Series: Computational Methods in Applied Sciences , Vol. 16
2008, XVI, 292 p., Hardcover
ISBN: 978-1-4020-8757-8
For more than 250 years partial differential equations have been clearly the most important tool available to mankind in order to understand a large variety of phenomena, natural at first and then those originating from human activity and technological development. Mechanics, physics and their engineering applications were the first to benefit from the impact of partial differential equations on modeling and design, but a little less than a century ago the Schrodinger equation was the key opening the door to the application of partial differential equations to quantum chemistry, for small atomic and molecular systems at first, but then for systems of fast growing complexity.
Part I. Discontinuous Galerkin and Mixed Finite Element Methods. 1. Discontinuous Galerkin Methods. 2. Mixed Finite Element Methods on Polyhedral Meshes for Diffusion Equations. 3. On the Numerical Solution of the Elliptic Monge--Ampere Equation in Dimension Two: A Least-Squares Approach. Part II. Linear and Nonlinear Hyperbolic Problems. 1. Higher Order Time Stepping for Second Order Hyperbolic Problems and Optimal CFL Conditions. 2. Comparison of Two Explicit Time Domain Unstructured Mesh Algorithms for Computational Electromagnetics. 3. The von Neumann Triple Point Paradox. Part III. Domain Decomposition Methods. 1. A Lagrange Multiplier Based Domain Decomposition Method for the Solution of a Wave Problem with Discontinuous Coefficients. 2. Domain Decomposition and Electronic Structure Computations: A Promising Approach. Part IV. Free Surface, Moving Boundaries and Spectral Geometry Problems. 1. Numerical Analysis of a Finite Element/Volume Penalty Method. 2. A Numerical Method for Fluid Flows with Complex Free Surfaces. 3. Modelling and Simulating the Adhesion and Detachment of Chondrocytes in Shear Flow. Part V. Inverse Problems. 1. A Fixed Domain Approach in Shape Optimization Problems with Neumann Boundary Conditions. 2. Reduced-Order Modelling of Dispersion. Part VI. Finance (Option Pricing)
Series: Springer Monographs in Mathematics
2008, XII, 196 p. 29 illus., Hardcover
ISBN: 978-0-387-76364-4
Due: October 2008
This clearly written text is the first book on unitals embedded in finite projective planes. Unitals are key structures in square order projective planes, and have connections with other structures in algebra. They provide a link between groups and geometries. There is a considerable number of research articles concerning unitals, and there also exist many open problems. This book is a thorough survey of the research literature on embedded unitals which collects this material in book form for the first time. The book is aimed at graduate students and researchers who want to learn about this topic without reading all the original articles.
The primary proof techniques used involve linear algebraic arguments, finite field arithmetic, some elementary number theory, and combinatorial enumeration. Some computer results not previously found in the literature also are mentioned in the text. The authors have included a comprehensive bibliography which will become an invaluable resource.
Gary Ebert is Professor of Mathematics at the University of Delaware, USA. Susan Barwick is a Senior Lecturer of Mathematics at the University of Adelaide, Australia.
Preface.- Preliminaries.- Hermitian curves and unitals.- Translation planes.- Unitals embedded in desarguesian planes.- Unitals embedded in non-desarguesian planes.- Combinatorial questions and associated configurations.- Characterization results.- Open problems.- Nomenclature of unitals.- Group theoretic characterizations of unitals.- References.- Notation index.- Index.-
2008, VI, 212 p. 5 illus., Hardcover
ISBN: 978-0-387-79714-4
Due: October 2008
Illustrates what it was like to grow up in Japan during World War II
Details the life of one of the greatest mathematicians of the 20th century
Provides a rare insiders glimpse into the mathematical community
In this book, the author writes freely and often humorously about his life, beginning with his earliest childhood days. He describes his survival of American bombing raids when he was a teenager in Japan, his emergence as a researcher in a post-war university system that was seriously deficient, and his life as a mature mathematician in Princeton and in the international academic community. Every page of this memoir contains personal observations and striking stories. Such luminaries as Chevalley, Oppenheimer, Siegel, and Weil figure prominently in its anecdotes.
Goro Shimura is Professor Emeritus of Mathematics at Princeton University. In 1996, he received the Leroy P. Steele Prize for Lifetime Achievement from the American Mathematical Society. He is the author of Elementary Dirichlet Series and Modular Forms (Springer 2007), Arithmeticity in the Theory of Automorphic Forms (AMS 2000), and Introduction to the Arithmetic Theory of Automorphic Functions (Princeton University Press 1971).
Preface.- Childhood.- As a student.- As a mathematician.- A long epilogue.- Appendix.- Afterword.-
Series: Information Science and Statistics
2008, XVI, 602 p. 25 illus., 2 in color., Hardcover
ISBN: 978-0-387-77241-7
Explains the principles that make support vector machines a successful modeling and prediction tool for a variety of applications
Rigorous treatment of state-of-the-art results on support vector machines
Suitable for both graduate students and researchers in statistical machine learning
This book explains the principles that make support vector machines (SVMs) a successful modelling and prediction tool for a variety of applications. The authors present the basic ideas of SVMs together with the latest developments and current research questions in a unified style. They identify three reasons for the success of SVMs: their ability to learn well with only a very small number of free parameters, their robustness against several types of model violations and outliers, and their computational efficiency compared to several other methods.
Since their appearance in the early nineties, support vector machines and related kernel-based methods have been successfully applied in diverse fields of application such as bioinformatics, fraud detection, construction of insurance tariffs, direct marketing, and data and text mining. As a consequence, SVMs now play an important role in statistical machine learning and are used not only by statisticians, mathematicians, and computer scientists, but also by engineers and data analysts.
The book provides a unique in-depth treatment of both fundamental and recent material on SVMs that so far has been scattered in the literature. The book can thus serve as both a basis for graduate courses and an introduction for statisticians, mathematicians, and computer scientists. It further provides a valuable reference for researchers working in the field.
Preface.- Introduction.- Loss functions and their risks.- Surrogate loss functions.- Kernels and reproducing kernel Hilbert spaces.- Infinite samples versions of support vector machines.- Basic statistical analysis of SVMs.- Advanced statistical analysis of SVMs.- Support vector machines for classification.- Support vector machines for regression.- Robustness.- Computational aspects.- Data mining.- Appendix.- Notation and symbols.- Abbreviations.- Author index.- Subject index.- References
2009, XXVI, 430 p. 103 illus., 3 in color., Hardcover
ISBN: 978-3-540-85297-1
Due: November 12, 2008
Excellent introduction to the field
Suited for the non-specialist
Very successful book now in a completely revised new edition
"Number Theory in Science and Communication" is a well-known introduction for non-mathematicians to this fascinating and useful branch of applied mathematics . It stresses intuitive understanding rather than abstract theory and highlights important concepts such as continued fractions, the golden ratio, quadratic residues and Chinese remainders, trapdoor functions, pseudoprimes and primitive elements. Their applications to problems in the real world are one of the main themes of the book. This revised fifth edition is augmented by recent advances in coding theory, permutations and derangements and a chapter in quantum cryptography.
"I continue to find [Schroeder’s] Number Theory a goldmine of valuable information. It is a marvellous book, in touch with the most recent applications of number theory and written with great clarity and humor.’ Philip Morrison (Scientific American)
"A light-hearted and readable volume with a wide range of applications to which the author has been a productive contributor ? useful mathematics outside the formalities of theorem and proof." Martin Gardner
Introduction.- The Natural Numbers.- Primes.- The Prime Distribution.- Fractions: Continued, Egyptian and Farey.- Linear Congruences.- Diophantine Equations.- The Theorems of Fermat, Wilson and Euler.- Permutation, Cycles and Derangements.- Euler Trap Doors and Public-Key Encryption.- The Divisor Functions.- The Prime Divisor Functions.- Certified Signatures.- Primitive Roots.- Knapsack Encryption.- Quadratic Residues.- The Chinese Remainder Theorem and Simultaneous Congruences.- Fast Transformations and Kronecker Products.- Quadratic Congruences.- Psudoprimes, Poker and Remote Coin Tossing.- The Mobius Function and the Mobius Transform.- From Error Correction Codes to Covering Sets.- Generating Functions and Partitions.- Cyclotomic Polynomials.- Linear Systems and Polynomials.- Polynomial Theory.- Galois Fields.- Spectral Properties of Galois Sequences.- Random Number Generators.- Waveforms and Radiation Patterns.- Number Theory, Randomness and "Art".