Mathematical Sciences: Inverse Boundary Value Problems
{'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 to be done on this project is a continuation of                       mathematical analysis of inverse problems having roots in several               applications to the physical world.  The fundamental problem,                   known in the engineering literature as electrical impedance                     imaging or impedance computed tomography, is that of determining                the unknown conductivity inside a body from knowledge of steady                 state direct current measurements at the boundary.  Its                         successful resolution will provide a valuable diagnostic tool for               both the medical and biological sciences.  There are, however,                  serious mathematical as well as experimental difficulties.  The                 fact that the boundary measurements contain sufficient                          information to distinguish any isotropic conductivity was only                  recently established for three dimensional bodies.  In two-                     dimensions, the global uniqueness question - an essential first                 step - is still unresolved.                                                          There are related and more difficult questions still to be                 pursued in three dimensions.  In particular, the problem of                     continuous dependence of solutions on the boundary values is only               partially understood.  To date, the bounds measuring continuity                 are weak (logarithmic) and require further study.  Work will also               be done on reconstruction of solutions and a characterization of                the class of functions which can act as conductivity potentials.                     This research has natural relationships with other inverse                 problems such as multi-dimensional scattering and d-bar methods                 from several complex variables.                                                      Finally, it should be noted that the important anisotropic                 case will have to play a role in constructive approaches to the                 isotropic and will force researchers to understand more about                   this more general problem area.
[{'FirstName': 'John', 'LastName': 'Sylvester', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'John Sylvester', 'EmailAddress': 'sylvest@uw.edu', 'NSF_ID': '000148525', 'StartDate': '06/15/1988', 'EndDate': None, 'RoleCode': 'Co-Principal Investigator'}, {'FirstName': 'Gunther', 'LastName': 'Uhlmann', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Gunther Uhlmann', 'EmailAddress': 'gunther@math.washington.edu', 'NSF_ID': '000105393', 'StartDate': '06/15/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}]
{'Name': 'University of Washington', 'CityName': 'SEATTLE', 'ZipCode': '981951016', 'PhoneNumber': '2065434043', 'StreetAddress': '4333 BROOKLYN AVE NE', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Washington', 'StateCode': 'WA', 'CONGRESSDISTRICT': '07', 'CONGRESS_DISTRICT_ORG': 'WA07', 'ORG_UEI_NUM': 'HD1WMN6945W6', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF WASHINGTON', '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': '126100', 'Text': 'CLASSICAL ANALYSIS'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1988&All=true', 'xml': '8800153.xml'}