RAND has explored, among other math-related topics, mathematics curricula in primary education and the role of mathematics in innovation, e.g., in the evaluation of new medical technologies or the development of methodologies such as game theory.
Report
A discussion of the process of finding a feasible solution of a linear programming problem by means of the simplex method. It is shown how certain rules regarding the details of the process result in the "composite" algorithm, a procedure used in se...
Report
The development of the algebraic solution of the linear-logarithmic programming problem, derived by means of Lagrange multipliers. Two numerical methods for solving the problem are then given, one of which is a generalization of a method previously ...
Report
One of the basic supporting studies in mathematics concerned with optimization processes. This one deals with optimal control of dynamic systems involving random variables. Optimal control rules are developed and evaluated, and the superiority of f...
Report
A basic supporting study in mathematics. A large number of problems of mathematical physics may be reduced to the solution of the equation u = f+lambda T(u), where T is a linear transformation. This Memorandum reduces a recent proposal to treat such ...
Report
A specialization of a theorem of Fritz John to the case of mathematical programming.
Report
A review of basic supporting studies in mathematics. Three earlier papers on a particular problem of optimal control, wherein a constraint is placed on the state variable, are considered, in order to show that the three sets of results are actually e...
Report
A method of allowing for uncertainties in the constant terms (i.e., right-hand sides) of a linear programming problem, and hence of producing realistic "safety margins" in the solution. This is done by fitting a mixture of uniform distributions to th...
Report
A talk given on linear programming, a mathematical technique that has enjoyed a flourishing growth since 1947, both in theory and in application. The paper discusses the role of linear programming in solving the optimal diet problem, the theory of li...
Report
An algorithm for optimal "matrix scaling"- multiplying rows and columns of a rectangular matrix by different factors so as to optimize its condition. The method is expected to improve the compu-tational solution of linear programming problems....
Report
A study concerned with an infinite Markov process with a finite number of states in which the transition probabilities for each stage range independently over sets that either are finite or are convex polyhedra. A finite computational procedure is gi...
Report
The solution of an infinite-dimensional linear- programming problem, which involves basic mathe- matical research. The problem, proposed by W. Prager, arose in an elastico-plastic structural-design context....
Report
A presentation of a new technique for resolving degeneracy in the simplex-method solution of linear programming problems. Unlike other lexicographic techniques, it uses only data associated with the right-hand side of the linear programming problem a...
Report
A discussion of the solution of the partial differential equations of applied mathematics on automatic digital computing machines through approximations by difference equations. The memorandum investigates the determination of discrete approximations...
Report
A translation from the German of an article appearing in Archives for Mathematics, Vol. I, No. 13, 1949. The paper deals with the representation of stationary stochastic processes in terms of simple functions of time.
RAND® is a registered trademark. Copyright © 1994-2013 RAND Corporation. Last Modified: November 09, 2012 Site Feedback »
