- Table View
- List View
Modern Methods in the Calculus of Variations: L^p Spaces (Springer Monographs in Mathematics)
by Irene Fonseca Giovanni LeoniThis is the first of two books on methods and techniques in the calculus of variations. Contemporary arguments are used throughout the text to streamline and present in a unified way classical results, and to provide novel contributions at the forefront of the theory. This book addresses fundamental questions related to lower semicontinuity and relaxation of functionals within the unconstrained setting, mainly in L^p spaces. It prepares the ground for the second volume where the variational treatment of functionals involving fields and their derivatives will be undertaken within the framework of Sobolev spaces. This book is self-contained. All the statements are fully justified and proved, with the exception of basic results in measure theory, which may be found in any good textbook on the subject. It also contains several exercises. Therefore,it may be used both as a graduate textbook as well as a reference text for researchers in the field. Irene Fonseca is the Mellon College of Science Professor of Mathematics and is currently the Director of the Center for Nonlinear Analysis in the Department of Mathematical Sciences at Carnegie Mellon University. Her research interests lie in the areas of continuum mechanics, calculus of variations, geometric measure theory and partial differential equations. Giovanni Leoni is also a professor in the Department of Mathematical Sciences at Carnegie Mellon University. He focuses his research on calculus of variations, partial differential equations and geometric measure theory with special emphasis on applications to problems in continuum mechanics and in materials science.
Stochastic Simulation: Algorithms and Analysis (Stochastic Modelling and Applied Probability #57)
by Søren Asmussen Peter W. GlynnSampling-based computational methods have become a fundamental part of the numerical toolset of practitioners and researchers across an enormous number of different applied domains and academic disciplines. This book provides a broad treatment of such sampling-based methods, as well as accompanying mathematical analysis of the convergence properties of the methods discussed. The reach of the ideas is illustrated by discussing a wide range of applications and the models that have found wide usage. The first half of the book focuses on general methods; the second half discusses model-specific algorithms. Exercises and illustrations are included.
Stochastic Learning and Optimization: A Sensitivity-Based Approach
by Xi-Ren CaoPerformance optimization is vital in the design and operation of modern engineering systems, including communications, manufacturing, robotics, and logistics. Most engineering systems are too complicated to model, or the system parameters cannot be easily identified, so learning techniques have to be applied. This book provides a unified framework based on a sensitivity point of view. It also introduces new approaches and proposes new research topics within this sensitivity-based framework. This new perspective on a popular topic is presented by a well respected expert in the field.
Einstein's General Theory of Relativity: With Modern Applications in Cosmology
by Øyvind Grøn Sigbjorn HervikThis book introduces the general theory of relativity and includes applications to cosmology. The book provides a thorough introduction to tensor calculus and curved manifolds. After the necessary mathematical tools are introduced, the authors offer a thorough presentation of the theory of relativity. Also included are some advanced topics not previously covered by textbooks, including Kaluza-Klein theory, Israel's formalism and branes. Anisotropic cosmological models are also included. The book contains a large number of new exercises and examples, each with separate headings. The reader will benefit from an updated introduction to general relativity including the most recent developments in cosmology.
Mathématiques et Technologie (Springer Undergraduate Texts in Mathematics and Technology)
by Christiane Rousseau Yvan Saint-AubinCe livre introduit de nombreux concepts mathématiques élégants dans le cadre d'applications réelles, pour la plupart modernes. Les divers sujets sont présentés avec clarté et les mathématiques toujours discutées à partir de connaissances de base. À de rares exceptions près, les chapitres sont indépendants et peuvent être lus dans n'importe quel ordre. Chacun suggère de nombreux exercices, certains élémentaires pour renforcer la compréhension, d'autres plus avancés pour explorer de nouvelles problématiques. Une mise en contexte historique de certains concepts mathématiques ou de l'évolution d'une technologique enrichit le texte. Mathématiques et Technologie s'adresse aux étudiants en mathématiques du premier cycle universitaire (undergraduates du système nord-américain) et aux futurs maîtres du secondaire. Enfin, deux qualités le rendent accessible à un grand éventail de lecteurs curieux : le calcul différentiel et intégral n'y joue pas un rôle de premier plan et les chapitres indiquent clairement lorsque des outils mathématiques plus avancés sont utilisés (ceci ne se produit que dans les dernières sections de quelques chapitres).
Mathematics and Technology (Springer Undergraduate Texts in Mathematics and Technology)
by Christiane Rousseau Yvan Saint-AubinThis book introduces the student to numerous modern applications of mathematics in technology. The authors write with clarity and present the mathematics in a clear and straightforward way making it an interesting and easy book to read. Numerous exercises at the end of every section provide practice and reinforce the material in the chapter. An engaging quality of this book is that the authors also present the mathematical material in a historical context and not just the practical one. Mathematics and Technology is intended for undergraduate students in mathematics, instructors and high school teachers. Additionally, its lack of calculus centricity as well as a clear indication of the more difficult topics and relatively advanced references make it suitable for any curious individual with a decent command of high school math.
Mathematical Problems from Applied Logic II: Logics for the XXIst Century (International Mathematical Series #5)
by Michael Zakharyaschev Dov Gabbay Sergei GoncharovThis book presents contributions from world-renowned logicians, discussing important topics of logic from the point of view of their further development in light of requirements arising from successful application in Computer Science and AI language. Coverage includes: the logic of provability, computability theory applied to biology, psychology, physics, chemistry, economics, and other basic sciences; computability theory and computable models; logic and space-time geometry; hybrid systems; logic and region-based theory of space.
Variational Methods in Imaging (Applied Mathematical Sciences #167)
by Otmar Scherzer Markus Grasmair Harald Grossauer Markus Haltmeier Frank LenzenThis book is devoted to the study of variational methods in imaging. The presentation is mathematically rigorous and covers a detailed treatment of the approach from an inverse problems point of view. Many numerical examples accompany the theory throughout the text. It is geared towards graduate students and researchers in applied mathematics. Researchers in the area of imaging science will also find this book appealing. It can serve as a main text in courses in image processing or as a supplemental text for courses on regularization and inverse problems at the graduate level.
Knowledge Management for Educational Innovation: IFIP WG 3.7 7th Conference on Information Technology in Educational Management (ITEM), Hamamatsu, Japan, July 23-26, 2006 (IFIP Advances in Information and Communication Technology #230)
by Toshio Okamoto Adrie Visscher Arthur TatnallThis book contains selected papers presented at the seventh Conference on Working Group 3.7 of the International Federation for Information Processing. The focus of Working Group 3.7 is on ITEM: Information Technology in Educational Management. The overall goal of the conference was to demonstrate and explore directions for developing and improving all types of educational institutions through ITEM.
Introduction to Calculus and Classical Analysis (Undergraduate Texts in Mathematics)
by Omar HijabIntended for an honors calculus course or for an introduction to analysis, this is an ideal text for undergraduate majors since it covers rigorous analysis, computational dexterity, and a breadth of applications. The book contains many remarkable features: * complete avoidance of /epsilon-/delta arguments by using sequences instead * definition of the integral as the area under the graph, while area is defined for every subset of the plane * complete avoidance of complex numbers * heavy emphasis on computational problems * applications from many parts of analysis, e.g. convex conjugates, Cantor set, continued fractions, Bessel functions, the zeta functions, and many more * 344 problems with solutions in the back of the book.
Data Mining in Biomedicine (Springer Optimization and Its Applications #7)
by Panos M. Pardalos Vladimir L. Boginski Alkis VazacopoulosThis volume presents an extensive collection of contributions covering aspects of the exciting and important research field of data mining techniques in biomedicine. Coverage includes new approaches for the analysis of biomedical data; applications of data mining techniques to real-life problems in medical practice; comprehensive reviews of recent trends in the field. The book addresses incorporation of data mining in fundamental areas of biomedical research: genomics, proteomics, protein characterization, and neuroscience.
Nonlinear Time Series: Nonparametric and Parametric Methods (Springer Series in Statistics)
by Jianqing Fan Qiwei YaoThis is the first book that integrates useful parametric and nonparametric techniques with time series modeling and prediction, the two important goals of time series analysis. Such a book will benefit researchers and practitioners in various fields such as econometricians, meteorologists, biologists, among others who wish to learn useful time series methods within a short period of time. The book also intends to serve as a reference or text book for graduate students in statistics and econometrics.
Tensors: The Mathematics of Relativity Theory and Continuum Mechanics
by Anadi Jiban DasHere is a modern introduction to the theory of tensor algebra and tensor analysis. It discusses tensor algebra and introduces differential manifold. Coverage also details tensor analysis, differential forms, connection forms, and curvature tensor. In addition, the book investigates Riemannian and pseudo-Riemannian manifolds in great detail. Throughout, examples and problems are furnished from the theory of relativity and continuum mechanics.
Optics: Learning by Computing, with Examples Using Maple, MathCad®, Matlab®, Mathematica®, and Maple®
by Karl Dieter MoellerThis new edition is intended for a one semester course in optics for juniors and seniors in science and engineering. It uses scripts from Maple, MathCad, Mathematica, and MATLAB to provide a simulated laboratory where students can learn by exploration and discovery instead of passive absorption. The text covers all the standard topics of a traditional optics course. It contains step by step derivations of all basic formulas in geometrical, wave and Fourier optics. The threefold arrangement of text, applications, and files makes the book suitable for "self-learning" by scientists or engineers who would like to refresh their knowledge of optics.
Data Quality and Record Linkage Techniques
by Thomas N. Herzog Fritz J. Scheuren William E. WinklerThis book offers a practical understanding of issues involved in improving data quality through editing, imputation, and record linkage. The first part of the book deals with methods and models, focusing on the Fellegi-Holt edit-imputation model, the Little-Rubin multiple-imputation scheme, and the Fellegi-Sunter record linkage model. The second part presents case studies in which these techniques are applied in a variety of areas, including mortgage guarantee insurance, medical, biomedical, highway safety, and social insurance as well as the construction of list frames and administrative lists. This book offers a mixture of practical advice, mathematical rigor, management insight and philosophy.
Set-Valued Mappings and Enlargements of Monotone Operators (Springer Optimization and Its Applications #8)
by Regina S. Burachik Alfredo N. IusemThis is the first comprehensive book treatment of the emerging subdiscipline of set-valued mapping and enlargements of maximal monotone operators. It features several important new results and applications in the field. Throughout the text, examples help readers make the bridge from theory to application. Numerous exercises are also offered to enable readers to apply and build their own skills and knowledge.
The Statistical Analysis of Recurrent Events (Statistics for Biology and Health)
by Richard J. Cook Jerald LawlessThis book presents models and statistical methods for the analysis of recurrent event data. The authors provide broad, detailed coverage of the major approaches to analysis, while emphasizing the modeling assumptions that they are based on. More general intensity-based models are also considered, as well as simpler models that focus on rate or mean functions. Parametric, nonparametric and semiparametric methodologies are all covered, with procedures for estimation, testing and model checking.
Permutation Methods: A Distance Function Approach (Springer Series in Statistics)
by Paul W. Mielke Kenneth J. BerryThis is the second edition of the comprehensive treatment of statistical inference using permutation techniques. It makes available to practitioners a variety of useful and powerful data analytic tools that rely on very few distributional assumptions. Although many of these procedures have appeared in journal articles, they are not readily available to practitioners. This new and updated edition places increased emphasis on the use of alternative permutation statistical tests based on metric Euclidean distance functions that have excellent robustness characteristics. These alternative permutation techniques provide many powerful multivariate tests including multivariate multiple regression analyses.
The Arithmetic of Dynamical Systems (Graduate Texts in Mathematics #241)
by J.H. SilvermanThis book provides an introduction to the relatively new discipline of arithmetic dynamics. Whereas classical discrete dynamics is the study of iteration of self-maps of the complex plane or real line, arithmetic dynamics is the study of the number-theoretic properties of rational and algebraic points under repeated application of a polynomial or rational function. A principal theme of arithmetic dynamics is that many of the fundamental problems in the theory of Diophantine equations have dynamical analogs.This graduate-level text provides an entry for students into an active field of research and serves as a standard reference for researchers.
Weak Dependence: With Examples and Applications (Lecture Notes in Statistics #190)
by Jérome Dedecker Paul Doukhan Gabriel Lang José Rafael Leon Sana Louhichi Clémentine PrieurThis book develops Doukhan/Louhichi's 1999 idea to measure asymptotic independence of a random process. The authors, who helped develop this theory, propose examples of models fitting such conditions: stable Markov chains, dynamical systems or more complicated models, nonlinear, non-Markovian, and heteroskedastic models with infinite memory. Applications are still needed to develop a method of analysis for nonlinear times series, and this book provides a strong basis for additional studies.
Semi-Markov Risk Models for Finance, Insurance and Reliability
by Jacques Janssen Raimondo MancaEveryone working in related fields from applied mathematicians to statisticians to actuaries and operations researchers will find this a brilliantly useful practical text. The book presents applications of semi-Markov processes in finance, insurance and reliability, using real-life problems as examples. After a presentation of the main probabilistic tools necessary for understanding of the book, the authors show how to apply semi-Markov processes in finance, starting from the axiomatic definition and continuing eventually to the most advanced financial tools.
Indirect Sampling (Springer Series in Statistics)
by Pierre LavalléeThis book is the reference on indirect sampling and the generalised weight share method. It reviews the different developments done by the author on these subjects. In addition to the underlying theory, the book presents different possible applications that drive its interest. The reader will find in this book the answer to questions that come, inevitably, when working in a context of indirect sampling.
Aging and Chronic Disorders
by Stephen J. Morewitz Mark L. GoldsteinFocusing on the most prevalent conditions affecting seniors - including diabetes, cardiovascular disease, osteoporosis, arthritis, and fibromyalgia - Morewitz and Goldstein analyze the impact of chronic disease on aging. Separate chapters are devoted to cognitive changes, psychological problems, and trends in health care utilization, and all chapters are amplified by current research findings.
Matrix Algebra: Theory, Computations, and Applications in Statistics (Springer Texts in Statistics)
by James E. GentleMatrix algebra is one of the most important areas of mathematics for data analysis and for statistical theory. This much-needed work presents the relevant aspects of the theory of matrix algebra for applications in statistics. It moves on to consider the various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes the special properties of those matrices. Finally, it covers numerical linear algebra, beginning with a discussion of the basics of numerical computations, and following up with accurate and efficient algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors.
Multiscale Modeling: A Bayesian Perspective (Springer Series in Statistics)
by Marco A.R. Ferreira Herbert K.H. LeeThis highly useful book contains methodology for the analysis of data that arise from multiscale processes. It brings together a number of recent developments and makes them accessible to a wider audience. Taking a Bayesian approach allows for full accounting of uncertainty, and also addresses the delicate issue of uncertainty at multiple scales. These methods can handle different amounts of prior knowledge at different scales, as often occurs in practice.