This book contains a collection of papers covering recent progress in a number of areas of singularity theory. Topics include blow analyticity, recent progress in the research on equivalence relations of maps and functions, sufficiency of jets, and the transversality theorem. . Geometric and analytic studies of partial differential equations have been developed independently of one another, but the shock wave solutions appearing in natural phenomena are not well understood. Singularity theory may unify these studies and a survey based on this viewpoint is presented in which a new notion of weak solution is introduced. There are also reports on the recent progress in Zariski's conjecture on multiplicities of hypersurfaces, transcendency of analytic sets and on the topology of weighted homogeneous polynomials. This book will be of particular interest to specialists in singularities, partial differential equations, algebraic geometry and control theory.

by Toshisumi Fukui, Shuichi Izumiya, Satoshi Koike, Toshisumi Fukuda. Published December 12, 1997 by Chapman & Hall/CRC.

Toshisumi Fukui, Shuichi Izumiya, Satoshi Koike, Toshisumi Fukuda. Geometric and analytic studies of partial differential equations have been developed independently of one another, but the shock wave solutions appearing in natural phenomena are not well understood.

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By Toshisumi Fukui, Shuichi Izumiya, Satoshi Koike, Toshisumi Fukuda. Chapman and Hall/CRC. This book will be of particular interest to specialists in singularities, partial differential equations, algebraic geometry and control theory. List of participants. Tzee-Char Kuo's contributions to real singularities. Blow-analytic equisingularities, properties, problems and progress. Learn mor. Advanced Mathematics. Analysis - Mathematics. Differential Equations.

Fukui introduced an invariant for the blow-analytic equivalence of real singularities. For a nondegenerate analytic function (germ) f, he discovered a formula for computing the one-dimensional invariant, denoted by A(f) : A 1(f). We find a formula for A(f) for any f (real or complex, degenerate or not). In this note, we give another characterization of C 0 -sufficiency of jets by using the after blowing-up functions. In practice, this criterion is often easier to check than the above one. Here we describe the results about C 0 -sufficiency in ℰ (n,1) only.

This complements our previous definition of the weight filtration of Borel–Moore homology. Mathematics Subject Classification (2000). Primary: 14P25 Secondary: 14P10. To Heisuke Hironaka on the occasion of his 80th birthday.

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Fukiu, Shuichi Izumiya. Be the first to ask a question about Real Analytic and Algebraic Singularities. Lists with This Book. This book is not yet featured on Listopia. This book contains a collection of papers covering recent progress in a number of areas of singularity theory.

Paperback: 224 pages. ISBN-13: 978-1584881254. Product Dimensions: . x . inches. Shipping Weight: 1. ounces (View shipping rates and policies).

C44 2003 512 . 5-dc21 2003040911. Contents 1 Introductio n 2 Characteristic spaces and algebraic reductio n 2. 1 Characteristic spaces for ideals o f polynomial s 2. 2 Algebraic reduction for analytic Hilbert module s 2. 3 Submodules with ﬁnite ran k 2. 4 AF-cosubmodule s 2. 5 Finite codimensiona l submodules o f Bergman module s 2. 6 Remarks on Chapter 2 3 Rigidity for analytic.

Fukui Fukuda, Shuichi Izumiya, Satoshi Koike, Takuo Fukuda, T. Fukuda Paperback, 232 Pages, Published 1997 by Chapman And Hall/Crc ISBN-13: 978-0-582-32874-7, ISBN: 0-582-32874-8.