Mathematical Sciences: Singular Perturbations in Applied    Mathematics: Methods and Applications
{'Code': '03040101', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'Alan Izenman', 'PO_EMAI': None, 'PO_PHON': None}
This research will develop and apply new singular perturbation          methods to boundary value problems for nonlinear ordinary differential          equations and for partial integro-differential-difference equations.            The results will enable us to calculate the stationary distribution of          fluctuations about, and the rate of transitions from                            (deterministically) stable states of dynamical systems subject to               noise.  Stochastic integro-differential-difference equations and their          associated forward and backward Kolmogorov equations will also be               analyzed.                                                                               The research will have direct applications to a variety                 of problems in science and engineering.  Among them are                         computer performance evaluation, customer service queue arrangements,           chemical physics, noise induced transitions between stable                      configurations of a dynamical system, etc.
{'FirstName': 'Bernard', 'LastName': 'Matkowsky', 'PI_MID_INIT': 'J', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Bernard J Matkowsky', 'EmailAddress': 'b-matkowsky@northwestern.edu', 'NSF_ID': '000164107', 'StartDate': '07/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Northwestern University', 'CityName': 'EVANSTON', 'ZipCode': '602080001', 'PhoneNumber': '3125037955', 'StreetAddress': '633 CLARK ST', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Illinois', 'StateCode': 'IL', 'CONGRESSDISTRICT': '09', 'CONGRESS_DISTRICT_ORG': 'IL09', 'ORG_UEI_NUM': 'EXZVPWZBLUE8', 'ORG_LGL_BUS_NAME': 'NORTHWESTERN UNIVERSITY', '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': '1266', 'Text': 'APPLIED MATHEMATICS'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1987&All=true', 'xml': '8703011.xml'}