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Soliton Management in Periodic Systems

During the past ten years, there has been intensive development in theoretical and experimental research of solitons in periodic media. This book provides a unique and informative account of the state-of-the-art in the field. The volume opens with a review of the existence of robust solitary pulses in systems built as a periodic concatenation of very different elements. Among the most famous examples of this type of systems are the dispersion management in fiber-optic telecommunication links, and (more recently) photonic crystals. A number of other systems belonging to the same broad class of spatially periodic strongly inhomogeneous media (such as the split-step and tandem models) have recently been identified in nonlinear optics, and transmission of solitary pulses in them was investigated in detail. Similar soliton dynamics occurs in temporal-domain counterparts of such systems, where they are subject to strong time-periodic modulation (for instance, the Feshbach-resonance management in Bose-Einstein condensates). Basis results obtained for all these systems are reviewed in the book. This timely work will serve as a useful resource for the soliton community.

Markov Chains: Models, Algorithms and Applications (International Series in Operations Research & Management Science #83)

Markov chains are a particularly powerful and widely used tool for analyzing a variety of stochastic (probabilistic) systems over time. This monograph will present a series of Markov models, starting from the basic models and then building up to higher-order models. Included in the higher-order discussions are multivariate models, higher-order multivariate models, and higher-order hidden models. In each case, the focus is on the important kinds of applications that can be made with the class of models being considered in the current chapter. Special attention is given to numerical algorithms that can efficiently solve the models. Therefore, 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.

Bioinformatics and Computational Biology Solutions Using R and Bioconductor (Statistics for Biology and Health)

Full four-color book. Some of the editors created the Bioconductor project and Robert Gentleman is one of the two originators of R. All methods are illustrated with publicly available data, and a major section of the book is devoted to fully worked case studies. Code underlying all of the computations that are shown is made available on a companion website, and readers can reproduce every number, figure, and table on their own computers.

Probability and Partial Differential Equations in Modern Applied Mathematics (The IMA Volumes in Mathematics and its Applications #140)

"Probability and Partial Differential Equations in Modern Applied Mathematics" is devoted to the role of probabilistic methods in modern applied mathematics from the perspectives of both a tool for analysis and as a tool in modeling. There is a recognition in the applied mathematics research community that stochastic methods are playing an increasingly prominent role in the formulation and analysis of diverse problems of contemporary interest in the sciences and engineering. A probabilistic representation of solutions to partial differential equations that arise as deterministic models allows one to exploit the power of stochastic calculus and probabilistic limit theory in the analysis of deterministic problems, as well as to offer new perspectives on the phenomena for modeling purposes. There is also a growing appreciation of the role for the inclusion of stochastic effects in the modeling of complex systems. This has led to interesting new mathematical problems at the interface of probability, dynamical systems, numerical analysis, and partial differential equations. This volume will be useful to researchers and graduate students interested in probabilistic methods, dynamical systems approaches and numerical analysis for mathematical modeling in the sciences and engineering.

Riemannian Geometry (Graduate Texts in Mathematics #171)

This volume introduces techniques and theorems of Riemannian geometry, and opens the way to advanced topics. The text combines the geometric parts of Riemannian geometry with analytic aspects of the theory, and reviews recent research. The updated second edition includes a new coordinate-free formula that is easily remembered (the Koszul formula in disguise); an expanded number of coordinate calculations of connection and curvature; general fomulas for curvature on Lie Groups and submersions; variational calculus integrated into the text, allowing for an early treatment of the Sphere theorem using a forgotten proof by Berger; recent results regarding manifolds with positive curvature.

Bioinformatics of Genome Regulation and Structure II

The last 15 years in development of biology were marked with accumulation of unprecedentedly huge arrays of experimental data. The information was amassed with exclusively high rates due to the advent of highly efficient experimental technologies that provided for high throughput genomic sequencing; of functional genomics technologies allowing investigation of expression dynamics of large groups of genes using expression DNA chips; of proteomics methods giving the possibility to analyze protein compositions of cells, tissues, and organs, assess the dynamics of the cell proteome, and reconstruct the networks of protein-protein interactions; and of metabolomics, in particular, high resolution mass spectrometry study of cell metabolites, and distribution of metabolic fluxes in the cells with a concurrent investigation of the dynamics of thousands metabolites in an individual cell. Analysis, comprehension, and use of the tremendous volumes of experimental data reflecting the intricate processes underlying the functioning of molecular genetic systems are unfeasible in principle without the systems approach and involvement of the state-of-the-art information and computer technologies and efficient mathematical methods for data analysis and simulation of biological systems and processes. The need in solving these problems initiated the birth of a new science— postgenomic bioinformatics or systems biology in silico.

Applied Semi-Markov Processes

Aims to give to the reader the tools necessary to apply semi-Markov processes in real-life problems. The book is self-contained and, starting from a low level of probability concepts, gradually brings the reader to a deep knowledge of semi-Markov processes. Presents homogeneous and non-homogeneous semi-Markov processes, as well as Markov and semi-Markov rewards processes. The concepts are fundamental for many applications, but they are not as thoroughly presented in other books on the subject as they are here.

Multiscale Optimization Methods and Applications (Nonconvex Optimization and Its Applications #82)

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.

Non-Euclidean Geometries: János Bolyai Memorial Volume (Mathematics and Its Applications #581)

"From nothing I have created a new different world," wrote János 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 János 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 János 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.

Mathematical and Computational Models for Congestion Charging (Applied Optimization #101)

Rigorous treatments of issues related to congestion pricing are described in this book. It examines recent advances in areas such as mathematical and computational models for predicting traffic congestion, determining when, where, and how much to levy tolls, and analyzing the impact on transportation systems. The book follows recent schemes judged to be successful in London, Singapore, Norway, as well as a number of projects in the United States.

Mathematics Education in Different Cultural Traditions- A Comparative Study of East Asia and the West: The 13th ICMI Study (New ICMI Study Series #9)

The idea of the ICMI Study 13 is outlined as follows: Education in any social environment is influenced in many ways by the traditions of these environments. This study brings together leading experts to research and report on mathematics education in a global context. Mathematics education faces a split phenomenon of difference and correspondence. A study attempting a comparison between mathematics education in different traditions will be helpful to understanding this phenomenon.

Poverty, Inequality and Development: Essays in Honor of Erik Thorbecke (Economic Studies in Inequality, Social Exclusion and Well-Being #1)

This collection of essays honors a remarkable man and his work. Erik Thorbecke has made significant contributions to the microeconomic and the macroeconomic analysis of poverty, inequality and development, ranging from theory to empirics and policy. The essays in this volume display the same range. As a collection they make the fundamental point that deep understanding of these phenomena requires both the micro and the macro perspectives together, utilizing the strengths of each but also the special insights that come when the two are linked together. After an overview section which contains the introductory chapter and a chapter examining the historical roots of Erik Thorbecke's motivations, the essays in this volume are grouped into four parts, each part identifying a major strand of Erik's work—Measurement of Poverty and Inequality, Micro Behavior and Market Failure, SAMs and CGEs, and Institutions and Development. The range of topics covered in the essays, written by leading authorities in their own areas, highlight the extraordinary depth and breadth of Erik Thorbecke's influence in research and policy on poverty, inequality and development. Acknowledgements These papers were presented at a conference in honor of Erik Thorbecke held at Cornell University on October 10-11, 2003. The conference was supported by the funds of the H. E. Babcock Chair in Food, Nutrition and Public Policy, and the T. H. Lee Chair in World Affairs at Cornell University.

Digital Communications Using Chaos and Nonlinear Dynamics (Institute for Nonlinear Science)

This book provides a summary of the research conducted at UCLA, Stanford University, and UCSD over the last ?ve years in the area of nonlinear dyn- ics and chaos as applied to digital communications. At ?rst blush, the term “chaotic communications” seems like an oxymoron; how could something as precise and deterministic as digital communications be chaotic? But as this book will demonstrate, the application of chaos and nonlinear dynamicstocommunicationsprovidesmanypromisingnewdirectionsinareas of coding, nonlinear optical communications, and ultra-wideband commu- cations. The eleven chapters of the book summarize many of the promising new approaches that have been developed, and point the way to new research directions in this ?eld. Digital communications techniques have been continuously developed and re?ned for the past ?fty years to the point where today they form the heart of a multi-hundred billion dollar per year industry employing hundreds of thousands of people on a worldwide basis. There is a continuing need for transmission and reception of digital signals at higher and higher data rates. There are a variety of physical limits that place an upper limit on these data rates, and so the question naturally arises: are there alternative communi- tion techniques that can overcome some of these limitations? Most digital communications today is carried out using electronic devices that are essentially “linear,” and linear system theory has been used to c- tinually re?ne their performance. In many cases, inherently nonlinear devices are linearized in order to achieve a certain level of linear system performance.

Modelling and Applications in Mathematics Education: The 14th ICMI Study (New ICMI Study Series #10)

The book aims at showing the state-of-the-art in the field of modeling and applications in mathematics education. This is the first volume to do this. The book deals with the question of how key competencies of applications and modeling at the heart of mathematical literacy may be developed; with the roles that applications and modeling may play in mathematics teaching, making mathematics more relevant for students.

18 Unconventional Essays on the Nature of Mathematics

Collection of the most interesting recent writings on the philosophy of mathematics written by highly respected researchers from philosophy, mathematics, physics, and chemistry Interdisciplinary book that will be useful in several fields—with a cross-disciplinary subject area, and contributions from researchers of various disciplines

Number Theory: An Introduction to Mathematics: Part A

This two-volume book is a modern introduction to the theory of numbers, emphasizing its connections with other branches of mathematics. Part A is accessible to first-year undergraduates and deals with elementary number theory. Part B is more advanced and gives the reader an idea of the scope of mathematics today. The connecting theme is the theory of numbers. By exploring its many connections with other branches a broad picture is obtained. The book contains a treasury of proofs, several of which are gems seldom seen in number theory books.

Number Theory: An Introduction to Mathematics: Part B

This two-volume book is a modern introduction to the theory of numbers, emphasizing its connections with other branches of mathematics. Part A is accessible to first-year undergraduates and deals with elementary number theory. Part B is more advanced and gives the reader an idea of the scope of mathematics today. The connecting theme is the theory of numbers. By exploring its many connections with other branches a broad picture is obtained. The book contains a treasury of proofs, several of which are gems seldom seen in number theory books.

Optimal Control Theory: Applications to Management Science and Economics

Optimal control methods are used to determine optimal ways to control a dynamic system. The theoretical work in this field serves as a foundation for the book, which the authors have applied to business management problems developed from their research and classroom instruction. Sethi and Thompson have provided management science and economics communities with a thoroughly revised edition of their classic text on Optimal Control Theory. The new edition has been completely refined with careful attention to the text and graphic material presentation. Chapters cover a range of topics including finance, production and inventory problems, marketing problems, machine maintenance and replacement, problems of optimal consumption of natural resources, and applications of control theory to economics. The book contains new results that were not available when the first edition was published, as well as an expansion of the material on stochastic optimal control theory.

Research Problems in Discrete Geometry

This book is the result of a 25-year-old project and comprises a collection of more than 500 attractive open problems in the field. The largely self-contained chapters provide a broad overview of discrete geometry, along with historical details and the most important partial results related to these problems. This book is intended as a source book for both professional mathematicians and graduate students who love beautiful mathematical questions, are willing to spend sleepless nights thinking about them, and who would like to get involved in mathematical research.

A First Course in Differential Equations (Undergraduate Texts in Mathematics)

Therearemanyexcellenttextsonelementarydi?erentialequationsdesignedfor the standard sophomore course. However, in spite of the fact that most courses are one semester in length, the texts have evolved into calculus-like pres- tations that include a large collection of methods and applications, packaged with student manuals, and Web-based notes, projects, and supplements. All of this comes in several hundred pages of text with busy formats. Most students do not have the time or desire to read voluminous texts and explore internet supplements. The format of this di?erential equations book is di?erent; it is a one-semester, brief treatment of the basic ideas, models, and solution methods. Itslimitedcoverageplacesitsomewherebetweenanoutlineandadetailedte- book. I have tried to write concisely, to the point, and in plain language. Many worked examples and exercises are included. A student who works through this primer will have the tools to go to the next level in applying di?erential eq- tions to problems in engineering, science, and applied mathematics. It can give some instructors, who want more concise coverage, an alternative to existing texts.

Large-Scale Nonlinear Optimization (Nonconvex Optimization and Its Applications #83)

This book reviews and discusses recent advances in the development of methods and algorithms for nonlinear optimization and its applications, focusing on the large-dimensional case, the current forefront of much research. Individual chapters, contributed by eminent authorities, provide an up-to-date overview of the field from different and complementary standpoints, including theoretical analysis, algorithmic development, implementation issues and applications.

Numerical and Practical Exercises in Thermoluminescence

Thermoluminescence (TL) is a well-established technique widely used in do- metric and dating applications. Although several excellent reference books exist which document both the t- oretical and experimental aspects of TL, there is a general lack of books that deal withspeci?cnumericalandpracticalaspectsofanalyzingTLdata. Manytimesthe practicaldetailsofanalyzingnumericalTLglowcurvesandofapplyingtheoretical models are dif?cult to ?nd in the published literature. The purpose of this book is to provide a practical guide for both established researchers and for new graduate students entering the ?eld of TL and is intended to be used in conjunction with and as a practical supplement of standard textbooks in the ?eld. Chapter1laysthemathematicalgroundworkforsubsequentchaptersbyprese- ingthefundamentalmathematicalexpressionsmostcommonlyusedforanalyzing experimental TL data. Chapter2presentscomprehensiveexamplesofTLdataanalysisforglowcurves following ?rst-, second-, and general-order kinetics. Detailed analysis of num- ical data is presented by using a variety of methods found in the TL literature, with particular emphasis in the practical aspects and pitfalls that researchers may encounter. Special emphasis is placed on the need to use several different me- ods to analyze the same TL data, as well as on the necessity to analyze glow curves obtained under different experimental conditions. Unfortunately, the lit- ature contains many published papers that claim a speci?c kinetic order for a TL peak in a dosimetric material, based only on a peak shape analysis. It is hoped that the detailed examples provided in Chapter 2 will encourage more comprehensive studies of TL properties of materials, based on the simultaneous use of several different methods of analysis.

Data Monitoring in Clinical Trials: A Case Studies Approach

From the authors of "Fundamentals of Clinical Trials" which has sold over 15,000 copies world wide since its publication in 1998. No competition yet as the text does not focus on how to do clinical trials but on very specific situations that can be encountered during the process.

Encyclopedia of Algorithms (Springer Reference Ser.)

Encyclopedia of Machine Learning

This comprehensive encyclopedia, with over 250 entries in an A-Z format, provides easy access to relevant information for those seeking entry into any aspect within the broad field of machine learning. Most entries in this preeminent work include useful literature references.Topics for the Encyclopedia of Machine Learning were selected by a distinguished international advisory board. These peer-reviewed, highly-structured entries include definitions, illustrations, applications, bibliographies and links to related literature, providing the reader with a portal to more detailed information on any given topic.The style of the entries in the Encyclopedia of Machine Learning is expository and tutorial, making the book a practical resource for machine learning experts, as well as professionals in other fields who need to access this vital information but may not have the time to work their way through an entire text on their topic of interest.The authoritative reference is published both in print and online. The print publication includes an index of subjects and authors. The online edition supplements this index with hyperlinks as well as internal hyperlinks to related entries in the text, CrossRef citations, and links to additional significant research.