Accession Number : AD0264702

Title :   ON THE CONVEXITY OF THE OVALS OF LEMNISCATES

Corporate Author : HARVARD UNIV CAMBRIDGE MASS

Personal Author(s) : WALSH,J.L.

Report Date : SEP 1961

Pagination or Media Count : 1

Abstract : A lemniscate is defined as a locus in the zplane P(z) = M, where P(z) is a polynomial not identically constant and M is a constant. This locus consists of one or more Jordan curves (branches of the lemniscate), which are mutually exterior except that each one of a finite number of points may belong to several branches. Each branch is sometimes called an oval, and the question arises whether these curves are actually ovals in the sense of being convex, at least when M is sufficiently small. (Author)

Descriptors :   *CONVEX SETS, ALGEBRA, CONFORMAL MAPPING, FUNCTIONS(MATHEMATICS), POLYNOMIALS, THEORY

Distribution Statement : APPROVED FOR PUBLIC RELEASE