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Let K be a closed convex set in E superscript (m + 1) and L = (P = (P sub 0, ..., P sub m): P sub 1 = P sub 2 = ...P sub m = 0). Then for the simple problem: Minimize P sub 0 Subject to P = (P sub 0, P sub 1, ..., P sub m) epsilon the intersection of K and L, we prove a duality theorem and the convergence of a solution algorithm modeled on the duality theorem and the simplex method of linear programming respectively. Specialization of this general model to linear programming, convex programming, generalized programming, control theory, and the decomposition approach to mathematical programming yield the appropriate duality theorems and solution algorithms in each case.

A series of research projects is briefly summarized which includes investigations in the following areas: (1) mathematical programming problems for large system and infinite-dimensional spaces, (2) bounded-input bounded-output stability, (3) non-parametric approximations, and (4) differential games. A list of reports and papers which were published over the ten year period of research is included.

A series of research projects is briefly summarized which includes investigations in the following areas: (1) mathematical programming problems for large system and infinite-dimensional spaces, (2) bounded-input bounded-output stability, (3) non-parametric approximations, and (4) differential games. A list of reports and papers which were published over the ten year period of research is included.

1Our Atomic World: The Story of Atomic Energy

By C. Jackson Craven

This booklet is part of the "Understanding the Atom Series" published by the Division of Technical Information of the U.S. Atomic Energy Commission. From an introduction of atomic theory by the ancient Greeks through the development of the fission bomb, the author covers such areas as the discovery of the nucleus, the discovery of isotopes, fission and fusion including a chronology of atomic theory to 1963, and the development of the Atomic Energy Commission. (Summary by Larry Wilson)