The Australian Journal of Mathematical Analysis and Applications

 Home News Editors Volumes RGMIA Subscriptions Authors Contact

ISSN 1449-5910

Sorry death is imminent for file: ../public_html/searchroot/files/tex/v21n2/v21i2p1.tex
Sorry death is imminent for file: ../public_html/searchroot/files/tex/v21n2/v21i2p2.tex
Sorry death is imminent for file: ../public_html/searchroot/files/tex/v21n2/v21i2p3.tex
Sorry death is imminent for file: ../public_html/searchroot/files/tex/v21n2/v21i2p4.tex
You searched for willett
Total of 2 results found in site

2: Paper Source PDF document

Paper's Title:

Extreme Curvature of Polynomials and Level Sets

Author(s):

Stephanie P. Edwards, arah J. Jensen, Edward Niedermeyer, and Lindsay Willett

Department of Mathematics,
Hope College,
Holland, MI 49423,
U.S.A.
E-mail: sedwards@hope.edu
E-mail: tarahjaye@gmail.com
E-mail: eddie.niedermeyer@gmail.com
E-mail: willettlm1@gmail.com
WWW: http://math.hope.edu/sedwards/

Abstract:

Let f be a real polynomial of degree n. Determining the maximum number of zeros of kappa, the curvature of f, is an easy problem: since the zeros of kappa are the zeros of f'', the curvature of f is 0 at most n-2 times. A much more intriguing problem is to determine the maximum number of relative extreme values for the function kappa. Since kappa'=0 at each extreme point of kappa, we are interested in the maximum number of zeros of kappa'. In 2004, the first author and R. Gordon showed that if all the zeros of f'' are real, then f has at most n-1 points of extreme curvature. We use level curves and auxiliary functions to study the zeros of the derivatives of these functions. We provide a partial solution to this problem, showing that f has at most n-1 points of extreme curvature, given certain geometrical conditions. The conjecture that f has at most n-1 points of extreme curvature remains open.

Search and serve lasted 0 second(s).