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On the convexity of the ovals of lemniscates

Author: J L Walsh; Harvard University.; United States. Air Force. Office of Scientific Research.
Publisher: Washington, D.C. : Mathematical Sciences Directorate, Air Force Office of Scientific Research, 1961.
Series: United States. Air Force Office of Scientific Research, AFOSR 794.
Edition/Format:   Print book : National government publication : EnglishView all editions and formats
Summary:
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  Read more...
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Additional Physical Format: Online version:
Walsh, J. L. (Joseph Leonard), 1895-1973.
Convexity of the ovals of lemniscates
(OCoLC)1103292631
Material Type: Government publication, National government publication
Document Type: Book
All Authors / Contributors: J L Walsh; Harvard University.; United States. Air Force. Office of Scientific Research.
OCLC Number: 227268326
Notes: September, 1961.
Contract Number: AF 49(638)-845.
Description: 11 pages ; 28 cm.
Series Title: United States. Air Force Office of Scientific Research, AFOSR 794.
Other Titles: Technical Report Archive & Image Library (TRAIL)
Responsibility: J.L. Walsh, Harvard University.

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).

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