This book addresses a seemingly simple question: can a certain amount of gas be transported within a pipeline network? The question is difficult, however, when asked in relation to a meshed nationwide gas transportation network and when taking into account technical details and discrete decisions, as well as regulations, contracts, and varying demands involved. Evaluating Gas Network Capacities provides an introduction to the field of gas transportation planning and discusses in detail the advantages and disadvantages of several mathematical models that address gas transport within the context of the technical and regulatory framework. It shows how to solve the models using sophisticated mathematical optimization algorithms and includes examples of large-scale applications of mathematical optimization to this real-world industrial problem. Readers will also find a glossary of gas transport terms, tables listing the physical and technical quantities and constants used throughout the book, and a reference list of regulation and gas business literature.

The volume covers most of the topics addressed and discussed during the Workshop INdAM "Recent advances in kinetic equations and applications", which took place in Rome (Italy), from November 11th to November 15th, 2019. The volume contains results on kinetic equations for reactive and nonreactive mixtures and on collisional and noncollisional Vlasov equations for plasmas. Some contributions are devoted to the study of phase transition phenomena, kinetic problems with nontrivial boundary conditions and hierarchies of models. The book, addressed to researchers interested in the mathematical and numerical study of kinetic equations, provides an overview of recent advances in the field and future research directions.

Numerical analysis explains why numerical computations work - or fail. These are mathematical questions, and the book answers in kind, providing students with a very complete and sound presentation of the interface between mathematics and scientific computation. The book does not assume previous knowledge of numerical methods. It includes a large range of exercises, and will be suitable as a textbook at the advanced undergraduate level.

This textbook provides an accessible and concise introduction to numerical analysis for upper undergraduate and beginning graduate students from various backgrounds. It was developed from the lecture notes of four successful courses on numerical analysis taught within the MPhil of Scientific Computing at the University of Cambridge. The book is easily accessible, even to those with limited knowledge of mathematics. Students will get a concise, but thorough introduction to numerical analysis. In addition the algorithmic principles are emphasized to encourage a deeper understanding of why an algorithm is suitable, and sometimes unsuitable, for a particular problem. A Concise Introduction to Numerical Analysis strikes a balance between being mathematically comprehensive, but not overwhelming with mathematical detail. In some places where further detail was felt to be out of scope of the book, the reader is referred to further reading. The book uses MATLAB (R) implementations to demonstrate the workings of the method and thus MATLAB's own implementations are avoided, unless they are used as building blocks of an algorithm. In some cases the listings are printed in the book, but all are available online on the book's page at www.crcpress.com. Most implementations are in the form of functions returning the outcome of the algorithm. Also, examples for the use of the functions are given. Exercises are included in line with the text where appropriate, and each chapter ends with a selection of revision exercises. Solutions to odd-numbered exercises are also provided on the book's page at www.crcpress.com. This textbook is also an ideal resource for graduate students coming from other subjects who will use numerical techniques extensively in their graduate studies.

The book originates from the mini-symposium "Mathematical descriptions of traffic flow: micro, macro and kinetic models" organised by the editors within the ICIAM 2019 Congress held in Valencia, Spain, in July 2019. The book is composed of five chapters, which address new research lines in the mathematical modelling of vehicular traffic, at the cutting edge of contemporary research, including traffic automation by means of autonomous vehicles. The contributions span the three most representative scales of mathematical modelling: the microscopic scale of particles, the mesoscopic scale of statistical kinetic description and the macroscopic scale of partial differential equations.The work is addressed to researchers in the field.

The development of statistical computing has had a huge impact on the subject, freeing statisticians from the need to perform tedious calculations and allowing researchers to perform progressively more complex operations. This book gives a coherent presentation of the theory underlying the computations, and provides a framework where computer algorithms are used to do much of the calculation inherent in statistics. Beginning with an outline of algorithms to cover much of an undergraduate course in probability and statistics, it then goes on to discuss various common distributions, likelihood, bootstrap and sampling.

Using an approach that author Alan Laub calls "matrix analysis for grown-ups", this textbook introduces fundamental concepts of numerical linear algebra and their application to solving certain numerical problems arising in state-space control and systems theory. It is written for advanced undergraduate and beginning graduate students and can be used as a follow-up to Matrix Analysis for Scientists and Engineers (SIAM, 2005), a compact single-semester introduction to matrix analysis for engineers and computational scientists by the same author. Computational Matrix Analysis provides readers with:* A one-semester introduction to numerical linear algebra.* An introduction to statistical condition estimation in book form for the first time.* An overview of certain computational problems in control and systems theory. The book features a number of elements designed to help students learn to use numerical linear algebra in day-to-day computing or research, including:* A brief review of matrix analysis, including notation, and an introduction to finite (IEEE) arithmetic.* Discussion and examples of conditioning, stability, and rounding analysis.* An introduction to mathematical software topics related to numerical linear algebra.* A thorough introduction to Gaussian elimination, along with condition estimation techniques.* Coverage of linear least squares, with orthogonal reduction and QR factorization.* Variants of the QR algorithm.* Applications of the discussed algorithms.

The theory of complex dynamics, whose roots lie in 19th-century studies of the iteration of complex function conducted by Koenigs, Schoder, and others, flourished remarkably during the first half of the 20th century, when many of the central ideas and techniques of the subject developed. This book by Alexander, Iavernaro, and Rosa paints a robust picture of the field of complex dynamics between 1906 and 1942 through detailed discussions of the work of Fatou, Julia, Siegel, and several others. A recurrent theme of the authors' treatment is the center problem in complex dynamics. They present its complete history during this period and, in so doing, bring out analogies between complex dynamics and the study of differential equations, in particular, the problem of stability in Hamiltonian systems. Among these analogies are the use of iteration and problems involving small divisors which the authors examine in the work of Poincare and others, linking them to complex dynamics, principally via the work of Samuel Lattes, in the early 1900s, and Jurgen Moser, in the 1960s. Many details will be new to the reader, such as a history of Lattes functions (functions whose Julia set equals the Riemann sphere), complex dynamics in the United States around the time of World War I, a survey of complex dynamics around the world in the 1920s and 1930s, a discussion of the dynamical programs of Fatou and Julia during the 1920s, and biographical material on several key figures. The book contains graphical renderings of many of the mathematical objects the authors discuss, including some of the intriguing fractals Fatou and Julia studied, and concludes with several appendices by current researchers in complex dynamics which collectively attest to the impact of the work of Fatou, Julia, and others upon the present-day study.

This book presents an up-to-date exposition of the current `state of the art' of numerical methods for solving ordinary differential equations in a parallel computing environment. Although the main focus is on problems of initial value type, consideration will also be given to boundary value problems and partial differential equations. Furthermore, because linear algebra is an important component of the solution of differential equations, a complete chapter is devoted to the parallel solution of linear systems of equations. In addition to presenting an overview of parallel computing in general, two chapters are devoted to a summary of existing sequential differential equation methods. The parallel techniques discussed include parallelism across the method, parallelism across the step, parallelism across the system, and dynamic iteration. The book concludes with a chapter on the behaviour of a parallel code based on waveform relaxation. This comprehensive book is unique in its content and provides a balance between theoretical and practical issues by providing general frameworks in which to study parallel methods.

The fitting of a curve or surface through a set of observational data is a very frequent problem in different disciplines (mathematics, engineering, medicine, ...) with many interesting applications. This book describes the algorithms and mathematical fundamentals of a widely used software package for data fitting with (tensor product) splines. As such it gives a survey of possibilities and benefits but also of the problems to cope with when approximating with this popular type of function. In particular it is demonstrated in detail how the properties of B-splines can be fully exploited for improving the computational efficiency and for incorporating different boundary or shape preserving constraints. Special attention is also paid to strategies for an automatic and adaptive knot selection with intent to obtain serious data reductions. The practical use of the smoothing software is illustrated with many examples, academic as well as taken from real life.

Since the early 1980s, a series of International Conferences on Numerial Methods for Fluid Dynamics has been held at the Universities of Oxford and Reading, the majority of them under the aegis of the Institute for Computational Fluid Dynamics, a joint research organization set up in 1983 with the support of the SERC. This volume is the proceedings of the latest conference in the series, which was held at Reading University in April 1992, and attracted a large number of delegates from Europe and North America, who contributed talks on a wide range of topics in CFD. A full representation from industry and the universities took part. As in previous conferences, the aim was to bring together mathematicians, engineers and others working in the field of computational fluid dynamics to review recent advances in mathematical and computational fluid techniques for modelling fluid flows. Because the area is so vast, it was once again decided to highlight a number of main themes: inplicit methods in CFD; mesh generation and error analysis (including mesh quality); numerical boundary conditions (particularly non-reflective); multigrid and alternative methods for hyperbolic systems. As with al

Praise for the First Edition "...outstandingly appealing with regard to its style, contents, considerations of requirements of practice, choice of examples, and exercises." Zentralblatt MATH "...carefully structured with many detailed worked examples." The Mathematical Gazette The Second Edition of the highly regarded An Introduction to Numerical Methods and Analysis provides a fully revised guide to numerical approximation. The book continues to be accessible and expertly guides readers through the many available techniques of numerical methods and analysis. An Introduction to Numerical Methods and Analysis, Second Edition reflects the latest trends in the field, includes new material and revised exercises, and offers a unique emphasis on applications. The author clearly explains how to both construct and evaluate approximations for accuracy and performance, which are key skills in a variety of fields. A wide range of higher-level methods and solutions, including new topics such as the roots of polynomials, spectral collocation, finite element ideas, and Clenshaw-Curtis quadrature, are presented from an introductory perspective, and the Second Edition also features: * Chapters and sections that begin with basic, elementary material followed by gradual coverage of more advanced material * Exercises ranging from simple hand computations to challenging derivations and minor proofs to programming exercises * Widespread exposure and utilization of MATLAB * An appendix that contains proofs of various theorems and other material The book is an ideal textbook for students in advanced undergraduate mathematics and engineering courses who are interested in gaining an understanding of numerical methods and numerical analysis.

Computer science is the science of the future, and already underlies every facet of business and technology, and much of our everyday lives. In addition, it will play a crucial role in the science the 21st century, which will be dominated by biology and biochemistry, similar to the role of mathematics in the physical sciences of the 20th century. In this award-winning best-seller, the author and his co-author focus on the fundamentals of computer science, which revolve around the notion of the "algorithm." They discuss the design of algorithms, and their efficiency and correctness, the inherent limitations of algorithms and computation, quantum algorithms, concurrency, large systems and artificial intelligence. Throughout, the authors, in their own words, stress the 'fundamental and robust nature of the science in a form that is virtually independent of the details of specific computers, languages and formalisms'.

This version of the book is published to celebrate 25 years since its first edition, and in honor of the Alan M. Turing Centennial year. Turing was a true pioneer of computer science, whose work forms the underlying basis of much of this book. "

This book presents models and algorithms for complex scheduling problems. Besides resource-constrained project scheduling problems with applications also job-shop problems with flexible machines, transportation or limited buffers are discussed. Discrete optimization methods like linear and integer programming, constraint propagation techniques, shortest path and network flow algorithms, branch-and-bound methods, local search and genetic algorithms, and dynamic programming are presented. They are used in exact or heuristic procedures to solve the introduced complex scheduling problems. Furthermore, methods for calculating lower bounds are described. Most algorithms are formulated in detail and illustrated with examples. In this second edition some errors were corrected, some parts were explained in more detail, and new material has been added. In particular, further generalizations of the RCPSP, additional practical applications and some more algorithms were integrated.

A state-of-the-art edited survey covering all aspects of sampling theory. Theory, methods and applications are discussed in authoritative expositions ranging from multi-dimensional signal analysis to wavelet transforms. The book is an essential up-to-date resource.

This must-read textbook presents an essential introduction to Kolmogorov complexity (KC), a central theory and powerful tool in information science that deals with the quantity of information in individual objects. The text covers both the fundamental concepts and the most important practical applications, supported by a wealth of didactic features. This thoroughly revised and enhanced fourth edition includes new and updated material on, amongst other topics, the Miller-Yu theorem, the Gacs-Kucera theorem, the Day-Gacs theorem, increasing randomness, short lists computable from an input string containing the incomputable Kolmogorov complexity of the input, the Lovasz local lemma, sorting, the algorithmic full Slepian-Wolf theorem for individual strings, multiset normalized information distance and normalized web distance, and conditional universal distribution. Topics and features: describes the mathematical theory of KC, including the theories of algorithmic complexity and algorithmic probability; presents a general theory of inductive reasoning and its applications, and reviews the utility of the incompressibility method; covers the practical application of KC in great detail, including the normalized information distance (the similarity metric) and information diameter of multisets in phylogeny, language trees, music, heterogeneous files, and clustering; discusses the many applications of resource-bounded KC, and examines different physical theories from a KC point of view; includes numerous examples that elaborate the theory, and a range of exercises of varying difficulty (with solutions); offers explanatory asides on technical issues, and extensive historical sections; suggests structures for several one-semester courses in the preface. As the definitive textbook on Kolmogorov complexity, this comprehensive and self-contained work is an invaluable resource for advanced undergraduate students, graduate students, and researchers in all fields of science.

Linear algebra is a living, active branch of mathematics which is central to almost all other areas of mathematics, both pure and applied, as well as to computer science, to the physical, biological, and social sciences, and to engineering. It encompasses an extensive corpus of theoretical results as well as a large and rapidly-growing body of computational techniques. Unfortunately, in the past decade, the content of linear algebra courses required to complete an undergraduate degree in mathematics has been depleted to the extent that they fail to provide a sufficient theoretical or computational background. Students are not only less able to formulate or even follow mathematical proofs, they are also less able to understand the mathematics of the numerical algorithms they need for applications. Certainly, the material presented in the average undergraduate course is insufficient for graduate study. This book is intended to fill the gap which has developed by providing enough theoretical and computational material to allow the advanced undergraduate or beginning graduate student to overcome this deficiency and be able to work independently or in advanced courses. The book is intended to be used either as a self-study guide, a textbook for a course in advanced linear algebra, or as a reference book. It is also designed to prepare a student for the linear algebra portion of prelim exams or PhD qualifying exams. The volume is self-contained to the extent that it does not assume any previous formal knowledge of linear algebra, though the reader is assumed to have been exposed, at least informally, to some of the basic ideas and techniques, such as manipulation of small matrices and the solution of small systems of linear equations over the real numbers. More importantly, it assumes a seriousness of purpose, considerable motivation, and a modicum of mathematical sophistication on the part of the reader. In the latest edition, new major theorems have been added, as well as many new examples. There are over 130 additional exercises and many of the previous exercises have been revised or rewritten. In addition, a large number of additional biographical notes and thumbnail portraits of mathematicians have been included.

This book is concerned with discontinuous groups of motions of the unique connected and simply connected Riemannian 3-manifold of constant curva ture -1, which is traditionally called hyperbolic 3-space. This space is the 3-dimensional instance of an analogous Riemannian manifold which exists uniquely in every dimension n:::: 2. The hyperbolic spaces appeared first in the work of Lobachevski in the first half of the 19th century. Very early in the last century the group of isometries of these spaces was studied by Steiner, when he looked at the group generated by the inversions in spheres. The ge ometries underlying the hyperbolic spaces were of fundamental importance since Lobachevski, Bolyai and Gauss had observed that they do not satisfy the axiom of parallels. Already in the classical works several concrete coordinate models of hy perbolic 3-space have appeared. They make explicit computations possible and also give identifications of the full group of motions or isometries with well-known matrix groups. One such model, due to H. Poincare, is the upper 3 half-space IH in JR . The group of isometries is then identified with an exten sion of index 2 of the group PSL(2,"

Complex analysis, more than almost any other undergraduate topic in mathematics, runs the full pure/applied gamut from the most subtle, difficult, and ingenious proofs to the most direct, hands-on, engineering-based applications. This creates challenges for the instructor as much as for the very wide range of students whose various programmes require a secure grasp of complex analysis. Its techniques are indispensable to many, but skill in the use of a mathematical tool is hazardous and fallible without a sound understanding of why and when that tool is the right one to pick up. This kind of understanding develops only by combining careful exploration of ideas, analysis of proofs, and practice across a range of exercises. Integration with Complex Numbers: A Primer on Complex Analysis offers a reader-friendly contemporary balance between idea, proof, and practice, informed by several decades of classroom experience and a seasoned understanding of the backgrounds, motivation, and competing time pressures of today's student cohorts. To achieve its aim of supporting and sustaining such cohorts through those aspects of complex analysis that they encounter in first and second-year study, it also balances competing needs to be self-contained, comprehensive, accessible, and engaging - all in sufficient but not in excessive measures. In particular, it begins where most students are likely to be, and invests the time and effort that are required in order to deliver accessibility and introductory gradualness.

Complex analysis, more than almost any other undergraduate topic in mathematics, runs the full pure/applied gamut from the most subtle, difficult, and ingenious proofs to the most direct, hands-on, engineering-based applications. This creates challenges for the instructor as much as for the very wide range of students whose various programmes require a secure grasp of complex analysis. Its techniques are indispensable to many, but skill in the use of a mathematical tool is hazardous and fallible without a sound understanding of why and when that tool is the right one to pick up. This kind of understanding develops only by combining careful exploration of ideas, analysis of proofs, and practice across a range of exercises. Integration with Complex Numbers: A Primer on Complex Analysis offers a reader-friendly contemporary balance between idea, proof, and practice, informed by several decades of classroom experience and a seasoned understanding of the backgrounds, motivation, and competing time pressures of today's student cohorts. To achieve its aim of supporting and sustaining such cohorts through those aspects of complex analysis that they encounter in first and second-year study, it also balances competing needs to be self-contained, comprehensive, accessible, and engaging - all in sufficient but not in excessive measures. In particular, it begins where most students are likely to be, and invests the time and effort that are required in order to deliver accessibility and introductory gradualness.

Many situations exist in which solutions to problems are represented as function space integrals. Such representations can be used to study the qualitative properties of the solutions and to evaluate them numerically using Monte Carlo methods. The emphasis in this book is on the behavior of solutions in special situations when certain parameters get large or small.

Analysis underpins calculus, much as calculus underpins virtually all mathematical sciences. A sound understanding of analysis' results and techniques is therefore valuable for a wide range of disciplines both within mathematics itself and beyond its traditional boundaries. This text seeks to develop such an understanding for undergraduate students on mathematics and mathematically related programmes. Keenly aware of contemporary students' diversity of motivation, background knowledge and time pressures, it consistently strives to blend beneficial aspects of the workbook, the formal teaching text, and the informal and intuitive tutorial discussion. The authors devote ample space and time for development of confidence in handling the fundamental ideas of the topic. They also focus on learning through doing, presenting a comprehensive range of examples and exercises, some worked through in full detail, some supported by sketch solutions and hints, some left open to the reader's initiative. Without undervaluing the absolute necessity of secure logical argument, they legitimise the use of informal, heuristic, even imprecise initial explorations of problems aimed at deciding how to tackle them. In this respect they authors create an atmosphere like that of an apprenticeship, in which the trainee analyst can look over the shoulder of the experienced practitioner.

A fundamental issue in statistical analysis is testing the fit of a particular probability model to a set of observed data. Monte Carlo approximation to the null distribution of the test provides a convenient and powerful means of testing model fit. Nonparametric Monte Carlo Tests and Their Applications proposes a new Monte Carlo-based methodology to construct this type of approximation when the model is semistructured. When there are no nuisance parameters to be estimated, the nonparametric Monte Carlo test can exactly maintain the significance level, and when nuisance parameters exist, this method can allow the test to asymptotically maintain the level.

The author addresses both applied and theoretical aspects of nonparametric Monte Carlo tests. The new methodology has been used for model checking in many fields of statistics, such as multivariate distribution theory, parametric and semiparametric regression models, multivariate regression models, varying-coefficient models with longitudinal data, heteroscedasticity, and homogeneity of covariance matrices. This book will be of interest to both practitioners and researchers investigating goodness-of-fit tests and resampling approximations.

Every chapter of the book includes algorithms, simulations, and theoretical deductions. The prerequisites for a full appreciation of the book are a modest knowledge of mathematical statistics and limit theorems in probability/empirical process theory. The less mathematically sophisticated reader will find Chapters 1, 2 and 6 to be a comprehensible introduction on how and where the new method can apply and the rest of the book to be a valuable reference for Monte Carlo test approximation and goodness-of-fit tests.

Lixing Zhu is Associate Professor of Statistics at the University of Hong Kong. He is a winner of the Humboldt Research Award at Alexander-von Humboldt Foundation of Germany and an elected Fellow of the Institute of Mathematical Statistics.

From the reviews:

"These lecture notes discuss several topics in goodness-of-fit testing, a classical area in statistical analysis. ... The mathematical part contains detailed proofs of the theoretical results. Simulation studies illustrate the quality of the Monte Carlo approximation. ... this book constitutes a recommendable contribution to an active area of current research." Winfried Stute for Mathematical Reviews, Issue 2006

..".Overall, this is an interesting book, which gives a nice introduction to this new and specific field of resampling methods." Dongsheng Tu for Biometrics, September 2006

This graduate textbook provides an alternative to discrete event simulation. It describes how to formulate discrete event systems, how to convert them into Markov chains, and how to calculate their transient and equilibrium probabilities. The most appropriate methods for finding these probabilities are described in some detail, and templates for efficient algorithms are provided. These algorithms can be executed on any laptop, even in cases where the Markov chain has hundreds of thousands of states. This book features the probabilistic interpretation of Gaussian elimination, a concept that unifies many of the topics covered, such as embedded Markov chains and matrix analytic methods. The material provided should aid practitioners significantly to solve their problems. This book also provides an interesting approach to teaching courses of stochastic processes.