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A review of the Galton and Watson mathematical model that applies probability theory to the effects of chance on the development of populations, followed by a systematic development of branching processes (one of the generalizations from the Galton-Watson model), and a brief description of some of the important applications. The author develops the model for the neutron (one-group theory, isotropic case), for the Markov (continuous time) age-dependent branching processes, and for the branching processes in the theory of cosmic rays. Applications include transport and multiplication of neutrons and electron-photon cascades.

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