematical basis for the model and demonstrates the general feasibility of the approach. This memorandum describes the considerable improvements in the theory and the structure of the model. It also demonstrates the ability of the improved model to simulate satisfactorily, and in detail, the responses of the subsystem under a wide range of conditions. 193 pp. RM-3232-PR: Improved Asymptotic Properties of Error-Correcting Codes. AUTH: S.M. Johnson PAGES: 38, DATE: 1962 COST: $ 4.00 KEYS: Codes; Error analysis; Signal processing ABST: A refinement of the approach used in P-2294-2, "A New Upper Bound for Error Correcting Codes." The earlier study developed a new upper bound on nonsystematic, binary, error-correcting codes, using a sphere-packing approach and combinatorial analysis. The refinement of this approach, together with a study of the asymptotic behavior of the upper bound, makes it possible to show that any large code must correct almost all sequences with a larger number of errors than the code is designed for. This excess is expressed numerically as a fraction of the designed error-correcting capability of the code. The fraction is a function of the ratio of the sequence length and the designed error-correcting capability. A possible application might be in the use of a larger code giving almost certain error correction rather than a smaller one with certain correction capability. 38 pp. RM-3254-PR: Contract Negotiations and Results in Aircraft Procurement: Case Studies of the B-52 and B-58. AUTH: L.E. Preston PAGES: 120, DATE: 1962 COST: $ 10.00 KEYS: Bombers; Contracts; Cost analysis; Economics--Domestic; Weapon systems--Procurement ABST: A survey of the history of negotiations and contracts for two models of bomber aircraft: the B-52 and the B-58. Each of these two procurement histories reflects a distinct approach to contract negotiations. The first is a "work done" strategy in which the contractor's estimates of his own costs become the principal basis for negotiation, with an effort directed at examination and possible lowering of the cost estimates. The second is a "position" strategy which uses elements of the contract to establish a range of outcome from which the contractor may select various combinations of prices and profits. 120 pp. RM-3258-PR: The Simulation of Multi-Component Distillation. AUTH: E.C. Deland, M.B. Wolf PAGES: 43, DATE: 1962 COST: $ 4.00 KEYS: Chemistry; Computer simulation; Petroleum ABST: Part of a continuing Rand study in the simulation of steady-state chemical processes. A new method is proposed for the simulation of multicomponent petroleum distillation columns. This method takes advantage of the power of mathematical programming techniques for computing the equilibrium states of physiochemical processes. 43 pp. RM-3275-PR: A Brief Survey of Trajectory, Guidance, and Propulsion Aspects of Orbital Rendezvous. AUTH: H.B. Schechter PAGES: 59, DATE: 1963 COST: $ 7.50 KEYS: Orbits; Propulsion; Space technology; Trajectories ABST: A summary of some problems of orbital rendezvous, as shown in the open literature. The papers are discussed briefly and some of the data compared. The papers are generally of two classes: the first approaches the problem from the point of view of impulsive Keplerian orbital transfers; the second class analyzes the terminal portion of the rendezvous maneuver or, more specifically, the selecting of thrusting and guidance laws required to insure a soft contact between the maneuverable interceptor and the target satellite. The survey points out the need for a more general parametric study of the terminal phase of orbital rendezvous, particularly optimal guidance laws. 59 pp. RM-3316-PR: Rotation Tensors and Irrotational Motions in Einstein-Riemann Spaces. AUTH: D.G.B. Edelen PAGES: 14, DATE: 1963 COST: $ 4.00 KEYS: Field theory; Physics; Tensor analysis ABST: An examination of the rotation and Fermi-rotation tensors of an arbitrary C vector field. The Fermi-rotation tensor is shown to be the natural generalization of the classic concept of a rotation tensor, and conditions are obtained under which the usually encountered rotation tensor gives the same measure as the Fermi tensor. The two are equivalent if and only if the motion generated by the vector field is geodesic in conformally related space-time. Explicit characterizations of irrotational and Fermi-irrotational motions are obtained. Necessary and sufficient conditions are derived for an Einstein-Riemann space to admit such motions. RM-3354-PR: The Design and Objectives of Laboratory Problem IV. AUTH: I.K. Cohen PAGES: 45, DATE: 1963 COST: $ 4.00 KEYS: Computer simulation; Laboratory problem; Logistics; Maintenance NOTE: See also: RM-3281. ABST: A description of the fourth Logistics Laboratory Problem (LP-IV), designed primarily to study improvements in base-level maintenance management and information systems. LP-IV's secondary objectives are to develop a systems training capability for base maintenance management and to advance the state-of-the-art research in management. Several factors have determined the study's subject matter: a continuing squeeze on maintenance support resources; a need to weigh proposed refinements in AFM 66-1, as well as the value of advanced data processing systems; and a broad background of available RAND research data and techniques. The LP-IV study will intermix a number of research techniques, including man-machine simulation, all-computer simulation, and statistical analyses. (See also RM-3281.) 45 pp. RM-3378-PR: Flow Networks and Combinatorial Operations Research. AUTH: D.R. Fulkerson PAGES: 54, DATE: 1962 COST: $ 7.50 KEYS: Combinatorial analysis; Communication networks; Inventory management; KEYS: Management ABST: A survey of (1) the basic concepts and theorems concerning flows in capacity-constrained networks and (2) some practical combinatorial applications of network flow theory. These applications include problems involving optimal chains, equipment replacement, project planning, minimal chain coverings of acyclic networks, optimal assignment, production and inventory planning, and optimal capacity scheduling. A few other combinatorial problems that have no flow formulations are also discussed. 54 pp. RM-3403-PR: On Perfect Error-Correcting Codes. AUTH: S.M. Johnson PAGES: 24, DATE: 1962 COST: $ 4.00 KEYS: Codes; Information theory ABST: Some theoretical results concerning the existence of perfect, or close-packed, error-correcting codes. These codes are studied in connection with the maximum rate of error-free information transmission through a communications channel. The Memorandum develops conditions which show, for example, that there are no perfect codes, other than the trivial majority-rule ones, for correcting odd numbers of errors from 5 to 29. 24 pp. RM-3478-AFT: Transient Sound Propagation in a Simple Model of a Triple-Layered Medium. AUTH: A.D. Pierce PAGES: 91, DATE: 1963 COST: $ 7.50 KEYS: Acoustics; Nuclear explosions; Wave mechanics ABST: A discussion of a simple model of long-range sound transmission. The model makes possible a qualitative description of the atmospheric waves generated by nuclear explosions. 91 pp. RM-3486-NASA: Radiation Damage in Solar-Powered Satellites. AUTH: G.E. Modesitt PAGES: 33, DATE: 1963 COST: $ 4.00 KEYS: Communication satellites; Radiation; Solar energy ABST: An examination of the effect of radiation damage on solar-powered communication satellites. The damage depends on type of solar cell, amount of shielding, power requirements, and satellite orbit. Estimates are given for the lifetime of solar cells for several characteristic orbits. 33 pp. RM-3497-ARPA: Invariant Imbedding and Rarefied Gas Dynamics. AUTH: J. Aroesty, R.E. Bellman, R.E. Kalaba, S. Ueno PAGES: 18, DATE: 1963 COST: $ 4.00 KEYS: Gas dynamics; Invariant imbedding ABST: An application of the techniques of invariant imbedding to the study of rarefied gas flows. The problem of linearized Couette flow is investigated, and it is shown how the assumption of the Krook scattering model results in a formulation which is similar to that obtained in radiative transfer for conservative isotropic scattering in a plane-parallel atmosphere. By a simple enumeration of physical processes, the nonlinear integral-differential equation governing the reflection function is obtained, and a suitable transformation is shown to render this equation amenable to numerical computation. 18 pp. RM-3527-NASA: Acceleration of Charged Particles by Hydromagnetic Shock Waves. AUTH: J.W. Kern PAGES: 35, DATE: 1963 COST: $ 4.00 KEYS: Atmosphere; Geophysics; Magnetohydrodynamics; Wave mechanics ABST: A discussion of two mechanisms by which a single hydromagnetic (HM) shock wave can produce significant ring currents. One mechanism accelerates thermal electrons throughout the magnetosphere; the other affects energetic particles trapped in the magnetosphere, changing their energy and pitch-angle distributions. A single HM shock wave is shown to be capable of producing, by either (or both) mechanisms, significant ring currents. 35 pp. RM-3535-ISA: Kremlin Moods. AUTH: N. Leites PAGES: 309, DATE: 1964 COST: $ 25.00 KEYS: Communism; Soviet Union NOTE: See also: RM-3506, RM-3618. ABST: An examination of the published statements of various Bolshevik leaders, particularly Premier Khrushchev, up to the close of 1962. The aim of the study is to see, behind the public language of these figures, important clues to their state of mind and feelings and also to determine the Soviet leaders' views of themselves, the West, and the nature and extent of their concern for the successful establishment of world communism. (See also RM-3506, RM-3618.) 309 pp. RM-3554-PR: A Differential Correction Process for Nearly Circular Orbits. AUTH: F.T. Smith PAGES: 59, DATE: 1963 COST: $ 7.50 KEYS: Astronomy; Orbits ABST: A derivation of the explicit equations necessary for evaluating a differential correction process relating astronomical observations to orbital parameter corrections. The orbital parameters involved constitute a set particularly useful for orbits that are nearly circular. This Memorandum serves as a supplementary reference for orbit transfer studies already completed and orbital parameter estimation studies currently under way. 59 pp. RM-3564-PR: A Model of the Annual Temperature Variations at 30 Deg N and 60 Deg N Between 30 and 50 Km. AUTH: E.S. Batten PAGES: 41, DATE: 1963 COST: $ 4.00 KEYS: Atmosphere; Climatology; Meteorology ABST: A description of the seasonal and latitudinal variations in temperature at 30-deg N and 60-deg N between 30 and 50 kilometers altitude over the North American continent. At 30-deg N the observations indicate a tendency for two temperature maxima annually. A statistical analysis of the data at 30-deg N shows the significance of the seasonal variations at 35 and 40 km. The temperature variation at 60-deg N has a single summer maximum and a larger amplitude than at 30-deg N. The largest latitudinal differences occur during winter. 41 pp. RM-3619-PR: Soviet Philosophy, Science and Cybernetics. AUTH: F.J. Krieger PAGES: 26, DATE: 1963 COST: $ 4.00 KEYS: Communism; Soviet Union--Science ABST: A discussion of how all aspects of science, i.e., knowledge, are made to conform to the ideological mold of Marxism-Leninism in the Soviet Union. The larger part of this Memorandum consists of a thematic plan from [Voprosy Filosofii] (Problems of Philosophy), which lists over 300 topics suggested for discussion and study in the Soviet-planned society. 26 pp. RM-3756-PR: A New Method of Frequency Synthesis. AUTH: C.R. Lindholm, S.M. Johnson PAGES: 42, DATE: 1963 COST: $ 4.00 KEYS: Communication systems; Electronics; Signal processing ABST: A description of a number representation scheme applied to synthesizers such as are used in communication transmitters and receivers. The scheme permits a great number of frequencies to be synthesized from a much smaller set of fundamental frequencies. This approach has practical applications to a variety of different communication requirements. 42 pp. RM-3757-PR: Completely Coherent Sequential Detection with Application to Search Radar. AUTH: W.B. Kendall PAGES: 66, DATE: 1963 COST: $ 7.50 KEYS: Detection; Radar; Signal processing ABST: A study of completely coherent (synchronous) detection of signals in noise by sequential probability ratio tests (SPRT); i.e., sequential detection. The results are useful in any situation in which the signal to be detected is known at the receiver. In radar, this means when the r-f phase, arrival time, doppler shift, and amplitude at the pulses to be received are known. Other cases are also treated. 66 pp. RM-3759-PR: Performance of the Biased Square-Law Sequential Detector in the Absence of Signal. AUTH: W.B. Kendall PAGES: 32, DATE: 1963 COST: $ 4.00 KEYS: Detection; Radar; Signal processing ABST: A treatment of the incoherent sequential detection of a sinewave in Gaussian noise by a biased square-law receiver. The average number of pulses that might be integrated in each beam position and the resulting false-alarm probability are calculated. The results presented are the first available exact results for sequential detection with no restrictions on either the input signal-to-noise ratio or on the values of the detection thresholds. 32 pp. RM-3818/PR: The Soviet Succession Problem and U.S. Policy. AUTH: M. Rush PAGES: 138, DATE: 1963 COST: $ 10.00 KEYS: Communism; International relations; Soviet Union NOTE: See also: RM-2763-PR, P-2386-1, P-2615. ABST: An examination of the problems that the end of Krushchev's dictatorship will pose to the West. Succession crises are inevitable in the USSR when the dictator ceases to exercise his powers, although the seriousness of the crisis depends on circumstances. Krushchev is trying to temper the crisis that will follow his personal dictatorship by various institutional and personnel arrangements, but it is doubtful that the succession will proceed according to his plans. The crisis may be resolved quickly, but if it is prolonged the USSR will be weakened by it. Moreover, the resolution of the crisis could alter the regime in important respects. None of the various cold-war strategies advocated in the West--containment, counterpressure, facilitating moderation of the regime--is wholly adequate in itself because of the variability of the Soviet regime, especially as it passes through the succession crisis. RM-3824-PR: Concept and Measurement of Demand for Recoverable Components. AUTH: S. Campbell PAGES: 24, DATE: 1963 COST: $ 4.00 KEYS: Maintenance ABST: A restatement of some basic concepts of demand measurement, and an evaluation, in light of these concepts, of certain notions regarding accurate measurement of spares demand and sound control of reparables at air-base level. This Memorandum concludes: (1) in future procedures, the definition of demand for recoverable parts should be broadened; (2) the role of command policy in establishing critieria for demand measurement must be explicitly understood; and (3) present efforts to improve base-level demand and repair data should continue to receive due emphasis and support. 24 pp. RM-3833-PR: Communist China's Military Doctrine and Strategy. AUTH: A.L. Hsieh PAGES: 38, DATE: 1963 COST: $ 4.00 KEYS: China; Military strategy ABST: An analysis of 29 issues of a Communist Chinese military publication, [Kung-tso T'ung-hsun], from January to August 1961. The insights that can be gleaned from the 1961 material indicate that Chinese policy is based on a realistic assessment of the threat and of the risks involved in certain types of military operations. It shows China's recognition of her military-technological inferiority to the United States, her vulnerability to nuclear attack, and her inability to count on Soviet military backing in support of external objectives. This is strongly reflected in Peking's expressed intention to avoid, at least for the time being, any provocation that might lead to a direct confrontation with U.S. forces, conventional or nuclear. At the same time, however, the Chinese show an awareness that in areas or situations where U.S. military superiority cannot be brought to bear, or where Soviet help is not an important factor, opportunities exist to exploit China's ground forces for the sake of local political-military gains. 38 pp. RM-3860-PR: Two Charged Spherical Conductors in a Uniform Electric Field: Forces and Field Strength. AUTH: M.H. Davis PAGES: 45, DATE: 1964 COST: $ 4.00 KEYS: Magnetic fields; Meteorology; Physics ABST: A complete solution to the electrostatic boundary value problem of two charged conducting spheres in a uniform electric field. Rapidly convergent expressions are given for the forces acting on the spheres and for the maximum field strength between them. Numerical results are presented for a number of relative sphere sizes and separations. 45 pp. RM-3867-PR: Symposium on the Role of Airpower in Counterinsurgency and Unconventional Warfare: A Brief Summary of Viewpoints. AUTH: A.H. Peterson, G.C. Reinhardt, E.E. Conger PAGES: 38, DATE: 1964 COST: $ 4.00 KEYS: Air defenses; Airplanes; Counterinsurgency; Psychology; Reconnaissance ABST: A summary of material contained in RAND's symposium on "The role of airpower in counterinsurgency and unconventional warfare," together with some insights intended for use in future hardware and operations planning. 38 pp. RM-3869-PR: Three Papers on Radiative Transfer from Investigations of the Physics of the Atmosphere, No. 3, Academy of Sciences, Estonian S.S.R., 1962. AUTH: D. Deirmendjian PAGES: 115, DATE: 1963 COST: $ 10.00 KEYS: Atmosphere; Radiative transfer ABST: Translations of three Soviet papers written by Y. Malamaa, O. Avaste, H. Moldau, K. S. Schifrin. They include the formulation of equations for calculating the intensity of diffusely reflected and transmitted light; results of calculations of the spectral distribution of direct and scattered radiation for various conditions of atmospheric turbidity, with regard to the absorption of water vapor, carbon dioxide, and ozone; the achievement of greater accuracy for the approximate solutions to the problem of radiative transfer in the case of anisotropic scattering. Translations of three Soviet papers written by Y. Malamaa, O. Avaste, H. Moldau, K. S. Schifrin. They include the formulation of equations for calculating the intensity of diffusely reflected and transmitted light; results of calculations of the spectral distribution of direct and scattered radiation for various conditions of atmospheric turbidity, with regard to the absorption of water vapor, carbon dioxide, and ozone; the achievement of greater accuracy for the approximate solutions to the problem of radiative transfer in the case of anisotropic scattering. 115 pp. RM-3885-PR: Parametric Limits for the Upper Atmosphere of Mars. AUTH: G.F. Schilling PAGES: 55, DATE: 1963 COST: $ 7.50 KEYS: Atmosphere; Mars (planet); Planetary sciences ABST: Three self-consistent model atmospheres (maximum, minimum, and standard) showing probable limits for the distribution of atmospheric pressure and mass density in the upper atmosphere of Mars. They extend an earlier model (P-2639) to an altitude above 2,500 km and derive, in part, from J. W. Chamberlain's recent analysis of the probable thermal regime in upper atmospheres. 55 pp. RM-3888-NASA: Objectives, Measures of Effectiveness, and Criteria for Apollo Prelaunch Operations as They Affect Checkout Activities. AUTH: J.R. Brom, J.J. Ferrante, S.I. Firstman, L.T. Mast, D.S. Stoller PAGES: 44, DATE: 1963 COST: $ 4.00 KEYS: Checkout equipment; Launch vehicles; Project--Apollo; Space vehicles ABST: A description of objectives, and measures for attaining those objectives, for NASA's Apollo prelaunch operations. The objective-measures problem was considered early in 1963 at a meeting of members of a working panel consisting of representatives from Bellcom, Inc., The General Electric Company, and RAND. The report documents the preparatory work and results of that meeting. 44 pp. RM-3957-PR: Values of Large Market Games: Status of the Problem. AUTH: L.S. Shapley PAGES: 24, DATE: 1964 COST: $ 4.00 KEYS: Competition; Economic theory; Game theory NOTE: See also: RM-3518-1, RM-3553, RM-3853. ABST: A discussion of several models of exchange economies with many participants in which the game-theoretic "value" either coincides with, or converges to, the classical Walrasian solution based on price equilibrium. A connection is thereby indicated between "fair division" (in a collusive world) and "free competition" (in a noncollusive world). The discussion is informal, but technical. Appendixes detail the relevant mathematical models, both game-theoretic and economic. (See also RM-3518-1, RM-3553, RM-3853.) 24 pp. Bibliog. RM-3990-RC: Discretization in Galactic Structure and Cosmology. AUTH: T.Y. Thomas PAGES: 60, DATE: 1964 COST: $ 7.50 KEYS: Astronomy; Cosmology; Planetary sciences; Relativity theory NOTE: See also: RM-3941. ABST: Groundwork of a relativistic theory to explain discretization effects in the structure of galaxies. The basic assumption, referred to as the principle of similarity, expresses in invariant differential form the geometric concept of similarity transformation and leads to metrics that appear somewhat more general than those common in cosmological theory. This principle also leads to the introduction of a wave function that can be interpreted as directly representative of deviations from a static metric occurring within galaxian world tubes or on their boundaries as the result of the action of extraneous influences. That certain discretization effects are required for the existence of solutions of the wave equation satisfied by the function under steady-state conditions is discussed briefly for the special case of spherical galaxies. 60 pp. (See also RM-3941.) RM-4030-TAB: Systems Analysis for the Postattack Environment: Some Reflections and Suggestions. AUTH: R.D. Specht PAGES: 41, DATE: 1964 COST: $ 4.00 KEYS: Biology; Nuclear warfare; Post-nuclear attack environment; System KEYS: analysis ABST: A discussion of uses and limitations of mathematics and systems analysis in the study of biological and environmental consequences of nuclear war. The Memorandum suggests that a program of research on problems of the biosphere in the postattack environment should include not only detailed technical studies, but also some activities devoted to unifying the research approach, such as facilitating interdisciplinary communication, structuring the program, discovering what technical studies are needed, in what order, and to what degree of detail. Suggestions are made for such unifying aids, a contextual map, special conference design, and a pilot study. 41 pp. Bibliog. RM-4051-PR: Computational Aspects of Approximation Theory. AUTH: B.W. Boehm PAGES: 107, DATE: 1964 COST: $ 10.00 KEYS: Approximation theory ABST: A discussion of the theory of approximation by polynomials and rational functions, presenting some of the useful theoretical results, interrelations, and practical consequences. Topics include problems of existence, uniqueness, characterization, and error estimation of best approximations, as well as algorithms for interpolation and for obtaining best least-squares and Chebyshev approximations. 107 pp. Bibliog. RM-4103-PR: Statistical Descriptions of Free Boson Fields. AUTH: D. Holliday PAGES: 21, DATE: 1964 COST: $ 4.00 KEYS: Lasers; Nuclear physics; Statistics ABST: A demonstration showing that the rise of conventional stochastic methods in the Heisenberg picture to describe a light beam produced by a statistical ensemble of classical (c-number) sources is equivalent to representing the statistical state of the light beam by a density matrix having a Glauber P-representation. The relation between the classical and quantum statistical descriptions implied by Sudarshan's probability functional approach is shown to be purely formal and without physical meaning. Sudarshan's statement that the probability functional method can be used to prove that all correlation functions of the beam determine its density matrix is shown to be incorrect. 21 pp. RM-4110-RC: Radial Discretization in Spherical Galaxies. AUTH: T.Y. Thomas PAGES: 7, DATE: 1964 COST: $ 4.00 KEYS: Astronomy; Planetary sciences ABST: An extension of one avenue of previous RAND research on galactic scale discretization to obtain a five-parameter discretization for the diameter of spherical galaxies. 7 pp. RM-4113-PR: Chandrasekhar's X- and Y-Functions. AUTH: J.L. Carlstedt, T.W. Mullikin PAGES: 45, DATE: 1964 COST: $ 4.00 KEYS: Radiative transfer ABST: A description of some results obtained by applying the theory of singular integral equations to problems of radiative transfer in plane-parallel atmospheres. The theory is applied to Chandrasekhar's X- and Y-functions. Both exact and asymptotic formulae are given for the unique functions that are analytic functions of their argument. Computations are reduced to the solution of rapidly convergent Fredholm equations and to the calculation of various quadratures. Numerical tables are given for the case of isotropic scattering. 45 pp. Bibliog. RM-4140-PR: The Role of North Vietnam in the Southern Insurgency. AUTH: J.J. Zasloff PAGES: 111, DATE: 1964 COST: $ 10.00 KEYS: North vietnam; Revolutions; South vietnam ABST: An examination of the role that North Vietnam is playing in the present struggle in South Vietnam. The Momorandum also discusses the function of Laos and Cambodia in providing passage and safe haven for the insurgents. It covers the political and military control, personnel, materiel, and psychological contributions of Hanoi, and shows their likely effects on the South Vietnamese and American efforts. 111 pp. RM-4170-ISA: Army Operations in Malaya, 1947-1960. AUTH: R. Sunderland PAGES: 260, DATE: 1964 COST: $ 20.00 KEYS: Counterinsurgency; Great Britain; Malaysia; Southeast asia ABST: A study of military tactics and techniques of the British campaign against the Communist terrorists in Malaya between 1947 and 1960. Discussed are the characteristics and major problems of jungle warfare in general and of the situation in Malaya in particular. The chief approaches and methods that enabled the ground forces of the Commonwealth to defeat the insurgents are described. 260 pp. RM-4171-ISA: Organizing Counterinsurgency in Malaya, 1947-1960. AUTH: R. Sunderland PAGES: 96, DATE: 1964 COST: $ 7.50 KEYS: Counterinsurgency; Great Britain; Malaysia; Southeast asia ABST: A study of the organization of the counterinsurgent effort in Malaya during the British campaign against the Communist terrorists. The committee system established under the Briggs Plan is discussed and its functions in organizing counterinsurgent activities described. 96 pp. RM-4172-ISA: Antiguerrilla Intelligence in Malaya, 1948-1960. AUTH: R. Sunderland PAGES: 79, DATE: 1964 COST: $ 7.50 KEYS: Counterinsurgency; Great Britain; Intelligence; Malaysia; Southeast KEYS: asia ABST: A description of the improvement of intelligence techniques in Malaya, 1948-1960. In 1952 intelligence was given a place of paramount importance, and penetration of the guerrilla organization became the chief goal. In the ensuing years, skills increased, and ultimately agents were able to penetrate the highest levels of the Communist Party. The result was a rising number of guerrilla captures and casualties, a swing in popular support away from the guerrillas, and greater ease in recruiting reliable counterinsurgency agents. One case study, Operation JAYA, is presented in some detail. 79 pp. RM-4173-ISA: Resettlement and Food Control in Malaya. AUTH: R. Sunderland PAGES: 141, DATE: 1964 COST: $ 10.00 KEYS: Counterinsurgency; Food; Great Britain; Malaysia; Southeast asia ABST: A summary of the use of resettlement and food control in the British fight against guerrilla activities of the Malayan Communist Party between 1948 and 1960. To prevail, the government had to separate the guerrillas from the people and prevent passage of supplies and intelligence between them. It succeeded by resettling a half-million Chinese squatters and by strictly controlling food. This Memorandum details the programs for achieving resettlement and food control. Presentation of one case study dramatizes the impact of hunger, combined with military pressure, on the guerrillas' will to fight. 141 pp. RM-4174-ISA: Winning the Hearts and Minds of the People: Malaya, 1948-1960. AUTH: R. Sunderland PAGES: 68, DATE: 1964 COST: $ 7.50 KEYS: Counterinsurgency; Great Britain; Malaysia; Propaganda; Southeast KEYS: asia ABST: The last of a series of five Memoranda covering various aspects of the British campaign against the Communist terrorists in Malaya between 1947 and 1960. It describes the campaign of public information, civic action, and other persuasive measures by which the government won the support of the populace. 68 pp. RM-4175-NIH: A Three-Organ Drug Distribution Model Including the Kidney. AUTH: J.A. Jacquez, B. Kotkin, I. Cooper, J.D. Buell PAGES: 25, DATE: 1964 COST: $ 4.00 KEYS: Biochemistry; Biomathematics; Computer simulation; Drugs; Health--Research; KEYS: Kidneys ABST: The Bellman-Jacquez-Kalaba mathematical model of drug distribution was designed to investigate the effect of injecting an active chemical agent into the blood stream by studying the time course of the resulting drug concentrations throughout the body. In the initial studies of a two-organ being, where both organs were linked in parallel with the circulatory system, one of the organs represented an area of particular interest that was marked for selective localization and the other represented the remainder of the body. The model described in this memorandum includes a third organ, which performs certain functions of the kidney. The preliminary investigation is concerned with the effect of excretion on the concentrations of the drug in the body, rather than with a detailed model of the kidney itself. The Bellman-Jacquez-Kalaba mathematical model of drug distribution was designed to investigate the effect of injecting an active chemical agent into the blood stream by studying the time course of the resulting drug concentrations throughout the body. In the initial studies of a two-organ being, where both organs were linked in parallel with the circulatory system, one of the organs represented an area of particular interest that was marked for selective localization and the other represented the remainder of the body. The model described in this memorandum includes a third organ, which performs certain functions of the kidney. The preliminary investigation is concerned with the effect of excretion on the concentrations of the drug in the body, rather than with a detailed model of the kidney itself. 25 pp. RM-4200-NASA: Display Requirements for Prelaunch Checkout of Advanced Space Vehicles. AUTH: R.D. Pepler, J.G. Wohl PAGES: 188, DATE: 1964 COST: $ 15.00 KEYS: Checkout equipment; Project--Apollo; Space technology ABST: A guide to the establishment of computer-driven display requirements for earth prelaunch checkout of advanced space vehicles. This memorandum reviews existing uses of computer-driven displays; identifies the information, display format, coding requirements for prelaunch checkout systems; and develops a basis for determining computer-driven display requirements of checkout systems with differing levels of automation. A procedural guide is provided for developing the requirements of a prelaunch checkout computer-driven display system. 188 pp. RM-4205-PR: A Generalized Technique for Eliminating Species in Complex Chemical Equilibrium Calculations. AUTH: N.Z. Shapiro PAGES: 31, DATE: 1964 COST: $ 4.00 KEYS: Biomathematics; Chemistry; Numerical methods and approximations ABST: A consideration of multi- or single-phase chemical equilibrium problems, showing that under certain circumstances a problem involving a very large number of different chemical species may be replaced by one, of relatively few species, more amenable to numerical solution. 31 pp. RM-4208-PR: Dynamic Programming in Multiplicative Lattices. AUTH: T.A. Brown, R.E. Strauch PAGES: 19, DATE: 1964 COST: $ 4.00 KEYS: Lattice theory; Programming (mathematics) ABST: A demonstration that the methods of dynamic programming may be applied to problems involving partially ordered criterion functions. Specifically, the existence of optimal policies and the principle of optimality are established for a category of problems in which the criterion space is a conditionally complete multiplicative lattice. 19 pp. RM-4234-NIH: Detection of Functional Interactions Among Neurons: A Technique Using Repetitive Presentations of Stimuli. AUTH: D.H. Perkel PAGES: 37, DATE: 1964 COST: $ 4.00 KEYS: Biology; Communication networks; Computer simulation ABST: Description of a procedure for predicting the change in the cross-correlation function when a fixed stimulus is presented at regular intervals, under the assumption that the stimulus modifies the firing sequence of one or both observed neurons, but does not affect any interaction paths between two nerve cells. A comparison between the predicted and observed crosscorrelation densities then serves as a means of detecting the activation or modification of such interaction pathways by the stimulus. In this experimental situation, observations of spike trains and application of the prediction procedure enable differentiation among: (1) no interaction between the two cells; (2) interaction unaffected by the stimulus; and (3) interaction through pathways themselves affected by the stimulus. Digital-computer simulations of the corresponding neural networks illustrate these cases and the application of the technique. 37 pp. RM-4275-PR: Dynamic Programming and Hamilton-Jacobi Theory. AUTH: S.E. Dreyfus PAGES: 31, DATE: 1964 COST: $ 4.00 KEYS: Optimization; Programming (mathematics) ABST: Presents a new dynamic programming derivation of the classical Hamilton-Jacobi method of solving optimization problems, and develops and illustrates the connections with the usual dynamic programming approach. 31 pp. Ref. (Author) RM-4311-NASA: Astronaut-Crew Requirements for Apollo In-Flight Operations. AUTH: N.F. Kristy, H.P. Roth PAGES: 73, DATE: 1964 COST: $ 7.50 KEYS: Project--Apollo; Project--Gemini; Space flight ABST: An investigation of various questions on the crew performance of the Apollo mission. Most of the suggestions involve tests and experiments for the Gemini and Apollo orbital flights calculated to prove astronaut capabilities and provide data for planners of the lunar mission. 73 pp. Bibliog. RM-4330-PR: A Simple Probabilistic Proof of the Discrete Generalized Renewal Theorem. AUTH: S.C. Port PAGES: 13, DATE: 1964 COST: $ 4.00 KEYS: Mathematics; Probability ABST: Presentation of a new and simpler proof of the discrete generalized renewal theorem. 13 pp. RM-4347-PR: Fluid Balance and Electrolyte Distribution in the Human Body. AUTH: E.C. Deland, G.B. Bradham PAGES: 122, DATE: 1965 COST: $ 10.00 KEYS: Biochemistry; Health--Research; Physiology ABST: Presentation of a conceptual model and a mathematical method for computing the physiological fluid and electrolyte distribution for selected body compartments of an average, young, 70-kilogram human male. The mathematical procedure simulates the physiological subsystems by incorporating all the known chemical reactions and electrochemical relations that seem necessary to establish the fluid and electrolyte distribution. The construction of the model and the mathematical background are given in heuristic form only, with reference, for rigorous development, to earlier reports (RM-2519, RM-3212, RM-3707, RM-3935-1). The results of validation experiments, consisting of chemical stresses applied to the model, are discussed. 122 pp. Bibliog. RM-4374-PR: Invariant Imbedding and Nonlinear Filtering Theory. AUTH: R.E. Bellman, Harriet Kagiwada, R.E. Kalaba, R. Sridhar PAGES: 19, DATE: 1964 COST: $ 4.00 KEYS: Filtering theory; Invariant imbedding ABST: The Memorandum supposes a system undergoing a process which can be described by the differential equation dx/dt = g (x, t). On the time interval (O, T) the function x is observed, in a noisy manner, and this experimental function is denoted by the symbol y. Many problems of orbit determination and adaptive control are of this type. The study suggests a solution, in both the scalar and vector cases, which makes use of certain ideas from the theory of invariant imbedding. Some numerical examples are also provided. 19 pp. Bibliog. RM-4517-1-ISA: Some Impressions of the Effects of Military Operations on Viet Cong Behavior. AUTH: L. Goure PAGES: 21, DATE: 1965 COST: $ 4.00 KEYS: Interviewing; Military operations; Southeast asia; Viet cong ABST: Tentative findings from a study of a small sample of interviews of Viet Cong captives and defectors. Viet Cong are vulnerable to detection and attack from the air, thus intensified air surveillance and harassing activities by day and night are likely to have a major disruptive effect. The interviews suggest that intensified ground patrolling has a significant disruptive effect and that protracted ground sweeps should be assessed in terms of their harassing impact rather than according to the number of Viet Cong casualties. 21 pp. RM-4532-PR: Measurement of Similarity Between Nouns. AUTH: K.E. Harper PAGES: 26, DATE: 1965 COST: $ 4.00 KEYS: Linguistics; Translating and interpreting ABST: A study of distributional semantics, or the classification of words on a behavioral basis, in automatic language data processing. The Memorandum presents some of the relevant behavioral conditions, applies these conditions to specified words in a restricted text, and measures the similarity of behavior of words that are presumed to be similar in meaning. The experiment is intended as a test of the validity of the distributional approach to semantics. 26 pp. RM-4549-ARPA: Computational Aspects of Inverse Problems in Analytical Mechanics, Transport Theory, and Wave Propagation. AUTH: Harriet Kagiwada PAGES: 314, DATE: 1965 COST: $ 25.00 KEYS: Astrophysics; Planetary sciences; Radiative transfer; Wave mechanics ABST: An investigation of inverse problems as basic problems in science, in which physical systems are to be identified on the basis of experimental observations. These problems are especially important in astrophysics and astronomy, for their objects of investigation are frequently not observable in a direct fashion. Solar and stellar structure, for example, is estimated from the study of spectra, while the structure of a planetary atmosphere may be deduced from measurements of reflected sunlight. This Memorandum shows that a wide class of inverse problems may now be solved with high-speed computers and modern computational techniques. 314 pp. Bibliog. RM-4551-NASA: Note on Thermal Properties of Mars. AUTH: C.B. Leovy PAGES: 24, DATE: 1965 COST: $ 4.00 KEYS: Mars (planet); Planetary sciences; Thermodynamics ABST: A simplified theory of diurnal temperature variations, in which the effect of the atmosphere is included, suggests a very low thermal conductivity for the upper few centimeters of the Martian ground. Such low conductivities appear to be possible only if the material composing this layer is extremely fine powder whose characteristic size is not more than a few microns. 24 pp. Bibliog. RM-4552-1-ARPA: Evolution of a Vietnamese Village--Part I: The Present, After Eight Months of Pacification. AUTH: R.M. Pearce PAGES: 84, DATE: 1965 COST: $ 7.50 KEYS: Counterinsurgency; Interviewing; South vietnam; Southeast asia ABST: Part of a study of the evolution of a rural Vietnamese village as it passes from insurgent control through pacification to government control. The environs of the village, its inhabitants, and the present situation are described. Implementation of the rural pacification program is discussed, including security and civic defense aspects, economic activities, education and information programs, and the impact of the pacification program on the population. 84 pp. RM-4699-1-ISA/ARPA: Some Impressions of Viet Cong Vulnerabilities: An Interim Report. AUTH: L. Goure, C.A.H. Thomson PAGES: 105, DATE: 1965 COST: $ 10.00 KEYS: Counterinsurgency; Interviewing; South vietnam; Southeast asia; Viet KEYS: cong ABST: A study, based on an analysis of interviews with prisoners and defectors, of Viet Cong vulnerabilities resulting from increased GVN and U.S. military activities. Possible approaches to the psychological warfare exploitation of these vulnerabilities are discussed. 105 pp. RM-4744-AID/ISA: Security and Assistance in Thailand: Supplement on the Thai "Rice Premium.". AUTH: H. Heymann, G. Rosen, V.D. Taylor, D.A. Wilson, C.J. Zwick PAGES: 26, DATE: 1965 COST: $ 4.00 KEYS: Agriculture; Economics--Foreign; Southeast asia; Thailand ABST: A discussion of the rice premium and agricultural policy in Thailand. The effects of the rice taxes on the farmer, on retail prices, and on government revenues are described. It is concluded that economic incentives are distorted and production retarded, and that the burden of the rice tax is borne not by the farmer alone, but by all of Thailand. 26 pp. RM-4775-NASA: Computational Results for Diffuse Transmission and Reflection for Homogeneous Finite Slabs with Isotropic Scattering. AUTH: R.E. Bellman, Harriet Kagiwada, R.E. Kalaba, S. Ueno PAGES: 38, DATE: 1965 COST: $ 4.00 KEYS: Astrophysics; Numerical methods and approximations; Radiative transfer ABST: Part of a continuing study of numerical methods of solution of radiative transfer processes. Diffuse reflection and transmission coefficients are computed for radiative transfer in homogeneous slabs of finite thickness with isotropic scattering. The results are summarized in graphs of these coefficients for a complete range of albedos and thicknesses. Representative tables of transmission coefficients are also included. 38 pp. RM-4810-PR: Soviet Cybernetics Technology: V. Soviet Process Control Computers. AUTH: W.B. Holland, J.B. Gazley, Willis.H. Ware PAGES: 92, DATE: 1965 COST: $ 7.50 KEYS: Computers; Control systems; Soviet Union--Cybernetics ABST: Details of eight recently developed Soviet control computers. The translations from Soviet source material (where information on the machines appeared) are extensively annotated. All pictures and diagrams from the original source items are included, as well as several photographs from other sources. The editors have appended many explanatory notes and comments, and have carefully checked each machine description from a technological standpoint. An appendix contains an alphabetical listing of all abbreviations used in the original Russian texts. RM-4844-PR: Some Thoughts on Graduated Escalation. AUTH: A.L. George PAGES: 34, DATE: 1965 COST: $ 4.00 KEYS: Counterinsurgency; Escalation; South vietnam; Southeast asia ABST: An edited, expanded version of a briefing given at the joint meeting of AFAG and the Board of Trustees in Washington, November 1965. The author offers general, tentative observations that help place the graduated escalation strategy employed by the United States in Vietnam in a useful analytical perspective. He defines graduated escalation; discusses the requirements for optimal coercion, and the conditions that determine what kind of coercive escalation will be used; and analyzes three earlier crises, and compares their successes and failures with the experience of Vietnam. The special circumstances of Vietnam, including the difficulty of dealing with four opponents--the Viet Cong, Hanoi, China, and Russia--rather than with one, are noted. The Memorandum draws on work in progress on problems in the use of force as an instrument of U.S. policy in limited conflicts. 34 pp. P-156: Some Bounded Significance Level Tests for the Median. AUTH: J.E. Walsh PAGES: 10, DATE: 1960 COST: $ 4.00 KEYS: Statistical analysis ABST: A presentation of some tests of a population median whose significance levels are only approximate but cover a wide range of suitable values. The significance levels of these tests are exactly determined if the populations are symmetrical; they are bounded otherwise. (Published in [The Annals of Mathematical Statistics], March 1949.) 10 pp. P-1806-1: Parameter-Free and Nonparametric Tolerance Limits: The Exponential Case. AUTH: L.A. Goodman, A. Madansky PAGES: 39, DATE: 1961 COST: $ 4.00 KEYS: Statistical analysis ABST: The development of exact parameter-free tolerance intervals based on the first [r]-ordered observations from a sample of size [n] from an exponential distribution. The authors examine various criteria for goodness of tolerance intervals, as well as the asymptotic behavior and certain optimum properties of these intervals. Comparisons are made between these intervals and the nonparametric tolerance intervals. The paper also discusses the effect of assuming an exponential distribution, when in fact the distribution is a mixture of two exponentials. 39 pp. Ref. P-1882: A Model for Evaluating Fleets of Transport Aircraft. AUTH: J.R. Summerfield PAGES: 15, DATE: 1960 COST: $ 4.00 KEYS: Airlift; Transportation--Mathematical models ABST: A description of a Monte Carlo model used in evaluating the capability of both actual and possible transport systems to meet the airlift demands of the United States military establishment. The model includes peacetime flying activities, wartime deployments, and the transition from peace to war. It helps to make comparisons among different transport fleets and can also be used to detect bottlenecks in a particular transport system. 15 pp. P-2029: Conflict Resolution in the Sino-Soviet Alliance. AUTH: A.S. Whiting PAGES: 33, DATE: 1961 COST: $ 4.00 KEYS: China; Soviet Union--Foreign relations ABST: Remarks focusing on the key variables which have affected conflict resolution in the Moscow-Peking axis. Illustrative references are given supporting the inclusion of such factors as the need for consensus between Peking and Moscow, an image of negotiations to understand past phenomena and future developments, and the relations which Peking and Moscow have each enjoyed with Communist parties outside the bloc. 33 pp. P-2037: The Commercial Aircraft Bomb Hazard: A Possible Answer. AUTH: L.S. Hill PAGES: 5, DATE: 1960 COST: $ 4.00 ABST: A proposed solution to the commercial aircraft bomb problem: that of dispersing luggage so that the passenger and his luggage will never be carried on the same airplane (or if so, not to the traveler's knowledge). This scheme may be considered an interim measure until air transports strengthened in vulnerable areas are available. The airlines will be benefited because delays and flight cancellations will be diminished P-2188-1: On Stability In Deterrent Races. AUTH: M.W. Hoag PAGES: 42, DATE: 1961 COST: $ 4.00 KEYS: Defense; Deterrence (Strategy); Disarmament; Military strategy; Nuclear KEYS: warfare ABST: A discussion of the distinction between deterrence and defense as military objectives and the effect of the distinction on the arms race and prospects for arms control. 42 pp. P-2210: Computational Considerations for Some Deterministic and Adaptive Control Processes. AUTH: R.E. Kalaba PAGES: 40, DATE: 1961 COST: $ 4.00 ABST: A discussion of design and utilization considerations in the fields of guidance and control which lead to problems in the calculus of variations and dynamic programming. The resulting equations are frequently so complex that modern digital computers must be used in their resolution. It is shown that the quasilinearization method discussed in P-1163 can be used effectively to deal with some nonlinear Euler equations and their associated boundary values. It is also shown that the concepts of dynamic processes such as occur in sequential detection schemes in radar and communication. P-2262: Statistical Determination of Error in Parachute-Derived Wind Velocities. AUTH: R.R. Rapp PAGES: 5, DATE: 1961 COST: $ 4.00 KEYS: Wind ABST: An analysis of the error of high-level wind determinations based on data from six tests in which parachutes were tracked by two radars. The instrument error is shown to be less than 3m/sec; the error caused by the failure of the parachute to follow the wind is much smaller. 5 pp. P-2287: Economic Growth and Foreign Aid: A Proposal Concerning the Export of Industrial Plants. AUTH: F.T. Moore PAGES: 20, DATE: 1961 COST: $ 4.00 KEYS: Industry; Developing countries; United states--Economic assistance ABST: A description of a program that can contribute directly to the growth of the U.S. economy and can also supply needed productive capacity to underdeveloped countries in Asia, Africa, and Latin America. In essence, the program is (1) to make available for export complete U.S. industrial plants that are obsolescing or submarginal in terms of U.S. costs and (2) to provide a means for U.S. industry to replace those plants by investment, at very attractive terms, in more modern equipment. 20 pp. P-2296: Simulation and Tax Analysis: A Research Proposal. AUTH: W.A. Steger PAGES: 31, DATE: 1961 COST: $ 4.00 ABST: A description of a proposed simulation model for studying certain important aspects of tax policy. An attempt is made to acquaint public finance experts with the potential rewards which new management-science and econometric tools can yield in the analysis of alternative tax proposals. The model described appears not only feasible and relatively inexpensive, but also a systematic and rational approach to a problem area which has been fraught with incertitude and controversy. P-2322: The Use of Manned Simulation in the Design of an Operational Control System. AUTH: M.A. Geisler, W.A. Steger PAGES: 12, DATE: 1961 COST: $ 4.00 ABST: A study of the general features of the planning and operations phases of a new weapon system. The uncertainties inevitable in planning mea that considerable effort is made during the operations phase to adjust the weapon system and its resources to the actual environment it finds so as to attain the desired level off operational capability. The adjustment mechanism is called an oeprational control system, and its elements are described. The proposal is made that a better control system can be designed if simulation is used to help design it during the planning phase. The use of simulation will not only produce a better control system earlier, but it will permit the planners to adjust the other resources provided for the weapon system so that they are compatible with the environment and the control system. An example of such a designed system is included. P-2435: Status Prediction of Schedule Equipment. AUTH: R.E. Johnson, B.J. Marks PAGES: 37, DATE: 1961 COST: $ 4.00 ABST: Consideration of the problem of predicting equipment status when movements of units of equipment from one state to another are governed not only by the transition probabilities of a Markov chain, but also by a control process that involves a form of scheduling. In scheduling, reassignments of equipment from certain states to others are planned for various future times. Because the number of units actually available for reassignment is a random variable,"expected reassignments" are used in determining equipment status at each successive stage in the prediction process. Expected reassignments are used to modify equipment status at the beginning of a period, and then the transition probabilites of a Markov chain are used to determine the status of equipment at the end of that period. By using the resulting predictions, a decisionmaker is in a position to evaluate the future performance of the system and to adjust his schedule accordingly. P-2573: Set-Theoretic Formalization of Computational Algorithms, Computable Functions, and General-Purpose Computers. AUTH: R.E. Levien PAGES: " 35, DATE: 1962 COST: $ 4.00 KEYS: Mathematics ABST: A formalization of the notion of computational algorithms. The corresponding class of algorithmically computable functions is identified, and the results are used to more clearly define "general-purpose computer." 35 pp. P-2582: Econometric Variations on a Theme by Schneider. AUTH: B.F. Massell PAGES: 11, DATE: 1962 COST: $ 4.00 KEYS: Africa, East ABST: Harold K. Schneider's paper "Economics in East African Aboriginal Societies" provides evidence that the Turu, an aboriginal tribe in the central part of Tanganyika, are to a large extent motivated by economic considerations, notably maximization of profit and accumulation of wealth. Elementary econometric techniques are used here to analyze Professor Schnieder's data relating to Turu agricultural production. His qualitative observations on the relationship among the variables are supplemented by a more formal treatment that involves fitting a production function to cross-section data by means of multiple regression analysis. 11 pp. P-2688: What Is Resource Analysis? AUTH: G.H. Fisher PAGES: 14, DATE: 1963 COST: $ 4.00 KEYS: Resource management ABST: An attempt to provide a basis for understanding the meaning of resource analysis. The specific meaning of this term is heavily dependent on the context of the particular problem, and the main features of several possible contexts are sketched. The author then outlines the major characteristics of a resource analysis capability designed primarily to serve in a longrange planning type of context. While adherence to these characteristics is fundamentally important in developing and operating a resource analysis activity, it alone will not ensure good analytical studies, which are heavily dependent on experience, good judgment, hard work, and ingenuity in creating and using analytical methods and techniques. 14 pp. P-2714: Electronic Data Processing for Cities--The Broad Look. AUTH: E.F.R. Hearle PAGES: 11, DATE: 1963 COST: $ 4.00 KEYS: City planning; Computers; Data processing ABST: A summary of what electronic data processing equipment can do for cities now and in the near future. Modern automatic data processing equipment greatly increases the capability of municipal agencies to handle information, especially if an integrated system serving the entire municipal organization is developed, rather than a piecemeal mechanization of familiar clerical operations. 11 pp. P-2721: Some Comments on Program Budgeting in the Department of Defense. AUTH: G.H. Fisher PAGES: 10, DATE: 1963 COST: $ 4.00 KEYS: United States. Dept. of defense; Program analysis ABST: A discussion of the basic objectives of program budgeting and some speculations on the future. The author stresses the progress made through 1962 and the importance of having a new, improved framework for integrated planning, programming, and budgeting, something that had not before existed in the defense establishment. 10 pp. P-2762: Selected Readings in Aerial Reconnaissance: A Reissue of a Collection of Papers from 1946 and 1948. AUTH: A.H. Katz PAGES: ix, 55, DATE: 1963 COST: $ 7.50 KEYS: Aerial reconnaissance ABST: A presentation of papers fundamental to the study of aerial reconnaissance. Because the concepts presented in these papers are considered still valid, they are a basis for current research and development in the field. A presentation of papers fundamental to the study of aerial reconnaissance. Because the concepts presented in these papers are considered still valid, they are a basis for current research and development in the field. 58 pp. P-2809: Operations Research Applications in Support Planning for Manned Space Flight. AUTH: S.I. Firstman PAGES: 9, DATE: 1963 COST: $ 4.00 KEYS: Operations research; Project--Apollo; Space flight ABST: An exploration of applications of operations research to the planning of support aspects of the Apollo mission and system. Against this background the paper generalizes concerning the potential roles of operations research in planning for the support of manned space flight. RM/P-2825: Dynamic Modeling of Inventories Subject to Obsolescence. AUTH: G.W. Brown, J.Y. Lu, R.J. Wolfson PAGES: 24, DATE: 1963 COST: $ 4.00 KEYS: Inventory management ABST: Inventory control procedures ordinarily allow for obsolescence by making an arbitrary blanket charge to be distributed over all supply items. The models discussed in this paper are concerned with optimization of ordering and disposal decisions, leading to policies of the (s,S) type, incorporating specific elements descriptive of the uncertainty of future demand for the particular item. RM/P-2850: The Role of Project Histories in the Study of R&D. AUTH: T.A. Marschak PAGES: 126, DATE: 1964 COST: $ 10.00 KEYS: Air-to-surface missiles; Bombers; Engines; Fighters; Radar; Research KEYS: and development ABST: This paper illustrates the possibilities as well as the limitations of the project-history approach to testing conjectures about the nature of development. A number of histories are presented in each of several areas of military technology. The histories describe, with varying thoroughness, (1) the major uncertainties in the project's successive stages; (2) the commitments made at each stage; and (3) the size of the project's total effort and the technical advance achieved by the developed item. P2854: Review of [The Politics Of] [Scarcity] by M. Weiner, for the [American Economic Review]. AUTH: G. Rosen PAGES: 5, DATE: 1964 COST: $ 4.00 KEYS: Economics--Foreign; India ABST: The reviewer recommends Weiner's book as a valuable and well-written contribution to the study of the politics of growth in all underdeveloped countries including India. RM-2869: Economic Selection of Alternative Risk Investments. AUTH: J.M. English, R.H. Haase PAGES: 16, DATE: 1964 COST: $ 4.00 KEYS: Economics--Domestic ABST: A study of the selection of the best of alternative investments where they involve different cash flows. It proposes a method for comparing pairs of alternatives in terms of an acceptable minimal-risk rate-of-return. The projection of incomes and expenses is assumed to be approximated by, but not limited to, continuous functions. Values of future sums are discounted continuously. The criterion of choice introduces an expectation-variance principle such that the computed rate-of-return is set at some specified level of confidence. The technique provides a way of comparing alternatives in which the probabilities differ for the several alternatives. This method appears to offer a better way to account for risk than the usual procedure of including it in the interest rate. P-2885: Electrostatic Forces and Cloud-Droplet Interaction. AUTH: M.H. Davis PAGES: 10, DATE: 1964 COST: $ 4.00 KEYS: Atmosphere; Meteorology ABST: A discussion of the effects of electrostatic forces on cloud-droplet trajectories, coalescence, and charging. Commonly occurring charges and fields in stable clouds may lead to nonvanishing collision efficiencies for drops smaller than 20 micron radius, but do not appreciably affect larger drop collisions. Charge transfer mechanisms are briefly discussed. The pulse of energy that occurs upon droplet coalescence is proposed as the source for observed radio signals. (Author) P-2899: Theoretically Permissible Altitudes and Seasons for the Occurrence of Clouds near the Mesopause. AUTH: G.F. Schilling PAGES: 13, DATE: 1964 COST: $ 4.00 KEYS: Atmosphere; Meteorology ABST: A thermodynamic exclusion principle is used to determine those regions in the earth's upper atmosphere where the formation of clouds due to condensation or sublimation of water vapor is or is not possible. The probability of occurrence of such clouds is then determined from model atmospheres as a function of altitude for different latitudes and seasons. The theoretical results correspond well with actually observed locations, frequencies, and altitudes of noctilucent clouds. It is shown that statistical analysis of certain noctilucent cloud data should not only permit experimental tests of the theoretical study, but also provide, by inference, information about variations of the mesopause altitude with latitude, season, and solar activity. 13 pp. P-2990: Review of Two Books on Economic Development: P. N. Rosenstein-Rodan, [Capital Formation and Economic] [Development] and [Pricing and Fiscal] [Policies], Allen and Unwin, Ltd., London, 1964. AUTH: G. Rosen PAGES: 4, DATE: 1964 COST: $ 4.00 KEYS: Economics--Foreign; India; Planning ABST: A review of the second and third books in a series of studies by the Massachusetts Institute of Technology Center for International Studies in India. The major theme of these two volumes is the clarification of the contribution that the economist can make to the problems of development in a particular country. P-2997-1: Communication Satellite Output Devices. AUTH: N.E. Feldman PAGES: 48, DATE: 1965 COST: $ 4.00 KEYS: Communication satellites; Electronics ABST: A review of the field of power amplification at communication satellite frequencies. The relative ability of semiconductor devices and vacuum tube amplifiers to generate signal power efficiently at frequencies of 1 to 10 kMc and power levels of 0.1 to 100 watts is the primary concern of this paper. Bibliog. P-3019: On Conformally Related Metric Spaces One of Which Admits an Irrotational Isometry. AUTH: D.G.B. Edelen PAGES: 17, DATE: 1964 COST: $ 4.00 KEYS: Gravity; Relativity theory ABST: The title of this paper describes its contents. 17 pp. P-3047: On the Response of Linear Systems to Certain Non-Gaussian Random Inputs. AUTH: G.M. Northrop, P.M. Schultheiss PAGES: 2, DATE: 1964 COST: $ 4.00 KEYS: Markov processes ABST: Consideration of a special class of non-Gaussian inputs that can be generated by passing a Gaussian Markov process through a nonlinear device without energy storage whose input and output stand in 1 to 1 relation. P-3125: Computational Solution of Radiative Transfer Problems in Cloud Physics. PAGES: 11, DATE: 1965 COST: $ 4.00 KEYS: Meteorology; Radiative transfer ABST: Multiple scattering of light in clouds is both important and complex. It is necessary to deal with time-varying diffuse light fields in the presence of anisotropic scattering and polarization, the coupling of radiation with heat and moisture transfer, and other complicating aspects. For the sake of simplicity, this paper views the radiative transfer problem in clouds as that of multiple scattering with an anisotropic phase function, leaving out heat transfer and other effects. Anisotropic scattering processes also take place in lakes and oceans and in glacial ice. 11 pp. P-3134: Cost-Effectiveness: An Introduction and Overview. AUTH: E.S. Quade PAGES: 19, DATE: 1965 COST: $ 4.00 KEYS: Cost effectiveness; Decision-making; Defense; System analysis ABST: A discussion of cost-effectiveness analysis as an aid to decisionmaking. Cost-effectiveness analysis is defined, and its scope, methodology, advantages, and limitations are described. P-3145: The Difference Between Weather Forecasters and Weather Advisors. AUTH: R.R. Rapp PAGES: 11, DATE: 1965 COST: $ 4.00 KEYS: Weather ABST: A discussion of techniques by which the meteorologist can communicate weather information more directly to those who benefit from it. Many problems now make such communication difficult, but a link between meteorologist and user, called the "weather advisor," could be instituted. This link would combine the operational requirements of the users with the information of the meteorologist for direct application. P-3185: A Cosmological Kinematics with Peculiar Motions. AUTH: D.G.B. Edelen PAGES: 43, DATE: 1965 COST: $ 4.00 KEYS: Cosmology ABST: The study derives a line element without peculiar motions and uniform mass density assumptions. It then determines the kinematical consequences of such a line element, including peculiar motions from the start. Bibliog. P-3210: Developments for Modern Management. AUTH: R.J. Freeman PAGES: 6, DATE: 1965 COST: $ 4.00 KEYS: Management; Operations research ABST: A brief discussion of the rapid development of operations research management science in recent years. It emphasizes the scientific nature of the field, distinguishes its particular goals, and outlines its future role in industry. P-3213: Correlation in a Bivariate Normal Distribution When the Conditional Variances Are Known. AUTH: S.J. Press PAGES: 32, DATE: 1965 COST: $ 4.00 KEYS: Statistics ABST: A consideration of the problems of estimation and hypothesis testing for the correlation coefficient in a nonsingular bivariate normal distribution when the conditional variances are known. Such problems arise, for example, when each of the variables can be measured by an instrument, with the other variable held fixed, and when the instrument manufacturers specify the precision of the instruments. It is shown that the statistic of interest in this problem is the sample covariance, [v]. The distribution of [v] is derived, in addition to its moments, some properties, and its asymptotic behavior. Some percentage points of the null distribution are tabulated. P-3230-1: Rainer Rohler, Some Relationships Between the Average Energy of Quanta in a Visual Stimulus and the Color Response, (Einige Zusammenhange Zwischen Der Mittleren Grosse Der Quanten in Einem Lichtreiz Und Der Farbempfindung), Vision Research, Vol. 5, 1965, Pp. 361-377. AUTH: J.J. Sheppard, J.F. Gross PAGES: 27, DATE: 1965 COST: $ 4.00 KEYS: Color; Optics; Physics; Vision P-3246: Some Thoughts on Range Planning and Operation. AUTH: R.J. Freeman PAGES: 14, DATE: 1965 COST: $ 4.00 KEYS: Intercontinental ballistic missiles; Space flight; Test methods ABST: A discussion of various aspects of missile range planning and operations, including both short- and long-term problems. The author presents a satellite assignment and scheduling model, along with a mobile resources model, to illustrate the application of quantitative techniques to range planning and operations. P-3266: Political and Economic Interrelationships in the Economic Development Process. AUTH: G. Rosen PAGES: 14, DATE: 1965 COST: $ 4.00 KEYS: Economics--Foreign; Planning; Policy sciences; Political science ABST: Presentation of a simple equilibrium model of the interrelationships of economic and political change. Because the author has found that political decisions determine the speed, priorities, and methods of a country's economic policies, he has devised a set of concepts, which he believes will be useful in conducting research on the economics of developing countries. He stresses that an economist, who hopes to make suggestions that will be implemented, must be aware of the ideological climate of a country, the strength of various political groups, and the political, social, and economic effects of the policies upon these groups. 14 pp. R-0427-PR: Functions Whose Best Rational Tchebycheff Approximations Are Polynomials. AUTH: B.W. Boehm PAGES: 20, DATE: 1964 COST: $ 4.00 KEYS: Approximation theory ABST: Let r*(n,m,f) denote the best approximation to a function f by a rational function which is the quotient of a polynomial of degree n by a polynomial of degree m. The following results are typical. r*(n,m,f) is a polynomial for all n and m if and only if f is a constant. r*(n,n,f) is a polynomial for all n if and only if f is a constant plus a multiple of a Tchebycheff polynomial. For any c 1, there exist continuous nonpolynomial functions f such that, for all n, r*(cn,n,f) is a polynomial. 20 pp. R-0427-PR: Existence of Best Rational Tchebycheff Approximations. AUTH: B.W. Boehm PAGES: 22, DATE: 1964 COST: $ 4.00 KEYS: Approximation theory ABST: A general theorem is stated and proved on the existence of best rational Tchebycheff approximations. Further theorems assure the existence of best weighted Tchebycheff approximations and constrained Tchebycheff approximations by rational functions and by approximating functions of other similar forms. 22 pp. R-0427-PR: Convergence of Best Rational Tchebycheff Approximations. AUTH: B.W. Boehm PAGES: 26, DATE: 1964 COST: $ 4.00 KEYS: Approximation theory ABST: Some bounds are established for the maximum deviation of an approximating rational function from a given function, in terms of continuity properties of the given function and the degrees of the polynomials comprising the rational function. Estimates of the rapidity of convergence of best rational Tchebycheff approximations are given, along with examples of nonconvergence phenomena and of functions to which convergence is arbitrarily slow. 26 pp. RM-3067-PR: Identifying and Estimating R&D Costs: Quiz, Problems, and Possible Solutions. AUTH: J.W. Noah PAGES: 29, DATE: 1962 COST: $ 4.00 KEYS: Cost estimating; Research and development; Weapon systems--Procurement ABST: A supplement to RM-3067-PR that is intended for persons interested in working out problems using the specific estimating relationships given in RM-3067-PR. 29 pp. RM-3317-ISA: Foreign Aid Costs in 1961. AUTH: J. Pincus PAGES: 26, DATE: 1963 COST: $ 4.00 KEYS: Accounting and budgets; Cost analysis; Military assistance programs; KEYS: United states--Economic assistance ABST: A computation of the real cost of official bilateral and multilateral aid offered in 1961 and 1962 by seven Western European countries, the United States, and Canada. Results indicate, on basis of incomplete data, that all countries tend to overstate the cost of their foreign aid. 26 pp. RM-3515/ARPA: Cost Effectiveness of AICBM for the Defense of ICBM Sites--Part V. AUTH: T.F. Burke PAGES: 54, DATE: 1964 COST: $ 7.50 KEYS: Antimissile defense; Cost effectiveness; Missile bases ABST: The fifth and last part of a study of cost effectiveness competition between HPD for missiles and proliferation of the missiles. The formulation of the problem treated here is a more complicated version of that treated in Part III. The attacker's launch reliability is treated separately from the effects of CEP, yield, target hardness, etc., and the attacker is credited with a firing tactic using a follow-up round of fire to replace reliability failures in the initial round. Although the reliability-compensating firing tactic is widely believed to increase the net lethality of the attack so greatly as virtually to compel the defense to buy HPD, this conclusion is not supported by this analysis. On the contrary: relatively inexpensive HPD is a good buy for the defense under a wide variety of circumstances, but expensive HPD is generally a poor buy. Thus the conclusions reached here are in general agreement with those reached in the previous parts of the study. RM-3519-PR: The Economy of the Chinese Mainland: National Income and Economic Development, 1933-1959, Volume I. AUTH: T.C. Liu, K.C. Yeh, C. Twanmo PAGES: 449, DATE: 1963 COST: $ 25.00 KEYS: China; Economics--Foreign ABST: A quantitative study of the economic development of the Chinese Mainland during 1952-1959, and a comparison of changes over this period with the condition of the pre-Communist and prewar Chinese Mainland economy in the 1930s. The method is that of national income accounting: detailed estimates of domestic product by industrial origin, and domestic expenditures by end use are derived for the years 1933 and 1952 through 1957. Very tentative estimates are offered for 1958-1959. Major findings are: (1) Net domestic product is estimated to have grown in 1952-1957 at an average annual rate of 6 percent in 1952 prices. (2) Widely divergent growth rates are found. For factories, mining, construction they range from 17 to 23 percent, but agricultural output is estimated to have increased by 1.7 percent. (3) Lack of reliable data rules out anything but conjectural estimates of changes in domestic products in 1958-1959. However, there is reason to believe that the Communist claim of increases in national income by 34 percent in 1958 and 22 percent in 1959 is grossly exaggerated. 449 pp. Bibliog. (AR) RM-3519-PR: The Economy of the Chinese Mainland: National Income and Economic Development, 1933-1959, Volume II (Appendixes). AUTH: T.C. Liu, K.C. Yeh, C. Twanmo PAGES: 552, DATE: 1963 COST: $ 25.00 KEYS: China; Economics--Foreign ABST: Tables of data to accompany RM-3519, volume I. 552 pp. RM-3583: Introduction to the International Conference on State of Stress in the Earth's Crust. AUTH: W.R. Judd PAGES: 59, DATE: 1964 COST: $ 7.50 KEYS: Geology; Mechanics; Stress ABST: An illustration that rock mechanics research and application involve many scientific disciplines and engineering professions. Examples are presented of the major problems facing rock mechanics, including the apparent fallacies in currently used theories. The major theses are (1) the advisability of using the theory of elasticity as merely the starting point for rock mechanics analyses and (2) the desirability of extended research on the effects of loading-rate variations in testing of rock. This Memorandum introduces the major points discussed in detail in RM-3583. 59 pp. Bibliog. RM-3686-PR: Interzonal Trade in Germany, Part II: Interaction with Early Berlin Conflicts. AUTH: H. Mendershausen PAGES: 69, DATE: 1963 COST: $ 7.50 KEYS: Berlin, germany; Economics--Foreign; Germany; International trade KEYS: and finance ABST: The second part of a study of the economic relations between West and East Germany, and their interaction with political developments in the Berlin area and elsewhere. This Memorandum describes and analyzes the beginning of interzonal trade and the relations between this trade and the Berlin conflicts in the period 1948 to 1952. The study recalls some of the early phases of the general European struggle from Hitler's downfall to the present. It highlights the interrelations between economic and political conflicts in post-World War II Germany and in wider contexts. 69 pp. RM-3786-ARPA: Certain Effects of Culture and Social Organization on Internal Security in Thailand. AUTH: H.P. Phillips, D.A. Wilson PAGES: 54, DATE: 1964 COST: $ 7.50 KEYS: Political science; Social science; Thailand ABST: A discussion of the assumption that modifications in Thai society aimed at strengthening internal security are likely to be effective to the degree that they take into account the motivations and attitudes of the Thai people and the functioning and ritualism of Thai institutions. A program that satisfies some of their existing needs (by traditional means wherever possible) promises success. 54 pp. Bibliog. RM-3787-PR: Sino-Soviet Economic Relations, 1958-1962. AUTH: O. Hoeffding PAGES: 12, DATE: 1963 COST: $ 4.00 KEYS: China; Communist countries; Economics--Foreign; International relations; KEYS: Soviet Union--Economics ABST: A considerably shortened version of the author's "Sino-Soviet Economic Relations, 1958-1962" (RM-3787-PR). This abridgment examines the following information relevant to Sino-Soviet relations through mid-July 1963: (1) the peak period in trade, 1958-1959; (2) the period of heavy decline, 1960-1962; (3) developments in 1962-1963; (4) implications for China, the world's largest underdeveloped country, one of the poorest, and virtually the only one not receiving economic aid from any source. Published in The Annals of the American Academy of Political and Social Science, September 1963. 12 pp. RM-3987-PR: An Exploration of the Values of Active and Passive Defense. AUTH: R.E. Levien PAGES: 25, DATE: 1965 COST: $ 4.00 KEYS: Defense; Strategic warfare ABST: A discussion of the multiple values of defenses structured to emphasize their diverse nature and to clarify their interrelationships. The Memorandum is concerned with the value of such defense in a range of four phases of conflict: peacetime, initiation, wartime, and terminal. 25 pp. RM-4264-PR: Soviet Transport and Communications: Output Indexes, 1928-1962. AUTH: N.M. Kaplan PAGES: 16, DATE: 1965 COST: $ 4.00 KEYS: Communication systems; Economics--Foreign; Transportation; Soviet KEYS: Union--Economics ABST: This Supplement to RM-4264-PR, published November 1964, extends the Soviet output indexes to 1963 and amends some of the results in the original study. 16 pp. RM-4654-PR: PARSE: A System for Automatic Syntactic Analysis of English Text--Part II. AUTH: J.J. Robinson, S. Marks PAGES: 270, DATE: 1965 COST: $ 20.00 KEYS: English language; Grammar; Linguistics NOTE: See also: RM-3339-PR, RM-4654-PR, Part, I. ABST: A listing of the three major components of PARSE, a system for the automatic syntactic analysis of English sentences. It contains: (1) a glossary of the words used, grouped alphabetically by families; (2) a presentation of the words organized by the grammar codes devised for them; and (3) a listing of 26 words which, because of their excessive length, would not fit the format and had to be removed from the main body of the glossary. A final section lists errata. (See also RM-3339-PR, and RM-4654-PR, Part I.) 270 pp. RM-4670-PR: Aircraft Turbine Engines--Development and Procurement Cost. AUTH: A.F. Watts PAGES: 85, DATE: 1965 COST: $ 7.50 KEYS: Airplanes; Cost estimating; Engines; Weapon systems--Procurement ABST: An examination of the development and procurement costs of aircraft turbine engines. The results are based on the history of 14 engines costing approximately $8 billion. Engine size and quantity in addition to institutional and environmental influences bear on the cost estimates. This study is intended primarily for those involved in long-range planning exercises on manned military aircraft employing air-breathing engines. 85 pp. P-3118: Testimony Before the Commission on Manpower, Automation and Technology. AUTH: P. Armer PAGES: 9, DATE: 1965 COST: $ 4.00 KEYS: Employment; Industry; Labor supply; Management; Technology ABST: A discussion of the difficulties in determining the impact of automation on industries. A manager cannot accurately answer the question because he cannot run an experiment with all factors constant except automation. Because what is happening is less important than why, the author finds that solutions involving reduction of the total production by society are wrong. The paper concludes that too few scientists are working in the public sector to accommodate the great rate of change in the private sector. 9 pp. P-2780: The Insensitivity of Heat Transfer to the Inclusion of First Order Slip Boundary Conditions for Similar Laminar Hypersonic Boundary Layers. AUTH: J. Aroesty PAGES: 10, DATE: 1963 COST: $ 4.00 KEYS: Aerodynamics; Boundary layer; Heat transfer; Laminar flow ABST: A modification of the hypersonic similar laminar boundary layer problem to include first order slip boundary conditions. Their inclusion results in no change in the energy transfer to the wall from the no-slip values, implying that slip effects alone are not adequate to explain the appearance of the heat transfer "plateaus" observed near the leading edge of a sharp flat plate in hypersonic flow. In addition, it is shown how the inclusion of slip boundary condition as the only higher order effect results in complete disagreement with observed pressure measurements for the cold wall case. A modification of the hypersonic similar laminar boundary layer problem to include first order slip boundary conditions. Their inclusion results in no change in the energy transfer to the wall from the no-slip values, implying that slip effects alone are not adequate to explain the appearance of the heat transfer "plateaus" observed near the leading edge of a sharp flat plate in hypersonic flow. In addition, it is shown how the inclusion of slip boundary condition as the only higher order effect results in complete disagreement with observed pressure measurements for the cold wall case. 10 pp. P-3231: Inviscid Cone Flows with Surface Mass Transfer. AUTH: J. Aroesty, S.H. Davis PAGES: 7, DATE: 1965 COST: $ 4.00 KEYS: Aerodynamics ABST: A consideration of the effects of surface mass transfer on inviscid flows. The authors discuss a simple, exact solution of the inviscid equations of motion including the effect of surface mass transfer. 7 pp. RM-3938-PR: An Empirical Test of Exponential Smoothing. AUTH: M. Astrachan, C.C. Sherbrooke, C.C. Sherbrooke PAGES: 64, DATE: 1964 COST: $ 7.50 KEYS: Logistics; Maintenance; Spares; Statistics ABST: A comparative study of techniques for predicting spare parts demand. It attempts to discover the potential advantage of exponential smoothing over the moving average procedures now in use by the Air Force. In exponential smoothing, the predicted average is found by weighting the average computed at the end of the last time period with the observed demand during the current period. One may vary the weighting constant on the basis of how much weight is wanted on the last average. The application of the smoothing and averaging is shown with three sets of data. The conclusions of the study are presented. A comparative study of techniques for predicting spare parts demand. It attempts to discover the potential advantage of exponential smoothing over the moving average procedures now in use by the Air Force. In exponential smoothing, the predicted average is found by weighting the average computed at the end of the last time period with the observed demand during the current period. One may vary the weighting constant on the basis of how much weight is wanted on the last average. The application of the smoothing and averaging is shown with three sets of data. The conclusions of the study are presented. 64 pp. Bibliog. RM-3514-NASA: Design and Use of an Early Communication Satellite System. AUTH: L.D. Attaway, L.B. Early, N.E. Feldman, E.E. Reinhart, L.B. Early, N.E. Feldman, E.E. Reinhart PAGES: 128, DATE: 1963 COST: $ 10.00 KEYS: Communication satellites ABST: An analysis of the value of available communication satellite techniques for establishing, in the near future, either low or medium capacity worldwide communication networks. The low-capacity net primarily would enable U.S. government agencies to communicate with a large number of foreign ground stations. The medium capacity net would provide communications for underdeveloped nations. The analysis shows that such networks could be established using current technology in satellites, launch vehicles, and ground station equipment. Cost comparisons with conventional communication methods show that the satellite nets would be attractive only for the longest over-water links. When more advanced satellites are available, they will be able to compete over shorter links. An analysis of the value of available communication satellite techniques for establishing, in the near future, either low or medium capacity worldwide communication networks. The low-capacity net primarily would enable U.S. government agencies to communicate with a large number of foreign ground stations. The medium capacity net would provide communications for underdeveloped nations. The analysis shows that such networks could be established using current technology in satellites, launch vehicles, and ground station equipment. Cost comparisons with conventional communication methods show that the satellite nets would be attractive only for the longest over-water links. When more advanced satellites are available, they will be able to compete over shorter links. 128 pp. RM-3853-PR: Existence of Competitive Equilibria in Markets with a Continuum of Traders. AUTH: R.J. Aumann PAGES: 73, DATE: 1964 COST: $ 7.50 KEYS: Competition; Economic theory ABST: It is well known, and easy to establish, that there exist markets that do not have competitive equilibria, provided the traders do not have convex preferences-that is, that the set of commodity bundles preferred or indifferent to a given bundle is not always convex. It is proved, nevertheless, that in a market consisting of a continuum of traders, each one individually insignificant, there is always a competitive equilibrium, even when the preferences are not convex. It is well known, and easy to establish, that there exist markets that do not have competitive equilibria, provided the traders do not have convex preferences--that is, that the set of commodity bundles preferred or indifferent to a given bundle is not always convex. It is proved, nevertheless, that in a market consisting of a continuum of traders, each one individually insignificant, there is always a competitive equilibrium, even when the preferences are not convex. (See also RM-3518-PR, RM-3553-PR.) 73 pp. P-2488-1: Behavior of the Firm Subject to External Regulatory Constraint. AUTH: H.A. Averch, L.L. Johnson, H. Averch, L.L. Johnson PAGES: 25, DATE: 1962 COST: $ 4.00 KEYS: Competition; Economic theory; Government control; Telephone ABST: An attempt to develop a theory of the monopoly firm seeking to maximize profit, but which is subject to a constraint on its rate of return. This model is then applied to the domestic telephone and telegraph industry. As the firm does not equate marginal rates of factor substitution to the ratio of factor costs, it operates inefficiently in the sense that (social) cost is not minimized at the output it selects. The firm has an incentive to expand into other regulated markets, even if it operates at a (long run) loss in these markets. Therefore, it may drive out other firms, or discourage their entry into these other markets, even though the competing firms may be lower cost producers. In applying the analysis to the telephone and telegraph industry, it is found that the model does contribute to understanding market behavior. An attempt to develop a theory of the monopoly firm seeking to maximize profit, but which is subject to a constraint on its rate of return. This model is then applied to the domestic telephone and telegraph industry. As the firm does not equate marginal rates of factor substitution to the ratio of factor costs, it operates inefficiently in the sense that (social) cost is not minimized at the output it selects. The firm has an incentive to expand into other regulated markets, even if it operates at a (long run) loss in these markets. Therefore, it may drive out other firms, or discourage their entry into these other markets, even though the competing firms may be lower cost producers. In applying the analysis to the telephone and telegraph industry, it is found that the model does contribute to understanding market behavior. 25 pp. RM-3728-PR: Some Applications of Polynomial Approximation to Dynamic Programming. AUTH: S.P. Azen, R.E. Bellman, S.E. Dreyfus PAGES: 58, DATE: 1963 COST: $ 7.50 KEYS: Control systems; Programming (mathematics) ABST: An investigation of two polynomial approximation techniques: subregional approximation of a function by low-order Legendre polynomials over sufficiently small subdivisions of the original region of definition; and approximating a function by Chebychev polynomials over the whole region of definition. Numerical results were obtained from FORTRAN programs applying these techniques to allocation and bang-bang control problems. 58 pp. RM-3819-ARPA: On Computational Approaches to Some Mathematical Models of Turbulence. AUTH: S.P. Azen, R.E. Bellman, J.M. Richardson PAGES: 22, DATE: 1964 COST: $ 4.00 KEYS: Atmosphere; Differential equations ABST: The first in a series of studies on turbulence. In this series the authors investigate computational methods for the solution of the model equation of Burgers. This Memorandum studies the application of a classical method of converting a partial differential equation into an infinite system of ordinary differential equations. Numerical results obtained from a FORTRAN program are given. The first in a series of studies on turbulence. In this series the authors investigate computational methods for the solution of the model equation of Burgers. This Memorandum studies the application of a classical method of converting a partial differential equation into an infinite system of ordinary differential equations. Numerical results obtained from a FORTRAN program are given. 22 pp. (See also RM-3918-ARPA.) RM-3917-ARPA: Higher-Order Approximations to the Computational Solution of Partial Differential Equations. AUTH: S.P. Azen PAGES: 15, DATE: 1964 COST: $ 4.00 KEYS: Differential equations; Numerical methods and approximations ABST: An investigation of two techniques of approximating the solution to a partial differential equation. The first of these involves approximating the solution at each stage by a higher-order difference algorithm. The second is that of storing the function at each stage by a polynomial. Numerical results were obtained from a FORTRAN program applying these techniques. An investigation of two techniques of approximating the solution to a partial differential equation. The first of these involves approximating the solution at each stage by a higher-order difference algorithm. The second is that of storing the function at each stage by a polynomial. Numerical results were obtained from a FORTRAN program applying these techniques. 15 pp. RM-4211-NIH: Details of the Program for a Mathematical Model of Drug Distribution Assuming Mixing in the Large Blood Vessels. AUTH: S.P. Azen PAGES: 37, DATE: 1964 COST: $ 4.00 KEYS: Biomathematics; Blood; Chemotherapy; Computer simulation; Drugs ABST: A report on an aspect of research to develop a mathematical model of chemotherapy as an aid in studying problems relating to distribution and localization of drugs in the body. Specifically, the Memorandum presents the completed equations for a two-organ model in which there is exchange between the stationary and flowing phases in the large blood vessels. Results of a computer program are also given. A report on an aspect of research to develop a mathematical model of chemotherapy as an aid in studying problems relating to distribution and localization of drugs in the body. Specifically, the Memorandum presents the completed equations for a two-organ model in which there is exchange between the stationary and flowing phases in the large blood vessels. Results of a computer program are also given. 37 pp. Bibliog. RM-4162-PR: JOSS: Scenario of a Filmed Report. AUTH: C.L. Baker PAGES: 51, DATE: 1964 COST: $ 7.50 KEYS: JOSS (Electronic computer system); Online data processing ABST: A description of JOSS (Johnniac Open Shop System), an on-line, time-shared use of the Rand Johnniac computer, providing computational service at a number of remote eletric typewriter consoles. As many as eight users at once may communicate with JOSS by means of a smooth language, specifically designed for on-line problem solving. JOSS handles many formula evaluation problems, providing the facility of a printing desk calculator as well as the cpapbilities of a stored-program computer. It also provides various arithmetic and trigonometric functions and allows flexible output in user-specified formats. A console consists of a standard IBM 868 typewriter with a slightly modified character set and a small box with a few indicator lights and activating switches. It uses continuous-feed, sprocket-guide, single-ply paper in 8 1/2 x 11 sheets. The user's input of instructions and data is typed in green , and JOSS responses in black. This memorandum contains the narration accompanying the filmed demonstration. A description of JOSS (Johnniac Open Shop System), an on-line, time-shared use of the Rand Johnniac computer, providing computational service at a number of remote electric typewriter consoles. As many as eight users at once may communicate with JOSS by means of a smooth language, specifically designed for on-line problem solving. JOSS handles many formula evaluation problems, providing the facility of a printing desk calculator as well as the capabilities of a stored-program computer. It also provides various arithmetic and trigonometric functions and allows flexible output in user-specified formats. A console consists of a standard IBM 868 typewriter with a slightly modified character set and a small box with a few indicator lights and activating switches. It uses continuous-feed, sprocket-guide, single-ply paper in 8 1/2 x 11 sheets. The user's input of instructions and data is typed in green, and JOSS responses in black. This memorandum contains the narration accompanying the filmed demonstration. 51 pp. RM-3194-JPL: Venus: A Chapter from Issledovaniye Fizicheskih Uslovii Na Lunye I Planetakh (Investigations of the Physical Conditions of the Moon and Planets). AUTH: N.P. Barabashev, D.H. Scott, D.V. Mohr, D.H. Scott, D.V. Mohr PAGES: 41, DATE: 1962 COST: $ 4.00 KEYS: Astronomy; Planetary sciences; Venus (planet) ABST: A summary of important observational data about Venus, particularly its brightness distribution, albedo, color index, and indicatrix of scattering as obtained by Schoenberg, Muller, Danjon, King, Barabashev, and others. A summary of important observational data about Venus, particularly its brightness distribution, albedo, color index, and indicatrix of scattering as obtained by Schoenberg, Muller, Danjon, King, Barabashev, and others. 41 pp. RM-3097-PR: On Distributed Communications: V. History, Alternative Approaches, and Comparisons. AUTH: P. Baran PAGES: 61, DATE: 1964 COST: $ 7.50 KEYS: Communication networks; Communication systems ABST: One in a series of eleven Memoranda detailing the Distributed Adaptive Message Block Network, a proposed digital data communications system based on a distributed network concept. It is primarily a background paper acknowledging the efforts of people in many fields working toward the development of large communications systems where reliability and survivability are mandatory. As these requirements become increasingly stringent, one is forced to consider new and more complicated systems than might otherwise be preferred. Because this is a new field of study, its terminology has been borrowed from different specialties and is inconsistent. This Memorandum connects the previous items in the series, concerned with the system concept and early modeling studies, with the remaining volumes, detailing the actual design and implementation of a network of the type proposed. One in a series of eleven Memoranda detailing the Distributed Adaptive Message Block Network, a proposed digital data communications system based on a distributed network concept. It is primarily a background paper acknowledging the efforts of people in many fields working toward the development of large communications systems where reliability and survivability are mandatory. As these requirements become increasingly stringent, one is forced to consider new and more complicated systems than might otherwise be preferred. Because this is a new field of study, its terminology has been borrowed from different specialties and is inconsistent. This Memorandum connects the previous items in the series, concerned with the system concept and early modeling studies, with the remaining volumes, detailing the actual design and implementation of a network of the type proposed. 61 pp. RM-3420-PR: On Distributed Communications: I. Introduction to Distributed Communications Networks. AUTH: P. Baran PAGES: 44, DATE: 1964 COST: $ 4.00 KEYS: Communication networks; Communication systems; Survival ABST: One in a series of eleven Memoranda detailing the Distributed Adaptive Message Block Network, a proposed digital data communications system based on a distributed network concept. It introduces the system concept and outlines the requirements for and design considerations of such a system, especially in regard to implications for its use in the 1970's. In particular, the Memorandum is directed toward examining the use of redundancy as one means of building communications systems to withstand heavy enemy attacks. One in a series of eleven Memoranda detailing the Distributed Adaptive Message Block Network, a proposed digital data communications system based on a distributed network concept. It introduces the system concept and outlines the requirements for and design considerations of such a system, especially in regard to implications for its use in the 1970s. In particular, the Memorandum is directed toward examining the use of redundancy as one means of building communications systems to withstand heavy enemy attacks. 44 pp. RM-3638-PR: On Distributed Communications: IV. Priority, Precedence, and Overload. AUTH: P. Baran PAGES: 72, DATE: 1964 COST: $ 7.50 KEYS: Communication networks; Communication systems ABST: One in a series of eleven Memoranda detailing the Distributed Adaptive Message Block Network, a proposed digital data communications system based on a distributed network concept. It is concerned with the establishment of traffic precedence doctrines designed to achieve optimum utilization of the communications resource, especially within a seriously degraded and overloaded network. One in a series of eleven Memoranda detailing the Distributed Adaptive Message Block Network, a proposed digital data communications system based on a distributed network concept. It is concerned with the establishment of traffic precedence doctrines designed to achieve optimum utilization of the communications resource, especially within a seriously degraded and overloaded network. 72 pp. RM-3762-PR: On Distributed Communications: VI. Mini-Cost Microwave. AUTH: P. Baran PAGES: 111, DATE: 1964 COST: $ 10.00 KEYS: Communication networks; Communication systems; Microwaves ABST: One in a series of eleven Memoranda detailing the Distributed Adaptive Message Block Network, a proposed digital data communications system based on a distributed network concept. It is a detailed consideration of a possible design for the network's communication links, based on the use of microwave repeater stations. Of several possible link designs examined, the mini-cost microwave appears least expensive. The mini-cost system is designed solely for use in transmitting digital signals within the Distributed Adaptive Message Block Network. Many of its specific facets, however, may be of use in other microwave applications. One in a series of eleven Memoranda detailing the Distributed Adaptive Message Block Network, a proposed digital data communications system based on a distributed network concept. It is a detailed consideration of a possible design for the network's communication links, based on the use of microwave repeater stations. Of several possible link designs examined, the mini-cost microwave appears least expensive. The mini-cost system is designed solely for use in transmitting digital signals within the Distributed Adaptive Message Block Network. Many of its specific facets, however, may be of use in other microwave applications. 111 pp. RM-3763-PR: On Distributed Communications: VII. Tentative Engineering Specifications and Preliminary Design for a High-Data-Rate Distributed Network Switching Node. AUTH: P. Baran PAGES: 100, DATE: 1964 COST: $ 7.50 KEYS: Communication networks; Communication systems ABST: One in a series of eleven memoranda detailing the Distributed Adaptive Message Block Network, a proposed digital data communications system based on a distributed network concept. It considers the engineering specifications of the proposed system's switching node. It is felt that a small, unmanned switching node (yet having higher throughput rates than current large installations occupying thousands of square feet and requiring many people to maintain operations) can be built. The network proposal revolves around the feasibility of using this small, unmanned switching node. specifications of the proposed system's switching node. RM-3764-PR: On Distributed Communications: VIII. The Multiplexing Station. AUTH: P. Baran PAGES: 114, DATE: 1964 COST: $ 10.00 KEYS: Communication networks; Communication systems ABST: One in a series of eleven Memoranda detailing the Distributed Adaptive Message Block Network, a proposed digital data communications system based on a distributed network concept. It describes the multiplexing stations that connect subscribers to switching nodes (detailed in RM-3763-PR) of the proposed broadband distributed network. The description is presented in engineering detail, showing how the station can process simultaneously traffic from as many as 1024 separate users, sending a mixture of start-stop teletype signals and synchronous signals at various rates. One in a series of eleven Memoranda detailing the Distributed Adaptive Message Block Network, a proposed digital data communications system based on a distributed network concept. It describes the multiplexing stations that connect subscribers to switching nodes (detailed in RM-3763-PR) of the proposed broadband distributed network. The description is presented in engineering detail, showing how the station can process simultaneously traffic from as many as 1024 separate users, sending a mixture of start-stop teletype signals and synchronous signals at various rates. 114 pp. RM-3766-PR: On Distributed Communications: X. Cost Estimate. AUTH: P. Baran PAGES: 32, DATE: 1964 COST: $ 4.00 KEYS: Communication networks; Communication systems; Cost estimating ABST: One in a series of eleven Memoranda detailing the Distributed Adaptive Message Block Network, a proposed digital data communications system based on a distributed network concept. It presents the equipment cost estimates for a proposed system based on an arbitrary network configuration consisting of 400 switching nodes servicing 100,000 simultaneous users via 200 principal multiplexing stations. Potentially the network can be expanded to handle more than one million users. One in a series of eleven Memoranda detailing the Distributed Adaptive Message Block Network, a proposed digital data communications system based on a distributed network concept. It presents the equipment cost estimates for a proposed system based on an arbitrary network configuration consisting of 400 switching nodes servicing 100,000 simultaneous users via 200 principal multiplexing stations. Potentially the network can be expanded to handle more than one million users. 32 pp. RM-3767-PR: On Distributed Communications: Summary Overview. AUTH: P. Baran PAGES: 34, DATE: 1964 COST: $ 4.00 KEYS: Communication networks; Communication systems ABST: One in a series of eleven memoranda detailing the Distributed Adaptive Message Block Network, a proposed digital data communications system based on a distributed network concept. It summarizes the development of the system proposal. The more salient features of the system (given in greater detail in the other memoranda in the series) are outlined, giving the casual reader an overview of the network. A reading of the introductory number of the series (RM-3420) and this one should suffice for a general understanding of it. Additionally, the advantages and disadvantages of the system are given and will greatly facilitate critical evaluation of the system's feasibility. One in a series of eleven Memoranda detailing the Distributed Adaptive Message Block Network, a proposed digital data communications system based on a distributed network concept. It summarizes the development of the system proposal. The more salient features of the system (given in greater detail in the other Memoranda in the series) are outlined, giving the casual reader an overview of the network. A reading of the introductory number of the series (RM-3420) and this one should suffice for a general understanding of it. Additionally, the advantages and disadvantages of the system are given and will greatly facilitate critical evaluation of the system's feasibility. (See also RM-3097, RM-3103, RM-3420, RM-3578, RM-3638, RM-3762 through RM-3766.) 34 pp. P-1989: A Digital Simulation of an Aided Adaptive Character Reading Machine. AUTH: P. Baran, G. Estrin, G. Estrin PAGES: 26, DATE: 1960 COST: $ 4.00 ABST: A simulation, on an IBM 709 computer, of a pattern-recognition system using an initial man-machine learning phase. Transformations on a deformed set of 48 samples of each of ten numerals are used to form separation filters, while a second set of 480 similarly varied numerals serve as the "unknown" characters that are examined. Measured probability density distributions of the inked areas of all characters are established, and a weighted stencil or filter is created to distinguish each character relative to the possible set of characters. This experiment demonstrates the extent to which the actual value of the best "score of match" between the unknown and each character in the set provides confidence in recognition. Whenever the best score is too low, it is possible to call for more complex processes to aid recognition permitting the construction of recognition systems of greater accuracy than the basic reading mechanism. No abstract available. 26 pp. P-1990: An Aided Adaptive Character Reader for Machine Translation of Languages. AUTH: P. Baran, G. Estrin, G. Estrin PAGES: 45, DATE: 1960 COST: $ 4.00 ABST: A description of an elementary procedure for the synthesis of a character-recognition device based on a learning experiment. Using information derived from a significant sample of the set of characters to be read and given identification of the samples by a human operator, a computer defines a set of "filters." These filters may then be used to transform unknown characters having similar type characteristics. During the recognition process a probability matrix for each character in the alphabet is used to compute a figure of merit for the hypothesis that an unknown character is the same as a known character. It is shown that this elementary model may aid in constructing a fast input device for a language translation machine if it was able to make use of frequency distribution characteristics of the dictionary. A possible implementation with a raw character reading rate up to 500 characters a second appears feasible. P-2626: On Distributed Communications Networks. AUTH: P. Baran PAGES: 40, DATE: 1962 COST: $ 4.00 KEYS: Communication networks; Communication systems; Reliability ABST: A discussion of the problem of building digital communication networks using links with less than perfect reliability. The redundancy level used is defined as a measure of connectivity. The systems planner must choose that form of redundancy so that the form of the noise or interference appears to be somewhat statistically independent for each redundant element added. If this goal is completely met, there can be an exponential payoff for a linear increase of added elements. As an example, the Paper examines the synthesis of a system in which the form of the disturbance or noise is the simultaneous destruction of many geographically separated installations. The system considered is a high-speed digital data transmission network composed of unreliable links, but which exhibits any arbitrarily desired level of systems reliability or survivability. A discussion of the problem of building digital communication networks using links with less