Mathematical Sciences: Model Theory and Algebra
{'Code': '03040200', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'Ralph M. Krause', 'PO_EMAI': None, 'PO_PHON': None}
This project continues the development of a theory for                     treating decidability questions about analytic solutions of                     systems of differential equations.  For example, the principal                  investigator and J. Denef have previously shown that there is no                algorithm for deciding if a single ordinary differential equation               has an analytic solution on the non-negative real numbers, even                 given that it has a unique solution near zero.  Part 1 of the                   project is the development of a theory of nonarchimedean rigid                  semi-analytic and sub-analytic sets.  (By this is meant the                     theory of semi-analytic and sub-analytic sets over a                            nonarchimedean, algebraically closed, complete normed field.)                   This development will parallel the recent treatment of p-adic                   semi-analytic and sub-analytic sets of Denef and van den Dries.                 The principal investigator has proved an analytic elimination                   theorem (over nonarchimedean, algebraically closed, complete                    normed fields) which will facilitate the development of the                     theory.  Results sought include (a) that the complement of a                    rigid sub-analytic set is subanalytic; (b) that every subanalytic               set is a finite disjoint union of subanalytic manifolds; (c)                    nonarchimedean Lojasiewicz inequalities for rigid subanalytic                   sets and functions; and some further results.  In part 2 the                    principal investigator seeks to show that algebraic subsets of                  the p-adic integers Zp, defined by polynomials involving few                    monomials, if they are finite contain only few points in Zp.  In                part 3, he will investigate a decision problem about the                        existence of power series solutions of maximally overdetermined                 systems of partial differential equations.
{'FirstName': 'Leonard', 'LastName': 'Lipshitz', 'PI_MID_INIT': 'M', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Leonard M Lipshitz', 'EmailAddress': 'lipshitz@math.purdue.edu', 'NSF_ID': '000195513', 'StartDate': '06/15/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Purdue Research Foundation', 'CityName': 'WEST LAFAYETTE', 'ZipCode': '479064353', 'PhoneNumber': '3174946200', 'StreetAddress': '1281 WIN HENTSCHEL BLVD STE 2500', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Indiana', 'StateCode': 'IN', 'CONGRESSDISTRICT': '04', 'CONGRESS_DISTRICT_ORG': 'IN04', 'ORG_UEI_NUM': 'C1G1LGYJF5G5', 'ORG_LGL_BUS_NAME': 'PURDUE RESEARCH FOUNDATION', 'ORG_PRNT_UEI_NUM': 'YRXVL4JYCEF5'}
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{'Code': '1268', 'Text': 'FOUNDATIONS'}
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