Series: Modern Birkhauser Classics
1998, 1998, XIII, 213 p.
Softcover, ISBN 978-3-0348-0282-6
Due: January 31, 2012
Very well written monograph combining algebraic groups and number theory
Recommended reading for researchers of modular and automorphic forms
Up to date and structured collection of known results
The Jacobi group is a semidirect product of a symplectic group with a Heisenberg group. It is an important example for a non-reductive group and sets the frame within which to treat theta functions as well as elliptic functions - in particular, the universal elliptic curve.
This text gathers for the first time material from the representation theory of this group in both local (archimedean and non-archimedean) cases and in the global number field case. Via a bridge to Waldspurger's theory for the metaplectic group, complete classification theorems for irreducible representations are obtained. Further topics include differential operators, Whittaker models, Hecke operators, spherical representations and theta functions. The global theory is aimed at the correspondence between automorphic representations and Jacobi forms. This volume is thus a complement to the seminal book on Jacobi forms by M. Eichler and D. Zagier.
Incorporating results of the authors' original research, this exposition is meant for researchers and graduate students interested in algebraic groups and number theory, in particular, modular and automorphic forms.
Series: Algorithms and Combinatorics, Vol. 21
2012, 2012, XIX, 661 p. 77 illus.
Hardcover, ISBN 978-3-642-24487-2
Due: December 31, 2011
Well-written, popular textbook on combinatorial optimization
One of very few textbooks on this topic
Subject area has manifold applications
Offers complete but concise proofs, making it an invaluable practical tool for students
Updated fifth edition
This comprehensive textbook on combinatorial optimization places special emphasis on theoretical results and algorithms with provably good performance, in contrast to heuristics. It is based on numerous courses on combinatorial optimization and specialized topics, mostly at graduate level. This book reviews the fundamentals, covers the classical topics (paths, flows, matching, matroids, NP-completeness, approximation algorithms) in detail, and proceeds to advanced and recent topics, some of which have not appeared in a textbook before. Throughout, it contains complete but concise proofs, and also provides numerous exercises and references.
This fifth edition has again been updated, revised, and significantly extended, with more than 60 new exercises and new material on various topics, including Cayley's formula, blocking flows, faster b-matching separation, multidimensional knapsack, multicommodity max-flow min-cut ratio, and sparsest cut. Thus, this book represents the state of the art of combinatorial optimization.
1 Introduction.- 2 Graphs.- 3 Linear Programming.- 4 Linear Programming
Algorithms.- 5 Integer Programming.- 6 Spanning Trees and Arborescences.-
7 Shortest Paths.- 8 Network Flows.- 9 Minimum Cost Flows.- 10 Maximum
Matchings.- 11 Weighted Matching.- 12 b-Matchings and T -Joins.- 13 Matroids.-
14 Generalizations of Matroids.- 15 NP-Completeness.- 16 Approximation
Algorithms.- 17 The Knapsack Problem.- 18 Bin-Packing.- 19 Multicommodity
Flows and Edge-Disjoint Paths.- 20 Network Design Problems.- 21 The Traveling
Salesman Problem.- 22 Facility Location.- Indices.
Series: Lecture Notes in Mathematics, Vol. 2047
2012, 2012, X, 210 p.
Softcover, ISBN 978-3-642-27545-6
Due: April 30, 2012
44,95 ? .About this book.Impulsive differential equations are suitable for the mathematical simulation of evolutionary processes in which the parameters undergo relatively long periods of smooth variation followed by short-term rapid changes (that is, jumps) in their values. Processes of this type are often investigated in various fields of science and technology. The question of the existence and uniqueness of almost periodic solutions of differential equations is an age-old problem of great importance. The qualitative theory of impulsive differential equations is currently undergoing rapid development in relation to the investigation of various processes which are subject to impacts during their evolution, and many findings on the existence and uniqueness of almost periodic solutions of these equations are being made.
This book systematically presents findings related to almost periodic solutions of impulsive differential equations and illustrates their potential applications.
1 Impulsive Differential Equations and Almost Periodicity.- 2 Almost Periodic Solutions.- 3 Lyapunov Method and Almost Periodicity.- 4 Applications.
Series: Universitext
2012, 2012, VIII, 180 p.
Softcover, ISBN 978-1-4471-2738-3
Due: March 31, 2012
Provides a concise and rigorous introduction to linear algebra from the matrix theory viewpoint which is well-suited for statistical applications
Offers a compact introduction to estimation and testing in linear models covering the basic results required for further studies in linear models, multivariate analysis and design of experiments
Contains a large number of exercises, including over seventy five problems on rank, with hints and solutions
Linear Algebra and Linear Models comprises a concise and rigorous introduction to linear algebra required for statistics followed by the basic aspects of the theory of linear estimation and hypothesis testing. The emphasis is on the approach using generalized inverses. Topics such as the multivariate normal distribution and distribution of quadratic forms are included.
For this third edition, the material has been reorganised to develop the linear algebra in the first six chapters, to serve as a first course on linear algebra that is especially suitable for students of statistics or for those looking for a matrix theoretic approach to the subject. Other key features include:
* coverage of topics such as rank additivity, inequalities for eigenvalues and singular values;
* a new chapter on linear mixed models;
* over seventy additional problems on rank: the matrix rank is an important and rich topic with connections to many aspects of linear algebra such as generalized inverses, idempotent matrices and partitioned matrices.
This text is aimed primarily at advanced undergraduate and first-year graduate students taking courses in linear algebra, linear models, multivariate analysis and design of experiments. A wealth of exercises, complete with hints and solutions, help to consolidate understanding. Researchers in mathematics and statistics will also find the book a useful source of results and problems.
Vector Spaces and Subspaces.- Rank, Inner Product and Nonsingularity.- Eigenvalues and Positive Definite Matrices.- Generalized Inverses.- Inequalities for Eigenvalues and Singular Values.- Rank Additivity and Matrix Partial Orders.- Linear Estimation.- Tests of Linear Hypotheses.- Linear Mixed Models.- Miscellaneous Topics.- Additional Exercises on Rank.
1st Edition., 2012, Approx. 200 p. 5 illus.
Hardcover, ISBN 978-3-642-24887-0
Due: March 31, 2012
Deals with a special class of Finsler metrics -- Randers metrics
Presents core ideas and methods which are useful in Finsler geometry
Provides many interesting and important examples and results obtained by the authors and other mathematicians during the past decade
"Finsler Geometry: An Approach via Randers Spaces" exclusively deals with a special class of Finsler metrics -- Randers metrics, which are defined as the sum of a Riemannian metric and a 1-form. Randers metrics derive from the research on General Relativity Theory and have been applied in many areas of the natural sciences. They can also be naturally deduced as the solution of the Zermelo navigation problem. The book provides readers not only with essential findings on Randers metrics but also the core ideas and methods which are useful in Finsler geometry. It will be of significant interest to researchers and practitioners working in Finsler geometry, even in differential geometry or related natural fields.
Xinyue Cheng is a Professor at the School of Mathematics and Statistics of Chongqing University of Technology, China. Zhongmin Shen is a Professor at the Department of Mathematical Sciences of Indiana University Purdue University, USA.
Series: Applied and Numerical Harmonic Analysis
1st Edition., 2012, XX, 325 p. 50 illus., 19 in color.
ISBN 978-0-8176-8315-3
Due: March 31, 2012
The first book published on the topic of shearlets or geometric multiscale analysis
Unified notation used throughout
Comprehensive presentation of shearlet theory and applications
Valuable for an interdisciplinary audience of graduate students and researchers in applied mathematics, computer science, and engineering
Over the last 20 years, multiscale methods and wavelets have revolutionized the field of applied mathematics by providing efficient means for encoding isotropic phenomena. Directional multiscale systems, particularly shearlets, are currently having the same dramatic impact on the encoding of multivariate signals, which are usually dominated by anisotropic features. Since its introduction about six years ago, the theory of shearlets has rapidly developed and gained wide recognition as the superior approach for multiscale analysis of multivariate signals, providing a truly unified treatment of both the continuum and the digital setting. By now, this research field has reached full maturity, with deep mathematical results, efficient numerical methods, and a variety of high-impact applications.
Edited by the topic's two main pioneers, this volume systematically surveys the theory and applications of shearlets. Following a general survey of the subject, carefully selected contributions explore the current state of the field in greater detail. Specific areas covered include:
* analysis of anisotropic features;
* sparse approximations of multivariate data;
* shearlet smoothness spaces;
* numerical implementations;
* applications to image processing.
Shearlets is aimed at graduate students and researchers in the areas of applied mathematics, computer science, engineering, and any other field dealing with the development and applications of highly efficient methodologies for processing multivariate data. As the first monograph in the literature to survey shearlets, this volume offers both a unique state-of-the-art resource for scientists dealing with advanced multiscale methods and a supplemental textbook for graduate courses in applied harmonic analysis.
Introduction.- Shearlets and Microlocal Analysis.- Analysis and Identification of Multidimensional Singularities using the Continuous Shearlet Transform.- Multivariate Shearlet Transform, Shearlet Coorbit Spaces and their Structural Properties.- Shearlets and Optimally Sparse Approximations.- Shearlet Multiresolution and Multiple Refinement.- Digital Shearlet Transforms.- Imaging Applications.