As the demand for data reliability increases, coding for error control becomes increasingly important in data transmission systems and has become an integral part of almost all data communication system designs. In recent years, various trellis-based soft-decoding algorithms for linear block codes have been devised. New ideas developed in the study of trellis structure of block codes can be used for improving decoding and analyzing the trellis complexity of convolutional codes. These recent developments provide practicing communication engineers with more choices when designing error control systems. Trellises and Trellis-based Decoding Algorithms for Linear Block Codes combines trellises and trellis-based decoding algorithms for linear codes together in a simple and unified form. The approach is to explain the material in an easily understood manner with minimal mathematical rigor. Trellises and Trellis-based Decoding Algorithms for Linear Block Codes is intended for practicing communication engineers who want to have a fast grasp and understanding of the subject. Only material considered essential and useful for practical applications is included. This book can also be used as a text for advanced courses on the subject.

This book explains modern and interesting physics in heavy-fermion (HF) compounds to graduate students and researchers in condensed matter physics. It presents a theory of heavy-fermion (HF) compounds such as HF metals, quantum spin liquids, quasicrystals and two-dimensional Fermi systems. The basic low-temperature properties and the scaling behavior of the compounds are described within the framework of the theory of fermion condensation quantum phase transition (FCQPT). Upon reading the book, the reader finds that HF compounds with quite different microscopic nature exhibit the same non-Fermi liquid behavior, while the data collected on very different HF systems have a universal scaling behavior, and these compounds are unexpectedly uniform despite their diversity. For the reader's convenience, the analysis of compounds is carried out in the context of salient experimental results. The numerous calculations of the non-Fermi liquid behavior, thermodynamic, relaxation and transport properties, being in good agreement with experimental facts, offer the reader solid grounds to learn the theory's applications. Finally, the reader will learn that FCQPT develops unexpectedly simple, yet completely good description of HF compounds.

The second and revised edition of Network Economics: A Variational Inequality Approach provides an updated treatment of network economics through the inclusion of new theoretical results and new applications, as well as problems for self-study purposes and/or for use in the classroom. This volume remains true to the first edition in that it provides a unified treatment of finite-dimensional variational inequalities, algorithms, and applications. Physical networks are pervasive in today's society in the form of transportation networks, telecommunication networks, energy networks, and financial networks, whereas mathematical networks provide a mechanism for studying a plethora of economic equilibrium problems through a common graphic structure. Network Economics establishes the connections among economic equilibrium problems through their network structure and demonstrates how the structure can then be used to address policy interventions, as well as to construct efficient numerical schemes for the computation of equilibria. The network framework provides not only a mechanism for the graphic representation of economic problems and a means for visualizing their similarities and differences, but, in addition, a novel theoretical approach. Problems treated include: congested transportation systems, oligopolistic market equilibrium problems, problems of human migration, and general financial and economic equilibrium problems. New applications covered in this second edition include environmental networks and knowledge networks.

This thesis contains results of Dr. Guilong Gui during his PhD period with the aim to understand incompressible Navier-Stokes equations. It is devoted to the study of the stability to the incompressible Navier-Stokes equations. There is great potential for further theoretical and numerical research in this field. The techniques developed in carrying out this work are expected to be useful for other physical model equations. It is also hopeful that the thesis could serve as a valuable reference on current developments in research topics related to the incompressible Navier-Stokes equations. It was nominated by the Graduate University of Chinese Academy of Sciences as an outstanding PhD thesis.

In recent years topology has firmly established itself as an important part of the physicist's mathematical arsenal. Topology has profound relevance to quantum field theory-for example, topological nontrivial solutions of the classical equa tions of motion (solitons and instantons) allow the physicist to leave the frame work of perturbation theory. The significance of topology has increased even further with the development of string theory, which uses very sharp topologi cal methods-both in the study of strings, and in the pursuit of the transition to four-dimensional field theories by means of spontaneous compactification. Im portant applications of topology also occur in other areas of physics: the study of defects in condensed media, of singularities in the excitation spectrum of crystals, of the quantum Hall effect, and so on. Nowadays, a working knowledge of the basic concepts of topology is essential to quantum field theorists; there is no doubt that tomorrow this will also be true for specialists in many other areas of theoretical physics. The amount of topological information used in the physics literature is very large. Most common is homotopy theory. But other subjects also play an important role: homology theory, fibration theory (and characteristic classes in particular), and also branches of mathematics that are not directly a part of topology, but which use topological methods in an essential way: for example, the theory of indices of elliptic operators and the theory of complex manifolds."

This book focuses on problems at the interplay between the theory of partitions and optimal transport with a view toward applications. Topics covered include problems related to stable marriages and stable partitions, multipartitions, optimal transport for measures and optimal partitions, and finally cooperative and noncooperative partitions. All concepts presented are illustrated by examples from game theory, economics, and learning.

In studying General Equilibrium Theory the student must master first the theory and then apply it to solve problems. At the graduate level there is no book devoted exclusively to teaching problem solving. This book teaches for the first time the basic methods of proof and problem solving in General Equilibrium Theory. The problems cover the entire spectrum of difficulty; some are routine, some require a good grasp of the material involved, and some are exceptionally challenging. The book presents complete solutions to two hundred problems. In searching for the basic required techniques, the student will find a wealth of new material incorporated into the solutions. The student is challenged to produce solutions which are different from the ones presented in the book.

Commencing with a self-contained overview of atomic collision theory, this monograph presents recent developments of R-matrix theory and its applications to a wide-range of atomic molecular and optical processes. These developments include the electron and photon collisions with atoms, ions and molecules which are required in the analysis of laboratory and astrophysical plasmas, multiphoton processes required in the analysis of superintense laser interactions with atoms and molecules and positron collisions with atoms and molecules required in antimatter studies of scientific and technologial importance. Basic mathematical results and general and widely used R-matrix computer programs are summarized in the appendices.

Professor Sten Malmquist constructed the Malmquist quantity index and in doing so developed a distance function defined on a consumption space. This function is the consumer analog to the Shephard input distance function of producers and is used in ratio form to define the quantity index. This volume contains new contributions based on Malmquist's work nearly 50 years ago and provides modern perspectives on the value of this research.

The first comprehensive account of the theory of mass transportation problems and its applications. In Volume I, the authors systematically develop the theory with emphasis on the Monge-Kantorovich mass transportation and the Kantorovich-Rubinstein mass transshipment problems. They then discuss a variety of different approaches towards solving these problems and exploit the rich interrelations to several mathematical sciences - from functional analysis to probability theory and mathematical economics. The second volume is devoted to applications of the above problems to topics in applied probability, theory of moments and distributions with given marginals, queuing theory, risk theory of probability metrics and its applications to various fields, among them general limit theorems for Gaussian and non-Gaussian limiting laws, stochastic differential equations and algorithms, and rounding problems. Useful to graduates and researchers in theoretical and applied probability, operations research, computer science, and mathematical economics, the prerequisites for this book are graduate level probability theory and real and functional analysis.

Nominated as an outstanding thesis by the Department of Physics and Astronomy of the University of New Mexico, this thesis seeks to identify the gamma-ray burst (GRB) progenitor. GRBs are extragalactic explosions that briefly outshine entire galaxies, but the mechanism that can release that much energy over a < 100 second burst is still a mystery. The leading candidate for the GRB progenitor is currently a massive star which collapses to form a black hole-accretion disk system that powers the GRB. GRB afterglows, however, do not always show the expected behavior of a relativistic blast wave interacting with the stellar wind that such a progenitor should have produced before its collapse. In this book, the author uses the Zeus-MP astrophysical hydrodynamics code to model the environment around a stellar progenitor prior to the burst. He then develops a new semi-analytic MHD and emission model to produce light curves for GRBs encountering these realistic density profiles. The work ultimately shows that the circumburst medium surrounding a GRB at the time of the explosion is much more complex than a pure wind, and that observed afterglows are entirely consistent with a large subset of proposed stellar progenitors.

In recent years global optimization has found applications in many interesting areas of science and technology including molecular biology, chemical equilibrium problems, medical imaging and networks. The collection of papers in this book indicates the diverse applicability of global optimization. Furthermore, various algorithmic, theoretical developments and computational studies are presented. Audience: All researchers and students working in mathematical programming.

This is a masterly exposition and an encyclopedic presentation of the theory of hyperbolic conservation laws. It illustrates the essential role of continuum thermodynamics in providing motivation and direction for the development of the mathematical theory while also serving as the principal source of applications. The reader is expected to have a certain mathematical sophistication and to be familiar with (at least) the rudiments of analysis and the qualitative theory of partial differential equations, whereas prior exposure to continuum physics is not required. The target group of readers would consist of (a) experts in the mathematical theory of hyperbolic systems of conservation laws who wish to learn about the connection with classical physics; (b) specialists in continuum mechanics who may need analytical tools; (c) experts in numerical analysis who wish to learn the underlying mathematical theory; and (d) analysts and graduate students who seek introduction to the theory of hyperbolic systems of conservation laws. This new edition places increased emphasis on hyperbolic systems of balance laws with dissipative source, modeling relaxation phenomena. It also presents an account of recent developments on the Euler equations of compressible gas dynamics. Furthermore, the presentation of a number of topics in the previous edition has been revised, expanded and brought up to date, and has been enriched with new applications to elasticity and differential geometry. The bibliography, also expanded and updated, now comprises close to two thousand titles. From the reviews of the 3rd edition: "This is the third edition of the famous book by C.M. Dafermos. His masterly written book is, surely, the most complete exposition in the subject." Evgeniy Panov, Zentralblatt MATH "A monumental book encompassing all aspects of the mathematical theory of hyperbolic conservation laws, widely recognized as the "Bible" on the subject." Philippe G. LeFloch, Math. Reviews

From the reviews: "The account is quite detailed and is written in a manner that will appeal to analysts and numerical practitioners alike...they contain everything from rigorous proofs to tables of numerical calculations.... one of the strong features of these books...that they are designed not for the expert, but for those who whish to learn the subject matter starting from little or no background...there are numerous examples, and counter-examples, to back up the theory...To my knowledge, no other authors have given such a clear geometric account of convex analysis." "This innovative text is well written, copiously illustrated, and accessible to a wide audience"

Nonlinearoptimizationproblemscontainingbothcontinuousanddiscretevariables are called mixed integer nonlinear programs (MINLP). Such problems arise in many ?elds, such as process industry, engineering design, communications, and ?nance. There is currently a huge gap between MINLP and mixed integer linear programming(MIP) solvertechnology.With a modernstate-of-the-artMIP solver itispossibletosolvemodelswithmillionsofvariablesandconstraints,whereasthe dimensionofsolvableMINLPsisoftenlimitedbyanumberthatissmallerbythree or four orders of magnitude. It is theoretically possible to approximate a general MINLP by a MIP with arbitrary precision. However, good MIP approximations are usually much larger than the original problem. Moreover, the approximation of nonlinear functions by piecewise linear functions can be di?cult and ti- consuming. In this book relaxation and decomposition methods for solving nonconvex structured MINLPs are proposed. In particular, a generic branch-cut-and-price (BCP) framework for MINLP is presented. BCP is the underlying concept in almost all modern MIP solvers. Providing a powerful decomposition framework for both sequential and parallel solvers, it made the success of the current MIP technology possible. So far generic BCP frameworks have been developed only for MIP, for example,COIN/BCP (IBM, 2003) andABACUS (OREAS GmbH, 1999). In order to generalize MIP-BCP to MINLP-BCP, the following points have to be taken into account: * A given (sparse) MINLP is reformulated as a block-separable program with linear coupling constraints.The block structure makes it possible to generate Lagrangian cuts and to apply Lagrangian heuristics. * In order to facilitate the generation of polyhedral relaxations, nonlinear c- vex relaxations are constructed. * The MINLP separation and pricing subproblems for generating cuts and columns are solved with specialized MINLP solvers.

The study of quantum disorder has generated considerable research activity in mathematics and physics over past 40 years. While single-particle models have been extensively studied at a rigorous mathematical level, little was known about systems of several interacting particles, let alone systems with positive spatial particle density. Creating a consistent theory of disorder in multi-particle quantum systems is an important and challenging problem that largely remains open. Multi-scale Analysis for Random Quantum Systems with Interaction presents the progress that had been recently achieved in this area. The main focus of the book is on a rigorous derivation of the multi-particle localization in a strong random external potential field. To make the presentation accessible to a wider audience, the authors restrict attention to a relatively simple tight-binding Anderson model on a cubic lattice Zd. This book includes the following cutting-edge features: an introduction to the state-of-the-art single-particle localization theory an extensive discussion of relevant technical aspects of the localization theory a thorough comparison of the multi-particle model with its single-particle counterpart a self-contained rigorous derivation of both spectral and dynamical localization in the multi-particle tight-binding Anderson model. Required mathematical background for the book includes a knowledge of functional calculus, spectral theory (essentially reduced to the case of finite matrices) and basic probability theory. This is an excellent text for a year-long graduate course or seminar in mathematical physics. It also can serve as a standard reference for specialists.

This book serves a dual purpose: firstly to combine the treatment of circuits and digital electronics, and secondly, to establish a strong connection with the contemporary world of digital systems. The need for this approach arises from the observation that introducing digital electronics through a course in traditional circuit analysis is fast becoming obsolete. Our world has gone digital. Automata theory helps with the design of digital circuits such as parts of computers, telephone systems and control systems. A complete perspective is emphasized, because even the most elegant computer architecture will not function without adequate supporting circuits. The focus is on explaining the real-world implementation of complete digital systems. In doing so, the reader is prepared to immediately begin design and implementation work. This work serves as a bridge to take readers from the theoretical world to the everyday design world where solutions must be complete to be successful.

A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories. The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research.

The book collects contributions from experts worldwide addressing recent scholarship in social network analysis such as influence spread, link prediction, dynamic network biclustering, and delurking. It covers both new topics and new solutions to known problems. The contributions rely on established methods and techniques in graph theory, machine learning, stochastic modelling, user behavior analysis and natural language processing, just to name a few. This text provides an understanding of using such methods and techniques in order to manage practical problems and situations. Trends in Social Network Analysis: Information Propagation, User Behavior Modelling, Forecasting, and Vulnerability Assessment appeals to students, researchers, and professionals working in the field.

This thesis describes a high-quality, high-precision method for the data analysis of an interesting elementary particle reaction. The data was collected at the Japanese B-meson factory KEKB with the Belle detector, one of the most successful large-scale experiments worldwide. CP violation is a subtle quantum effect that makes the world look different when simultaneously left and right and matter and antimatter are exchanged. This being a prerequisite for our own world to have developed from the big bang, there are only a few experimental indications of such effects, and their detection requires very intricate techniques. The discovery of CP violation in B meson decays garnered Kobayashi and Maskawa, who had predicted these findings as early as 1973, the 2008 Nobel prize in physics. This thesis describes in great detail what are by far the best measurements of branching ratios and CP violation parameters in two special reactions with two charm mesons in the final state. It presents an in-depth but accessible overview of the theory, phenomenology, experimental setup, data collection, Monte Carlo simulations, (blind) statistical data analysis, and systematic uncertainty studies.

The book gives a comprehensive overview of the state-of-the-art research and engineering in theory and application of Lattice Automata in design and control of autonomous Robots. Automata and robots share the same notional meaning. Automata (originated from the latinization of the Greek word " ") as self-operating autonomous machines invented from ancient years can be easily considered the first steps of robotic-like efforts. Automata are mathematical models of Robots and also they are integral parts of robotic control systems. A Lattice Automaton is a regular array or a collective of finite state machines, or automata. The Automata update their states by the same rules depending on states of their immediate neighbours. In the context of this book, Lattice Automata are used in developing modular reconfigurable robotic systems, path planning and map exploration for robots, as robot controllers, synchronisation of robot collectives, robot vision, parallel robotic actuators. All chapters are written in an accessible manner and lavishly illustrated. The book will help computer and robotic scientists and engineers to understand mechanisms of decentralised functioning of robotic collectives and to design future and emergent reconfigurable, parallel and distributed robotic systems.

This dissertation focuses on the calculation of transport coefficients in the matter created in a relativistic heavy-ion collision after chemical freeze-out. This matter can be well approximated using a pion gas out of equilibrium. We describe the theoretical framework needed to obtain the shear and bulk viscosities, the thermal and electrical conductivities and the flavor diffusion coefficients of a meson gas at low temperatures. To describe the interactions of the degrees of freedom, we use effective field theories with chiral and heavy quark symmetries. We subsequently introduce the unitarization methods in order to obtain a scattering amplitude that satisfies the unitarity condition exactly, then go on to calculate the transport properties of the low-temperature phase of quantum chromodynamics - the hadronic medium - which can be used in hydrodynamic simulations of a relativistic heavy-ion collision and its subsequent evolution. We show that the shear viscosity over entropy density exhibits a minimum in a phase transition by studying this coefficient in atomic Argon (around the liquid-gas phase transition) and in the linear sigma model in the limit of a large number of scalar fields (which presents a chiral phase transition). Finally, we provide an experimental method for estimating the bulk viscosity in relativistic heavy-ion collisions by performing correlations of the fluctuating components of the stress-energy tensor.

The first comprehensive account of the theory of mass transportation problems and its applications. In Volume I, the authors systematically develop the theory with emphasis on the Monge-Kantorovich mass transportation and the Kantorovich-Rubinstein mass transshipment problems. They then discuss a variety of different approaches towards solving these problems and exploit the rich interrelations to several mathematical sciences - from functional analysis to probability theory and mathematical economics. The second volume is devoted to applications of the above problems to topics in applied probability, theory of moments and distributions with given marginals, queuing theory, risk theory of probability metrics and its applications to various fields, among them general limit theorems for Gaussian and non-Gaussian limiting laws, stochastic differential equations and algorithms, and rounding problems. Useful to graduates and researchers in theoretical and applied probability, operations research, computer science, and mathematical economics, the prerequisites for this book are graduate level probability theory and real and functional analysis.