Series: Lecture Notes in Mathematics , Vol. 1944
2008, Approx. 235 p., Softcover
ISBN: 978-3-540-78583-5
Due: May 7, 2008
Algebraic groups are treated in this volume from a group theoretical point of view and the obtained results are compared with the analogous issues in the theory of Lie groups. The main body of the text is devoted to a classification of algebraic groups and Lie groups having only few subgroups or few factor groups of different type. In particular, the diversity of the nature of algebraic groups over fields of positive characteristic and over fields of characteristic zero is emphasized. This is revealed by the plethora of three-dimensional unipotent algebraic groups over a perfect field of positive characteristic, as well as, by many concrete examples which cover an area systematically. In the final section, algebraic groups and Lie groups having many closed normal subgroups are determined
Preface.- 1.Prerequisites.- 2.Extensions.- 4.Chains.- 5.Groups with few types of isogenous factors.- 6.Three?dimensional affine groups.- 7.Normality of subgroups.- Notations.- Index.
Series: Universitext
2008, Approx. 310 p., Softcover
ISBN: 978-3-540-78601-6
Due: June 4, 2008
The book contains a complete presentation of some highly sophisticated proofs following new methods of pushing and pulling appearing mostly for the first time in a book. New in a book are also several diametric theorems for sequence spaces, bounds for list codes, and even the concepts of higher level and dimension constrained extremal problems, and splitting antichains. Furthermore for the first time some number-theoretical and combinatorial extremal problems are treated in parallel and thus connections are made more transparent.
The main focus of these lectures is basis extremal problems and inequalities ? two sides of the same coin. Additionally they prepare well for approaches and methods useful and applicable in a broader mathematical context.
Highlights of the book include a solution to the famous 4m-conjecture of Erdos/Ko/Rado 1938, one of the oldest problems in combinatorial extremal theory, an answer to a question of Erdos (1962) in combinatorial number theory "What is the maximal cardinality of a set of numbers smaller than n with no k+1 of its members pair wise relatively prime?", and the discovery that the AD-inequality implies more general and sharper number theoretical inequalities than for instance Behrend's inequality.
Several concepts and problems in the book arise in response to or by rephrasing questions from information theory, computer science, statistical physics. The interdisciplinary character creates an atmosphere rich of incentives for new discoveries and lends Ars Combinatoria a special status in mathematics.
At the end of each chapter, problems are presented in addition to exercises and sometimes conjectures that can open a readerfs eyes to new interconnections.
Conventions and Auxiliary Results.- Intersection and Diametric Problems.- Covering, Packing and List Codes.- Higher Level and Dimension Constrained Extremal Problems.- LYM-related AZ-Identities, Antichain Splittings and Correlation Inequalities.- Basic Problems from Combinatorial Number Theory.- Appendix: Supplementary Matrial and Research Problems.- References.- Index.
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Series: Springer Texts in Statistics
2008, XX, 356 p. 74 illus., 4 in color., Hardcover
ISBN: 978-0-387-77826-6
Due: June 2008
Statistical methods and models are of importance to quantitative finance
Exhibits links between finance theory, market practice and statistical modeling and decision making
Shows concrete examples and data from financial markets to illustrate the statistical methods
This book presents statistical methods and models of importance to quantitative finance and links finance theory to market practice via statistical modeling and decision making. Part I provides basic background in statistics, which includes linear regression and extensions to generalized linear models and nonlinear regression, multivariate analysis, likelihood inference and Bayesian methods, and time series analysis. It also describes applications of these methods to portfolio theory and dynamic models of asset returns and their volatilities. Part II presents advanced topics in quantitative finance and introduces a substantive-empirical modeling approach to address the discrepancy between finance theory and market data. It describes applications to option pricing, interest rate markets, statistical trading strategies, and risk management. Nonparametric regression, advanced multivariate and time series methods in financial econometrics, and statistical models for high-frequency transactions data are also introduced in this connection.
The book has been developed as a textbook for courses on statistical modeling in quantitative finance in master's level financial mathematics (or engineering) and computational (or mathematical) finance programs. It is also designed for self-study by quantitative analysts in the financial industry who want to learn more about the background and details of the statistical methods used by the industry. It can also be used as a reference for graduate statistics and econometrics courses on regression, multivariate analysis, likelihood and Bayesian inference, nonparametrics, and time series, providing concrete examples and data from financial markets to illustrate the statistical methods.
Linear regression models.- Multivariate analysis and likelihood inference.- Basic investment models and their statistical analysis.- Parametric models and bayesian methods.- Time series modeling forecasting.- Dynamic models of asset return and their volatilities.- Nonparametric regression and substantive-empirical modeling.- Option pricing and market data.- Advanced multivariate and time series methods in financial econometrics.- Interest rate markets.- Statistical trading strategies.- Statistical methods in risk management.- Appendix A.- Appendix B.- Appendix C.- References.- Index.
Series: Pseudo-differential Operators , Vol. 1
2008, Approx. 160 p., Softcover
ISBN: 978-3-7643-8790-7
Due: June 2008
The primary aim of this book is to create situations in which the zeta function, or other L-functions, will appear in spectral-theoretic questions. A secondary aim is to connect pseudo-differential analysis, or quantization theory, to analytic number theory. Both are attained through the analysis of operators on functions on the line by means of their diagonal matrix elements against families of arithmetic coherent states: these are families of discretely supported measures on the line, transforming in specific ways under the part of the metaplectic representation or, more generally, representations from the discrete series of SL(2,R), lying above an arithmetic group such as SL(2,Z).
Postgraduates and researchers working in analytic number theory, pseudo-differential analysis or quantization theory
Foreword.- Introduction.- Chapter 1. Weyl calculus and arithmetic.- Chapter 2. Quantization.- Chapter 3. Quantization and modular forms.- Bibliography.- Index
Series: Interdisciplinary Applied Mathematics , Vol. 8/1
2008, Approx. 700 p., Hardcover
ISBN: 978-0-387-75846-6
Due: August 2008
Mathematical Physiology provides an introduction into physiology using the tools and perspectives of mathematical modeling and analysis. It describes ways in which mathematical theory may be used to give insights into physiological questions and how physiological questions can in turn lead to new mathematical problems.
This first volume deals with the fundamental principles of cell physiology, and the second with the physiology of systems. In the first part, after an introduction to basic biochemistry and enzyme reactions, the authors discuss volume control, the membrane potential, ionic flow through channels, excitability, calcium dynamics, and electrical bursting. This first part concludes with spatial aspects such as a synaptic transmission, gap junctions, the linear cable equation, nonlinear wave propagation in neurons, and calcium waves.
This book will be of interest to researchers, to graduate students and advanced undergraduate students in applied mathematics who wish to learn how to build and analyze mathematical models and to become familiar with new areas of application, as well as to physiologists interested in learning about theoretical approaches to their work.
The inclusion of numerous exercises and models could be used to add further interest and challenge to traditional courses taught by applied mathematicians, bioengineers, and physiologists.
Winner of the prize for The Best Mathematics book of 1998 from the American Association of Publishers.
Preface & Acknowledgments * I Cellular Physiology * 1 Biochemical Reactions * 2 Cellular Homeostasis * 3 Membrane Ion Channels * 4 Passive Electrical Flow in Neurons* 5 Excitability * 6 Traveling Waves of Electrical Excitation * 7 Wave Propagation in Higher Dimensions* 8 Calcium Dynamics * 9 Intercellular Communication* 10 Neuroendocrine Cells * 11 Regulation of Cell Function * II 12 The Heart * 13 The Circulatory System * 14 Blood * 15 Respiration * 16 Muscle * 17 The Endocrine System * 18 Renal Physiology * 19 The Gastrointestinal System * 20 The Retina and Vision * 21 The Inner Ear *
Series: Probability and its Applications
2008, Approx. 440 p., Hardcover
ISBN: 978-0-387-78168-6
Due: July 2008
How is genetic variability shaped by natural selection, demographic factors, and random genetic drift? To approach this question, we introduce and analyze a number of probability models beginning with the basics, and ending at the frontiers of current research. Throughout the book, the theory is developed in close connection with examples from the biology literature that illustrate the use of these results. Along the way, there are many numerical examples and graphs to illustrate the conclusions.
This is the second edition and is twice the size of the first one. The material on recombination and the stepping stone model have been greatly expanded, there are many results form the last five years, and two new chapters on diffusion processes develop that viewpoint. This book is written for mathematicians and for biologists alike. No previous knowledge of concepts from biology is assumed, and only a basic knowledge of probability, including some familiarity with Markov chains and Poisson processes. The book has been restructured into a large number of subsections and written in a theorem-proof style, to more clearly highlight the main results and allow readers to find the results they need and to skip the proofs if they desire.
Rick Durrett received his Ph.D. in operations research from Stanford University in 1976. He taught in the UCLA mathematics department before coming to Cornell in 1985. He is the author of eight books and 160 research papers, most of which concern the use of probability models in genetics and ecology. He is the academic father of 39 Ph.D. students and was recently elected to the National Academy of Sciences.
Basic models - Estimation and hypothesis testing - Recombination - Population complications - Stepping stone model - Natural selection - Diffusion process - Multidimensional diffusions - Genome rearrangement.