Series: Publications des Archives Henri Poincare / Publications of the Henri Poincare Archives
Subseries: Science autour de / around 1900
2008, Approx. 300 p., Hardcover
ISBN: 978-3-7643-8652-8
Due: May 2008
About this book
With logicism and formalism, intuitionism is one of the main foundations for mathematics proposed in the twentieth century; and since the seventies, notably its views on logic have become important also outside foundational studies, with the development of theoretical computer science.
The aim of the book is threefold: to review and complete the historical account of intuitionism (in particular in relation to other varieties of constructivism); to present recent philosophical work on intuitionism; and to give examples of new technical advances and applications of intuitionism. This volume brings together 21 contributions by today's leading authors on these topics, and surveys the philosophical, logical and mathematical implications of the approach initiated in 1907 in L.E.J. Brouwer's dissertation.
Written for:
Researchers, teachers and students in the fields of philosophy, logic, mathematics, computer science, and history of science
Keywords:
Intuitionism
Series: Frontiers in Mathematics
2008, Approx. 400 p., Softcover
ISBN: 978-3-7643-8750-1
Due: July 2008
About this book
Based on algebraic techniques
First book entirely devoted to numerical analysis for additive operators
Covers various aspects of approximation methods for equations with conjugation arising in the boundary integral equation method
First book to present systematic study of approximation methods for the Muskhelishvili equation
Self-contained and accessible to graduate students
This book deals with numerical analysis for certain classes of additive operators and related equations, including singular integral operators with conjugation, the Riemann-Hilbert problem, Mellin operators with conjugation, double layer potential equation, and the Muskhelishvili equation. The authors propose a unified approach to the analysis of the approximation methods under consideration based on special real extensions of complex C*-algebras. The list of the methods considered includes spline Galerkin, spline collocation, qualocation, and quadrature methods.
Table of contents
Preface.- 1. Complex and Real Algebras.- 2. Integral Operators. Smooth Curves.- 3. Riemann-Hilbert Problem.- 4. Piecewise Smooth and Open Contours.- 5. Muskhelishvili Equation.- 6. Numerical Examples.- Bibliography.
Series: Operator Theory: Advances and Applications , Vol. 184
2008, Approx. 400 p., Hardcover
ISBN: 978-3-7643-8752-5
Due: July 2008
About this book
The present book deals with canonical factorization of matrix and operator functions that appear in state space form or that can be transformed into such a form. A unified geometric approach is used. The main results are all expressed explicitly in terms of matrices or operators, which are parameters of the state space representation. The applications concern different classes of convolution equations: the transport equation, singular integral equations, Wiener-Hopf equations with symbols analytic in a strip, and equations involving factorization of non-proper rational matrix functions. The analysis of canonical factorization for functions with symmetries, including spectral and J-spectral factorizations, related Ricatti equations, and elements of H-infinity control theory are also main topics.
This book is the second book written by the four authors in which the state space factorization method is systematically used and developed further. In their first book, released in 2007, the emphasis is on non-canonical factorizations and degree one factorizations, in particular. The present book concentrates on canonical factorization and its applications. Together both books present a rich and far reaching update of the 1979 monograph, the first book in the OTAA series, written by the first three authors.
Written for:
Graduates, postgraduates and researchers in operator theory, matrix theory and systems theory
Keywords:
factorization
matrix function
state space
Series: Modern Birkhauser Classics
Originally published in the series Mathematics: Theory and Application
1st ed. 1994. 2nd printing, 2008, Approx. 535 p. 30 illus., Softcover
ISBN: 978-0-8176-4770-4
Due: April 2008
About this book
The definitive text on eliminator theory
Revives the classical theory of resultants and discriminants
Presents both old and new results of the theory
"This book revives and vastly expands the classical theory of resultants and discriminants. Most of the main new results of the book have been published earlier in more than a dozen joint papers of the authors. The book nicely complements these original papers with many examples illustrating both old and new results of the theory."?Mathematical Reviews
"Collecting and extending the fundamental and highly original results of the authors, it presents a unique blend of classical mathematics and very recent developments in algebraic geometry, homological algebra, and combinatorial theory." ?Zentralblatt Math
"This book is highly recommended if you want to get into the thick of contemporary algebra, or if you wish to find some interesting problem to work on, whose solution will benefit mankind." ?Gian-Carlo Rota, Advanced Book Reviews
"cthe book is almost perfectly written, and thus I warmly recommend it not only to scholars but especially to students. The latter do need a text with broader views, which shows that mathematics is not just a sequence of apparently unrelated expositions of new theories, c but instead a very huge and intricate building whose edification may sometimes experience difficulties c but eventually progresses steadily." ?Bulletin of the American Mathematical Society
Table of contents
Preface.- Introduction.- General Discriminants and Resultants.- Projective Dual Varieties and General Discriminants.- The Cayley Method of Studying Discriminants.- Associated Varieties and General Resultants.- Chow Varieties.- Toric Varieties.- Newton Polytopes and Chow Polytopes.- Triangulations and Secondary Polytopes.- A-Resultants and Chow Polytopes of Toric Varieties.- A-Discriminants.- Principal A-Discriminants.- Regular A-Determinants and A-Discriminants.- Classical Discriminants and Resultants.- Discriminants and Resultants for Polynomials in One Variable.- Discriminants and Resultants for Forms in Several Variables.- Hyperdeterminants.- Appendix A. Determinants.- Appendix B. A. Cayley: On the Theory of Elimination.- Bibliography.- Notes and References.- List of Notation.- Index