Series: Nonconvex Optimization and Its Applications , Vol. 90
2009, Approx. 450 p., Hardcover
ISBN: 978-3-540-85670-2
Due: December 8, 2008
The present book discusses the Kuhn-Tucker Optimality, Karush-Kuhn-Tucker Necessary and Sufficient Optimality Conditions in presence of various types of generalized convexity assumptions. Wolfe-type Duality, Mond-Weir type Duality, Mixed type Duality for Multiobjective optimization problems such as Nonlinear programming problems, Fractional programming problems, Nonsmooth programming problems, Nondifferentiable programming problems, Variational and Control problems under various types of generalized convexity assumptions.
Introduction and Motivation.- Generalized Convex Functions.- Type I and Related Functions.- Optimality Conditions.- Duality Theory.- Second and Higher Order Duality.- Symmetric Duality.- Vector Variational-like Inequality Problems.
Series: Graduate Texts in Mathematics , Vol. 254
Originally published in the series: Universitext
2009, Approx. 365 p., Softcover
ISBN: 978-3-540-76877-7
Due: December 3, 2008
The theory of algebraic function fields has its origins in number theory, complex analysis (compact Riemann surfaces), and algebraic geometry. Since about 1980, function fields have found surprising applications in other branches of mathematics such as coding theory, cryptography, sphere packings and others. The main objective of this book is to provide a purely algebraic, self-contained and in-depth exposition of the theory of function fields.
This new edition, published in the series Graduate Texts in Mathematics, has been considerably expanded. Moreover, the present edition contains numerous exercises. Some of them are fairly easy and help the reader to understand the basic material. Other exercises are more advanced and cover additional material which could not be included in the text.
This volume is mainly addressed to graduate students in mathematics and theoretical computer science, cryptography, coding theory and electrical engineering.
1. Foundations of the Theory of Algebraic Function Fiels.- 2. Geometric Goppa Codes.- 3. Extensions of Algebraic Function Fields.- 4. Differentials of Algebraic Function Fields.- 5. Algebraic Function Fields over Finite Constant Fields.- 6. Examples of Algebraic Function Fields.- 7. More about Geometric Goppy Codes.- 8. Subfield Subcodes and Trace Codes.- Appendix A. Field Theory.- Appendix B. Algebraic Curves and Algebraic Function Fields.- Bibliography.- List of Notations.- Index
Series: Lecture Notes in Mathematics , Vol. 1966
2009, XII, 154 p., Softcover
ISBN: 978-3-540-88744-7
Due: November 20, 2008
The dramatic changes that came about in analysis during the twentieth century are truly amazing.
In the thirties, complex methods and Fourier series played a seminal role. After many improvements, mostly achieved by the Calderon-Zygmund school, the action today is taking place in spaces of homogeneous type. No group structure is available and the Fourier transform is missing, but a version of harmonic analysis is still available. Indeed the geometry is conducting the analysis.
The authors succeed in generalizing the construction of wavelet bases to spaces of homogeneous type. However wavelet bases are replaced by frames, which in many applications serve the same purpose.
1 Calderon-Zygmund Operator.- 2 Boundedness of CZO on Wavelet Space.- 3 Wavelet Expansions.- 4 Wavelets and Spaces of Functions.-5 Non Homogeneous Spaces
Series: Sources and Studies in the History of Mathematics and Physical Sciences
Original French edition published by Editions de l’Ecole Polytechnique, 2004
2009, Approx. 220 p. 10 illus., Softcover
ISBN: 978-0-387-87867-6
Due: January 2009
In 1915 and 1916 Emmy Noether was asked by Felix Klein and David Hilbert to assist them in understanding issues involved in any attempt to formulate a general theory of relativity, in particular the new ideas of Einstein. She was consulted particularly over the difficult issue of the form a law of conservation of energy could take in the new theory, and she succeeded brilliantly, finding two deep theorems.
But between 1916 and 1950, the theorem was poorly understood and Noether’s name disappeared almost entirely. People like Klein and Einstein did little more then mention her name in the various popular or historical accounts they wrote. Worse, earlier attempts which had been eclipsed by Noether’s achievements were remembered, and sometimes figure in quick ‘historical’ accounts of the time.
This book carries a translation of Noether’s original paper into English, and then describes the strange history of its reception and the responses to her work. Ultimately the theorems became decisive in a shift from basing fundamental physics on conservations laws to basing it on symmetries, or at the very least, in thoroughly explaining the connection between these two families of ideas. The real significance of this book is that it shows very clearly how long it took before mathematicians and physicists began to recognize the seminal importance of Noether’s results. This book is thoroughly researched and provides careful documentation of the textbook literature. Kosmann-Schwarzbach has thus thrown considerable light on this slow dance in which the mathematical tools necessary to study symmetry properties and conservation laws were apparently provided long before the orchestra arrives and the party begins.
Emmy Noether’s Paper, Invariant Variational Problems.- Introduction.- The Circumstances of the Composition of Noether’s Paper.- The Theorems of Noether.- The Appreciation of her Theorems by her Contemporaries and by Historians.- The Transmission of her Ideas, 1918-1951.- The Fortunate of the 2nd Theorem after 1950.- Since 1970, True Generalizations.- Conclusion.- Appendices I-IV.- Bibliography.- Index
Series: Lecture Notes in Mathematics , Vol. 1967
2009, Approx. 320 p., Softcover
ISBN: 978-3-540-89055-3
Due: January 14, 2009
The notion of an operad supplies both a conceptual and effective device to handle a variety of algebraic structures in various situations. Operads were introduced 40 years ago in algebraic topology in order to model the structure of iterated loop spaces. Since then, operads have been used fruitfully in many fields of mathematics and physics.
This monograph begins with a review of the basis of operad theory. The main purpose is to study structures of modules over operads as a new device to model functors between categories of algebras as effectively as operads model categories of algebras.
Part I. Categorical and operadic background.- 1 Symmetric monoidal categories for operads.- 2 Symmetric objects and functors.- 3 Operads and algebras in symmetric monoidal categories.- 4 Miscellaneous structures associated to algebras over operads.- Part II. The category of right modules over operads and functors.- 5 Definitions and basic constructions.- 6 Tensor products.- 7 Universal constructions on right modules over operads.- 8 Adjunction and embedding properties.- 9 Algebras in right modules over operads.- 10 Miscellaneous examples. - Part III. Homotopical background.-11 Symmetric monoidal model categories for operads.- 12 The homotopy of algebras over operads.- 13 The (co)homology of algebras over operads.- Part IV. The homotopy of modules over operads and functors.- 14 The model category of right modules.- 15 Modules and homotopy invariance of functors.- 16 Extension and restriction functors and model structures.- 17 Miscellaneous applications.- Part V. Appendix: technical verifications.- 18 Shifted modules over operads and functors.- 19 Shifted functors and pushout-products.- 20 Applications of pushout-products of shifted functors