Mathematical Sciences: Some Elementary Inequalities
{'Code': '03040103', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': None, 'PO_EMAI': None, 'PO_PHON': None}
The foundation upon which mathematical analysis rests is                 the real number system, which in turn depends upon the                          concept of completeness and limits.  Both in theory and                         practice, estimation and approximation of real numbers is a                     fundamental concept, crucial to all forms of scientific and                     engineering endeavor.  There are a few famous inequalities --                   those that bear the names Cauchy, Schwarz, Minkowski, and                       Holder, for example -- that were discovered long ago, and                       which are basic to the general theory of inequalities.  It is a                 rare and important event when a new inequality is discovered,                   for such an occurence surely foreshadows important and                          previously unsuspected or unobtainable applications.                                       Professor Bennett has the enviable distinction of having             recently discovered some new fundamental inequalities. They                     have led to solution of a number of outstanding problems in                     the theory of majorization.  Moreover, this work has allowed                    Professor Bennett to conjecture still more powerful                             extensions of his inequalities, which in turn would open new                    research directions in very basic subjects such as function                     theory, operator theory, eigenvalue distribution, orthogonal                    series, and matrix theory.  Professor Bennett will continue                     this unique and important research program.
{'FirstName': 'Grahame', 'LastName': 'Bennett', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Grahame Bennett', 'EmailAddress': 'bennettg@indiana.edu', 'NSF_ID': '000221869', 'StartDate': '07/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Indiana University', 'CityName': 'BLOOMINGTON', 'ZipCode': '474057000', 'PhoneNumber': '3172783473', 'StreetAddress': '107 S INDIANA AVE', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Indiana', 'StateCode': 'IN', 'CONGRESSDISTRICT': '09', 'CONGRESS_DISTRICT_ORG': 'IN09', 'ORG_UEI_NUM': 'YH86RTW2YVJ4', 'ORG_LGL_BUS_NAME': 'TRUSTEES OF INDIANA UNIVERSITY', 'ORG_PRNT_UEI_NUM': 'YH86RTW2YVJ4'}
{'Name': None, 'CityName': None, 'StateCode': None, 'ZipCode': None, 'StreetAddress': None, 'CountryCode': None, 'CountryName': None, 'StateName': None, 'CountryFlag': None, 'CONGRESSDISTRICT': None, 'CONGRESS_DISTRICT_PERF': '""'}
{'Code': '1262', 'Text': 'MODERN ANALYSIS'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1987&All=true', 'xml': '8702358.xml'}