Mathematical Sciences: Some Problems in Partial DifferentialEquations
{'Code': '03040102', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'John V. Ryff', 'PO_EMAI': None, 'PO_PHON': None}
Work will be done on problems arising in several areas of                  partial differential equations.  Efforts will be made to                        characterize the spectrum of an elliptic differential operator, a               fundamental question in both mathematics and physics.  Special                  attention will be given to multiparticle Schrodinger operators.                 In this context, focus will be placed on predicting the                         finiteness or infiniteness of bound states for N-body atomic                    Schrodinger operators using geometric methods.  These operators                 model an atom with an infinitely heavy nucleus and N - 1                        electrons moving about the nucleus.                                                  Work will also be done investigating the spectral and                      scattering theory for certain reduced wave equations which are                  obtained from acoustic equations by separation the time variable.               Emphasis will be placed on wave equations with singular                         coefficients which are strongly discontinuous or do not behave                  well at infinity.  Applications of this research may be made to                 the analysis of wave propagation such as occurs in acoustic                     imaging.                                                                             A third direction this work will take deals with the                       establishment of the classical Muntz approximation theorem for                  sets of positive measure.  The approach to resolving this                       longstanding conjecture will use recent work relating properties                of an associated discontinuos coefficient wave equation boundary                value problem.  A solution to this basic question will                          demonstrate that the so-called bang-bang principle in the theory                of time optimal control for the heat equation is also valid.
[{'FirstName': 'Roger', 'LastName': 'Lewis', 'PI_MID_INIT': 'T', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Roger T Lewis', 'EmailAddress': 'lewis@math.uab.edu', 'NSF_ID': '000346768', 'StartDate': '09/15/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}, {'FirstName': 'Ian', 'LastName': 'Knowles', 'PI_MID_INIT': 'W', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Ian W Knowles', 'EmailAddress': 'iknowles@uab.edu', 'NSF_ID': '000350251', 'StartDate': '09/15/1987', 'EndDate': None, 'RoleCode': 'Co-Principal Investigator'}, {'FirstName': 'Yoshimi', 'LastName': 'Saito', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Yoshimi Saito', 'EmailAddress': 'saito@math.uab.edu', 'NSF_ID': '000380110', 'StartDate': '09/15/1987', 'EndDate': None, 'RoleCode': 'Co-Principal Investigator'}]
{'Name': 'University of Alabama at Birmingham', 'CityName': 'BIRMINGHAM', 'ZipCode': '352940001', 'PhoneNumber': '2059345266', 'StreetAddress': '701 S 20TH STREET', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Alabama', 'StateCode': 'AL', 'CONGRESSDISTRICT': '07', 'CONGRESS_DISTRICT_ORG': 'AL07', 'ORG_UEI_NUM': 'YND4PLMC9AN7', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF ALABAMA AT BIRMINGHAM', 'ORG_PRNT_UEI_NUM': None}
{'Name': None, 'CityName': None, 'StateCode': None, 'ZipCode': None, 'StreetAddress': None, 'CountryCode': None, 'CountryName': None, 'StateName': None, 'CountryFlag': None, 'CONGRESSDISTRICT': None, 'CONGRESS_DISTRICT_PERF': '""'}
{'Code': '1261', 'Text': 'CLASSICAL ANALYSIS'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1987&All=true', 'xml': '8719027.xml'}