Accession Number : AD0696970

Title :   SOME UNSOLVED PROBLEMS CONCERNING CONVEX BODIES,

Corporate Author : BOEING SCIENTIFIC RESEARCH LABS SEATTLE WASH MATHEMATICS RESEARCH LAB

Personal Author(s) : Klee,Victor

Report Date : SEP 1969

Pagination or Media Count : 29

Abstract : The document contains five unrelated articles, each providing an exposition of certain unsolved problems concerning convex bodies. The titles of the five articles are as follows: 'Is a body spherical if its HA-measurements are constant', 'What is the expected volume of a simplex whose vertices are chosen at random from a given convex body', 'Can the boundary of a d-dimensional convex body contain segments in all directions', 'What are the intersection graphs of arcs in a circle', and 'What is the maximum length of a d-dimensional snake.' The problem of the first article is related to solid-state physics, of the second to the analysis of multicomponent phase diagrams, of the to approximation theory, of the fourth to molecular genetics, and of the fifth to the design of analog-to-digital conversion systems. These relationships are described in the articles.

Descriptors :   (*TOPOLOGY, *CONVEX BODIES), BAND THEORY OF SOLIDS, ANALOG-TO-DIGITAL CONVERTERS, CODING, GENETICS, SPHERES, CONVEX SETS, GRAPHICS, PROBABILITY, COMBINATORIAL ANALYSIS, APPROXIMATION(MATHEMATICS), PROBLEM SOLVING

Subject Categories : Statistics and Probability
      Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE