Ciarlet, Philippe G.

An Introduction to Differential Geometry with Applications to Elasticity

2006, Approx. 220 p., Hardcover
ISBN: 1-4020-4247-7
Due: December 2005

About this book

This book is based on a series of lectures delivered over the years by the author at the University Pierre et Marie Curie in Paris, at the University of Stuttgart, and at City University of Hong Kong. Its two-fold aim is to provide a thorough introduction to the basic theorems of differential geometry and to elasticity in curvilinear coordinates and shell theory.

To this end, the fundamental existence and uniqueness theorems are proved in great details. Such theorems include the fundamental theorem of surface theory, which asserts that the Gauss and Codazzi-Mainardi equations are sufficient for the existence of a surface with prescribed fundamental forms, as well as the corresponding rigidity theorem. Recent results, which have not yet appeared in book form are also included, such as the continuity of a surface as a function of its fundamental forms.

This book also provides a detailed description of the equations of nonlinear and linearized elasticity in curvilinear coordinates, together with a direct proof of the three-dimensional Korn inequality in curvilinear coordinates. The book also includes a detailed description of Koiter's equations for nonlinearly and linearly elastic shells, a complete analysis of the existence, uniqueness, and regularity of the solutions of Koiter's equations in the linear case.

The treatment is essentially self-contained and proofs are complete. In particular, no a priori knowledge of diferential geometry or elasticity theory or shell theory is assumed. Another highlight of this book is the focus on the interplay between "theoretical" and "applied" differential geometry. For instance, rather than being introduced in a formal way, covariant derivatives of a tensor field appear in a natural way in the course of the derivation of the basic boundary value problems of nonlinear elasticity in curvilinear coordinates and of shell theory.

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Ching, Wai-Ki, Ng, Michael K.

Markov Chains
Models, Algorithms and Applications

Series: International Series in Operations Research & Management Science, Vol. 83
2006, Approx. 220 p. 18 illus., Hardcover
ISBN: 0-387-29335-3
Due: December 2005

About this book

MARKOV CHAINS: Models, Algorithms and Applications outlines recent developments of Markov chain models for modeling queueing sequences, Internet, re-manufacturing systems, reverse logistics, inventory systems, bio-informatics, DNA sequences, genetic networks, data mining, and many other practical systems.

The book consists of eight chapters. Chapter 1 is a brief introduction to the classical theory on both discrete and continuous time Markov chains. The relationship between Markov chains of finite states and matrix theory is also discussed. Chapter 2 discusses the applications of continuous time Markov chains to model queueing systems and discrete time Markov chains for computing. Chapter 3 studies re-manufacturing systems and presents Markovian models for reverse manufacturing applications. In Chapter 4, Hidden Markov models are applied to classify customers. Chapter 5 discusses the Markov decision process for customer lifetime values. Customer Lifetime Values (CLV) is an important concept and quantity in marketing management. Chapter 6 covers higher-order Markov chain models. Multivariate Markov models are discussed in Chapter 7. It presents a class of multivariate Markov chain models with a lower order of model parameters. Chapter 8 studies higher-order hidden Markov models. It proposes a class of higher-order hidden Markov models with an efficient algorithm for solving the model parameters.

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Introduction.- Queueing systems and the web.- Re-manufacturing systems.- Hidden Markov model for customers classification.- Markov decision process for customer lifetime value.- Higher-order Markov decision process.- Multivariate Markov chains.- Hidden Markov chains.- References.- Index.

This book is aimed at students, professionals, practitioners, and researchers in applied mathematics, scientific computing, and operational research, who are interested in the formulation and computation of queueing and manufacturing systems.

Gabbay, Dov; Goncharov, Sergei; Zakharyaschev, Michael (Eds.)

Mathematical Problems from Applied Logic I
Logics for the XXIst Century

Series: International Mathematical Series, Vol. 4
Volume package: Mathematical Problems from Applied Logic
2006, XXVIII, 348 p. 50 illus., Hardcover
ISBN: 0-387-28688-8

About this book

Mathematical Problems from Applied Logic I presents chapters from selected, world renowned, logicians. Important topics of logic are discussed from the point of view of their further development in light of requirements arising from their successful application in areas such as Computer Science and AI language. An overview of the current state as well as open problems and perspectives are clarified in such fields as non-standard inferences in description logics, logic of provability, logical dynamics, and computability theory. The book contains interesting contributions concerning the role of logic today, including some unexpected aspects of contemporary logic and the application of logic.

Contributors include: Franz Baader (Germany) and Ralf Kusters (Germany), Lev Beklemishev (The Netherlands/Russia) and Albert Visser (The Netherlands), Johan van Benthem (The Netherlands/USA), S Barry Cooper (UK), John N Crossley (Australia), Wilfrid A Hodges (UK), and Lawrence S Moss (USA).

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Borwein, Jonathan, Lewis, Adrian S.

Convex Analysis and Nonlinear Optimization
Theory and Examples

Series: CMS Books in Mathematics
2nd ed., 2006, Approx. 310 p., Hardcover
ISBN: 0-387-29570-4
Due: January 2006

About this textbook

Optimization is a rich and thriving mathematical discipline. The theory underlying current computational optimization techniques grows ever more sophisticated. The powerful and elegant language of convex analysis unifies much of this theory. The aim of this book is to provide a concise, accessible account of convex analysis and its applications and extensions, for a broad audience. It can serve as a teaching text, at roughly the level of first year graduate students. While the main body of the text is self-contained, each section concludes with an often extensive set of optional exercises. The new edition adds material on semismooth optimization, as well as several new proofs that will make this book even more self-contained.

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Hager, W.W.; Huang, S.-J.; Pardalos, P.M.; Prokopyev, O.A. (Eds.)

Multiscale Optimization Methods and Applications

Series: Nonconvex Optimization and Its Applications, Vol. 82
2006, XVIII, 408 p., Hardcover
ISBN: 0-387-29549-6
Due: January 2006

About this book

As optimization researchers tackle larger and larger problems, scale interactions play an increasingly important role. One general strategy for dealing with a large or difficult problem is to partition it into smaller ones, which are hopefully much easier to solve, and then work backwards towards the solution of original problem, using a solution from a previous level as a starting guess at the next level. This volume contains 22 chapters highlighting some recent research. The topics of the chapters selected for this volume are focused on the development of new solution methodologies, including general multilevel solution techniques, for tackling difficult, large-scale optimization problems that arise in science and industry. Applications presented in the book include but are not limited to the circuit placement problem in VLSI design, a wireless sensor location problem, optimal dosages in the treatment of cancer by radiation therapy, and facility location.

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Prekopa, Andras; Molnar, Emil (Eds.)

Non-Euclidean Geometries
Janos Bolyai Memorial Volume

Series: Mathematics and Its Applications, Vol. 581
2006, XIV, 506 p. 75 illus., Hardcover
ISBN: 0-387-29554-2

About this book

"From nothing I have created a new different world," wrote Janos Bolyai to his father, Wolgang Bolyai, on November 3, 1823, to let him know his discovery of non-Euclidean geometry, as we call it today. The results of Bolyai and the co-discoverer, the Russian Lobachevskii, changed the course of mathematics, opened the way for modern physical theories of the twentieth century, and had an impact on the history of human culture.

The papers in this volume, which commemorates the 200th anniversary of the birth of Janos Bolyai, were written by leading scientists of non-Euclidean geometry, its history, and its applications. Some of the papers present new discoveries about the life and works of Janos Bolyai and the history of non-Euclidean geometry, others deal with geometrical axiomatics; polyhedra; fractals; hyperbolic, Riemannian and discrete geometry; tilings; visualization; and applications in physics.

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Nelsen, Roger B.

An Introduction to Copulas, 2nd ed.

Series: Springer Series in Statistics
2006, XIV, 270 p., Hardcover
ISBN: 0-387-28659-4
Due: March 2006

About this book

Copulas are functions that join multivariate distribution functions to their one-dimensional margins. The study of copulas and their role in statistics is a new but vigorously growing field. In this book the student or practitioner of statistics and probability will find discussions of the fundamental properties of copulas and some of their primary applications. The applications include the study of dependence and measures of association, and the construction of families of bivariate distributions. With nearly a hundred examples and over 150 exercises, this book is suitable as a text or for self-study. The only prerequisite is an upper level undergraduate course in probability and mathematical statistics, although some familiarity with nonparametric statistics would be useful. Knowledge of measure-theoretic probability is not required. Roger B. Nelsen is Professor of Mathematics at Lewis & Clark College in Portland, Oregon. He is also the author of "Proofs Without Words: Exercises in Visual Thinking," published by the Mathematical Association of America.

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Petersen, Peter

Riemannian Geometry,2nd ed.

Series: Graduate Texts in Mathematics, Vol. 171
2006, Approx. 460 p. 59 illus., Hardcover
ISBN: 0-387-29246-2

About this textbook

Intended for a one year course, this volume serves as a single source, introducing students to the important techniques and theorems, while also containing enough background on advanced topics to appeal to those students wishing to specialize in Riemannian geometry. This is one of the few works to combine both the geometric parts of Riemannian geometry and the analytic aspects of the theory, while also presenting the most up-to-date research. This book will appeal to readers with a knowledge of standard manifold theory, including such topics as tensors and Stokes theorem. Various exercises are scattered throughout the text, helping motivate readers to deepen their understanding of the subject.

Important additions to this new edition include:

* A completely new coordinate free formula that is easily remembered, and is, in fact, the Koszul formula in disguise;

* An increased number of coordinate calculations of connection and curvature;

* General fomulas for curvature on Lie Groups and submersions;

* Variational calculus has been integrated into the text, which allows for an early treatment of the Sphere theorem using a forgottten proof by Berger;

* Several recent results about manifolds with positive curvature.

Table of contents

Introduction.- Riemannian Metrics.- Curvature.- Examples.- Hypersurfaces.- Geodesics and Distance.- Sectional Curvature Comparison I.- The Bochner Technique.- Symmetric Spaces and Holony.- Ricci Curvature Comparison.- Convergence.- Sectional Curvature Comparison II.- Bibliography.