This award continues an Research Experiences for Undergraduates site at Rice University for a research project for 8 students. The project involves the detailed study of the heat kernel on the n-dimensional unit sphere in (n+1)-dimensional Euclidean space. The special functions involved in such problems are trigonometric for n = 1, Legendre polynomials for n = 2, and ultraspherical polynomials for larger n. Unsolved problems for research for the students include the monotonic properties of the heat kernel. For fixed time, the monotonicity with respect to the location on the sphere was solved, essentially by the Research Experiences for Undergraduates site at Rice last year. For fixed location interesting questions abound in investigating its behavior as a function or time.

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Type
Standard Grant (Standard)
Application #
8804455
Program Officer
Bernard McDonald
Project Start
Project End
Budget Start
1988-05-01
Budget End
1989-10-31
Support Year
Fiscal Year
1988
Total Cost
$32,000
Indirect Cost
Name
Rice University
Department
Type
DUNS #
City
Houston
State
TX
Country
United States
Zip Code
77005