Accession Number:

AD0683773

Title:

INTERSECTION THEOREMS FOR POSITIVE SETS

Descriptive Note:

Corporate Author:

BOEING SCIENTIFIC RESEARCH LABS SEATTLE WA MATHEMATICS RESEARCH LAB

Personal Author(s):

Report Date:

1969-01-01

Pagination or Media Count:

15.0

Abstract:

In a vector space over an ordered field, a positive set is one that is closed under the operation of forming linear combinations with nonnegative coefficients it may be described alternatively as a convex cone whose apex is the origin. Such sets arise naturally as solutions of systems of homogeneous linear inequalities, and the intersection theorems proved here can be reformulated as consistency theorems for such systems. The main tool used in proving the intersection theorems is a characterization and classification of sets which enjoy a strong independence property with respect to the formation of nonnegative linear combinations.

Subject Categories:

  • Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE