Series: Selected Works in Probability and Statistics
1st Edition., 2012, X, 1040 p. 1 illus.
Hardcover, ISBN 978-1-4614-1411-7
Due: December 28, 2011
These volumes present a selection of Erich L. Lehmann’s monumental contributions to Statistics. These works are multifaceted. His early work included fundamental contributions to hypothesis testing, theory of point estimation, and more generally to decision theory. His work in Nonparametric Statistics was groundbreaking. His fundamental contributions in this area include results that came to assuage the anxiety of statisticians that were skeptical of nonparametric methodologies, and his work on concepts of dependence has created a large literature. The two volumes are divided into chapters of related works. Invited contributors have critiqued the papers in each chapter, and the reprinted group of papers follows each commentary. A complete bibliography that contains links to recorded talks by Erich Lehmann ? and which are freely accessible to the public ? and a list of Ph.D. students are also included. These volumes belong in every statistician’s personal collection and are a required holding for any institutional library.
Decision Theory.- Hypothesis Testing.- Estimation.- Nonparametrics I.- Nonparametrics II.- Asymptotics.- Multiple Decisions.- Orderings of Probability Distributions.- Probability Theory.- Biographical Work.- Historical Work.- Philosophical Work.- Books.- PhD Students.
Series: Algebra and Applications, Vol. 17
1st Edition., 2012, XXIV, 260 p.
Hardcover, ISBN 978-1-4471-2293-7
Due: December 31, 2011
The most important invariant of a topological space is its fundamental
group. When this is trivial, the resulting homotopy theory is well researched
and familiar. In the general case, however, homotopy theory over nontrivial
fundamental groups is much more problematic and far less well understood.
Syzygies and Homotopy Theory explores the problem of nonsimply connected homotopy in the first nontrivial cases and presents, for the first time, a systematic rehabilitation of Hilbert's method of syzygies in the context of non-simply connected homotopy theory. The first part of the book is theoretical, formulated to allow a general finitely presented group as a fundamental group. The innovation here is to regard syzygies as stable modules rather than minimal modules. Inevitably this forces a reconsideration of the problems of noncancellation; these are confronted in the second, practical, part of the book. In particular, the second part of the book considers how the theory works out in detail for the specific examples Fn ´F where Fn is a free group of rank n and F is finite. Another innovation is to parametrize the first syzygy in terms of the more familiar class of stably free modules. Furthermore, detailed description of these stably free modules is effected by a suitable modification of the method of Milnor squares.
The theory developed within this book has potential applications in various branches of algebra, including homological algebra, ring theory and K-theory. Syzygies and Homotopy Theory will be of interest to researchers and also to graduate students with a background in algebra and algebraic topology.
Preliminaries.- The restricted linear group.- The calculus of corners and squares.- Extensions of modules.- The derived module category.- Finiteness conditions.- The Swan mapping.- Classification of algebraic complexes.- Rings with stably free cancellation.- Group rings of cyclic groups.- Group rings of dihedral groups.- Group rings of quaternionic groups.- Parametrizing W1 (Z) : generic case.- Parametrizing W1 (Z) : singular case.- Generalized Swan modules.- Parametrizing W1 (Z) : G = C\ ´ F.- Conclusion?.
Series: Algorithms and Combinatorics, Vol. 27
2012, 2012, XVI, 612 p. 70 illus.
Hardcover, ISBN 978-3-642-24507-7
Due: December 31, 2011
Boolean circuit complexity is the combinatorics of computer science and involves many intriguing problems that are easy to state and explain, even for the layman. This book is a comprehensive description of basic lower bound arguments, covering many of the gems of this “complexity Waterloo” that have been discovered over the past several decades, right up to results from the last year or two. Many open problems, marked as Research Problems, are mentioned along the way. The problems are mainly of combinatorial flavor but their solutions could have great consequences in circuit complexity and computer science. The book will be of interest to graduate students and researchers in the fields of computer science and discrete mathematics.
Part I Basics.- Part II Communication Complexity.- Part III Circuit Complexity.- Part IV Bounded Depth Circuits.- Part V Branching Programs.- Part VI Fragments of Proof Complexity.- A Epilog.- B Mathematical Background.- References.- Index.
Series: Interdisciplinary Applied Mathematics, Vol. 37
1st Edition., 2012, XX, 446 p. 202 illus., 79 in color.
Hardcover, ISBN 978-1-4614-1507-7
Due: December 28, 2011
This introductory and self-contained book gathers as much explicit mathematical results on the linear-elastic and heat-conduction solutions in the neighborhood of singular points in two-dimensional domains, and singular edges and vertices in three-dimensional domains. These are presented in an engineering terminology for practical usage. The author treats the mathematical formulations from an engineering viewpoint and presents high-order finite-element methods for the computation of singular solutions in isotropic and anisotropic materials, and multi-material interfaces. The proper interpretation of the results in engineering practice is advocated, so that the computed data can be correlated to experimental observations. The book is divided into fourteen chapters, each containing several sections. Most of it (the first nine Chapters) addresses two-dimensional domains, where only singular points exist. The solution in a vicinity of these points admits an asymptotic expansion composed of eigenpairs and associated generalized flux/stress intensity factors (GFIFs/GSIFs), which are being computed analytically when possible or by finite element methods otherwise. Singular points associated with weakly coupled thermoelasticity in the vicinity of singularities are also addressed and thermal GSIFs are computed. The computed data is important in engineering practice for predicting failure initiation in brittle materials on a daily basis. Several failure laws for two-dimensional domains with V-notches are presented and their validity is examined by comparison to experimental observations. A sufficient simple and reliable condition for predicting failure initiation (crack formation) in micron level electronic devices, involving singular points, is still a topic of active research and interest, and is addressed herein. Explicit singular solutions in the vicinity of vertices and edges in three-dimensional domains are provided in the remaining five chapters. New methods for the computation of generalized edge flux/stress intensity functions along singular edges are presented and demonstrated by several example problems from the field of fracture mechanics; including anisotropic domains and bimaterial interfaces. Circular edges are also presented and the author concludes with some remarks on open questions. This well illustrated book will appeal to both applied mathematicians and engineers working in the field of fracture mechanics and singularities.
Preface.- Introduction.-An Introduction to the p- and hp-versions of the Finite Element Method.-Eigen-pairs Computation for Two-Dimensional Heat Conduction Singularities.-Computation of GFIFs for Two-Dimensional Heat Conduction Problems.-Eigen-pairs for two-dimensional elasticity.-Computing Generalized Stress Intensity Factors.-Thermal Generalized Stress Intensity Factors in 2-D Domains.-Failure Criteria for Brittle Elastic Materials.-Thermo-Mechanical Failure Criterion at the Micron Scale in Electronic Devices.-Singular solutions of the heat conduction equation in polyhedra domains.-Computation of the Edge Flux Intensity Functions associated with polyhedra domains.-Vertex singularities associated with conical points for the 3-D Laplace equation.-Edge eigen-pairs and ESIFs of 3-D elastic problems.-Summary and Open Questions.
Series: Oberwolfach Seminars, Vol. 43
2012, 2012, X, 111 p.
ISBN 978-3-0348-0259-8
Due: November 30, 2011
The seminar focuses on a recent solution, by the authors, of a long standing problem concerning the stable module category (of not necessarily finite dimensional representations) of a finite group. The proof draws on ideas from commutative algebra, cohomology of groups, and stable homotopy theory. The unifying theme is a notion of support which provides a geometric approach for studying various algebraic structures. The prototype for this has been Daniel Quillen’s description of the algebraic variety corresponding to the cohomology ring of a finite group, based on which Jon Carlson introduced support varieties for modular representations. This has made it possible to apply methods of algebraic geometry to obtain representation theoretic information. Their work has inspired the development of analogous theories in various contexts, notably modules over commutative complete intersection rings and over cocommutative Hopf algebras. One of the threads in this development has been the classification of thick or localizing subcategories of various triangulated categories of representations. This story started with Mike Hopkins’ classification of thick subcategories of the perfect complexes over a commutative Noetherian ring, followed by a classification of localizing subcategories of its full derived category, due to Amnon Neeman. The authors have been developing an approach to address such classification problems, based on a construction of local cohomology functors and support for triangulated categories with ring of operators. The book serves as an introduction to this circle of ideas.
Series: Progress in Mathematics, Vol. 296
1st Edition., 2012, XXII, 437 p. 90 illus., 18 in color.
ISBN 978-0-8176-8276-7
Due: December 28, 2011
A Marcus Wallenberg Symposium on Perspectives in Analysis, Geometry, and Topology was held at Stockholm University in May 2008. The choice of subjects of the Symposium and present volume was motivated by the work and mathematical interests of Oleg Viro to whom the Symposium and this volume are dedicated. As a professor of Uppsala University, Viro has made invaluable contributions to Swedish research by complementing the country's longstanding tradition in analysis with his own renowned expertise in geometry and topology. Consolidating in a single volume a major portion of the recent, impressive encounters among the fields of analysis, geometry, and topology would be too ambitious. The collection of papers in this work still should give some sense of the development of the fields and their interactions. The topics presented by leading experts in their respective fields include: algebraic geometry, in particular, real algebraic geometry, differential geometry, symplectic and contact geometry, complex analysis, three- and four-dimensional manifolds, and invariants of links. Also included in the book is the opening speech of the Symposium by Lennart Carleson on the Unity of Mathematics. Contributors: S. Akbulut K. Baker R. Berman A. Degtyarev J.-P. Demailly T. Ekholm Y. Eliashberg M. Entov J. Etnyre D. Gay G. Henkin I. Itenberg L. Kauffman K. Kaveh M. Khanevsky V. Kharlamov A. Khovanskii C. Manolescu N. Mishachev N. Mok S. Orevkov L. Polterovich P. Py N. Reshetikhin A. Shumakovitch E. Shustin A. Stipsicz C. Stroppel B. Webster C. Woodward
Preface.- 1 Selman Akbulut, Exotic structures on smooth 4-manifolds.- 2 Kenneth Baker, John Etnyre, Rational linking and contact geometry.- 3 Robert Berman, Jean-Pierre Demailly, Regularity of plurisubharmonic upper envelopes in big cohomology classes.- 4 Alex Degtarev, Towards the generalized Shapiro and Shapiro conjecture.-5 Alex Degtarev, Ilia Itenberg, Viatcheslav Kharlamov, On the number of components of a complete intersection of real quadrics.- 6 Tobias Ekholm, Rational Symplectic Field Theory and linearized Legendrian contact homology.- 7 Yakov Eliashberg, N. Mishachev, Wrinkling IV: Mappings with prescribed singularities.- 8 Michael Entov, Leonid Polterovich, Pierre Py, On continuity of quasimorphisms for symplectic maps. With an appendix by Michael Khanevsky.- 9 David Gay, Andras Stipsicz, On symplectic caps.- 10 Gennadi Henkin, Cauchy-Pompeiu type formulas for a on affine algebraic Riemann surfaces and some applications.-11 Kiumars Kaveh, A. G. Khovanskii, Algebraic equations and convex bodies.- 12 Louis Kauffman, Graphical Bracket Invariants of Virtual Links.- 13 Ciprian Manolescu, Christopher Woodward, Floer homology on the extended moduli space.- 14 Ngaiming Mok, Projective-algebraicity of minimal compactifications of complex-hyperbolic space forms of finite volume.- 15 Stepan Orevkov, Some examples of real algebraic and real pseudoholomorphic curves.- 16 Nicolai Reshetikhin, Topological invariants related to quantum groups at roots of unity.- 17 Alexander Shumakovitch: Khovanov Homology Theories and Their Applications.- 18 Eugenii Shustin, Patchworking theorem for tropical curves with multiple points