Mathematical Sciences: The Laplace Operator On Spheres (REU)
{'Code': '03040106', 'Directorate': {'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'Bernard McDonald'}
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.
{'FirstName': 'B. Frank', 'LastName': 'Jones', 'EmailAddress': None, 'StartDate': '05/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'William Marsh Rice University', 'CityName': 'Houston', 'ZipCode': '770051827', 'PhoneNumber': '7133484820', 'StreetAddress': '6100 MAIN ST', 'CountryName': 'United States', 'StateName': 'Texas', 'StateCode': 'TX'}
{'Code': '1260', 'Text': 'INFRASTRUCTURE PROGRAM'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1988&All=true', 'xml': '8804455.xml'}