Martin Hairer's Books

A Course on Rough Paths

With an Introduction to Regularity Structures

By: Peter K. Friz,Martin Hairer

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A Course on Rough Paths

With an Introduction to Regularity Structures

By: Peter K. Friz,Martin Hairer

With many updates and additional exercises, the second edition of this book continues to provide readers with a gentle introduction to rough path analysis and regularity structures, theories that have yielded many new insights into the analysis of stochastic differential equations, and, most recently, stochastic partial differential equations. Rough path analysis provides the means for constructing a pathwise solution theory for stochastic differential equations which, in many respects, behaves like the theory of deterministic differential equations and permits a clean break between analytical and probabilistic arguments. Together with the theory of regularity structures, it forms a robust toolbox, allowing the recovery of many classical results without having to rely on specific probabilistic properties such as adaptedness or the martingale property. Essentially self-contained, this textbook puts the emphasis on ideas and short arguments, rather than aiming for the strongest possible statements. A typical reader will have been exposed to upper undergraduate analysis and probability courses, with little more than Itô-integration against Brownian motion required for most of the text. From the reviews of the first edition: "Can easily be used as a support for a graduate course ... Presents in an accessible way the unique point of view of two experts who themselves have largely contributed to the theory" - Fabrice Baudouin in the Mathematical Reviews "It is easy to base a graduate course on rough paths on this ... A researcher who carefully works her way through all of the exercises will have a very good impression of the current state of the art" - Nicolas Perkowski in Zentralblatt MATH

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354

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Springer Nature

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ISBN 10

3030415562

ISBN 13

9783030415563

Scientific Computing - An Introduction using Maple and MATLAB

By: Walter Gander,Martin J. Gander,Felix Kwok

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Scientific Computing - An Introduction using Maple and MATLAB

By: Walter Gander,Martin J. Gander,Felix Kwok

Scientific computing is the study of how to use computers effectively to solve problems that arise from the mathematical modeling of phenomena in science and engineering. It is based on mathematics, numerical and symbolic/algebraic computations and visualization. This book serves as an introduction to both the theory and practice of scientific computing, with each chapter presenting the basic algorithms that serve as the workhorses of many scientific codes; we explain both the theory behind these algorithms and how they must be implemented in order to work reliably in finite-precision arithmetic. The book includes many programs written in Matlab and Maple – Maple is often used to derive numerical algorithms, whereas Matlab is used to implement them. The theory is developed in such a way that students can learn by themselves as they work through the text. Each chapter contains numerous examples and problems to help readers understand the material “hands-on”.

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926

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Springer Science & Business

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ISBN 10

3319043250

ISBN 13

9783319043258

Computational Methods in Physics

Compendium for Students

By: Simon Širca,Martin Horvat

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Computational Methods in Physics

Compendium for Students

By: Simon Širca,Martin Horvat

This book is intended to help advanced undergraduate, graduate, and postdoctoral students in their daily work by offering them a compendium of numerical methods. The choice of methods pays significant attention to error estimates, stability and convergence issues, as well as optimization of program execution speeds. Numerous examples are given throughout the chapters, followed by comprehensive end-of-chapter problems with a more pronounced physics background, while less stress is given to the explanation of individual algorithms. The readers are encouraged to develop a certain amount of skepticism and scrutiny instead of blindly following readily available commercial tools. The second edition has been enriched by a chapter on inverse problems dealing with the solution of integral equations, inverse Sturm-Liouville problems, as well as retrospective and recovery problems for partial differential equations. The revised text now includes an introduction to sparse matrix methods, the solution of matrix equations, and pseudospectra of matrices; it discusses the sparse Fourier, non-uniform Fourier and discrete wavelet transformations, the basics of non-linear regression and the Kolmogorov-Smirnov test; it demonstrates the key concepts in solving stiff differential equations and the asymptotics of Sturm-Liouville eigenvalues and eigenfunctions. Among other updates, it also presents the techniques of state-space reconstruction, methods to calculate the matrix exponential, generate random permutations and compute stable derivatives.

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894

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Springer

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ISBN 10

3319786199

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9783319786193

Time Parallel Time Integration

By: Martin J. Gander,Thibaut Lunet

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Time Parallel Time Integration

By: Martin J. Gander,Thibaut Lunet

Predicting the future is a difficult task but, as with the weather, it is possible with good models. But how does one predict the far future before the near future is known? Time parallel time integration, also known as PinT (Parallel-in-Time) methods, aims to predict the near and far future simultaneously. In this self-contained book, the first on the topic, readers will find a comprehensive and up-to-date description of methods and techniques that have been developed to do just this. The authors describe the four main classes of PinT methods: shooting-type methods, waveform relaxation methods, time parallel multigrid methods, and direct time parallel methods. In addition, they provide historical background for each of the method classes, complete convergence analyses for the most representative variants of the methods in each class, and illustrations and runnable MATLAB code. An ideal introduction to this exciting and very active research field, Time Parallel Time Integration can be used for independent study or for a graduate course.

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273

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SIAM

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ISBN 10

1611978025

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9781611978025

Local Lipschitz Continuity in the Initial Value and Strong Completeness for Nonlinear Stochastic Differential Equations

By: Sonja Cox,Martin Hutzenthaler,Arnulf Jentzen

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Local Lipschitz Continuity in the Initial Value and Strong Completeness for Nonlinear Stochastic Differential Equations

By: Sonja Cox,Martin Hutzenthaler,Arnulf Jentzen

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102

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American Mathematical Society

Published Date

ISBN 10

1470467011

ISBN 13

9781470467012

Exact and Truncated Difference Schemes for Boundary Value ODEs

By: Ivan Gavrilyuk,Martin Hermann,Volodymyr Makarov,Myroslav V. Kutniv

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Exact and Truncated Difference Schemes for Boundary Value ODEs

By: Ivan Gavrilyuk,Martin Hermann,Volodymyr Makarov,Myroslav V. Kutniv

The book provides a comprehensive introduction to compact finite difference methods for solving boundary value ODEs with high accuracy. The corresponding theory is based on exact difference schemes (EDS) from which the implementable truncated difference schemes (TDS) are derived. The TDS are now competitive in terms of efficiency and accuracy with the well-studied numerical algorithms for the solution of initial value ODEs. Moreover, various a posteriori error estimators are presented which can be used in adaptive algorithms as important building blocks. The new class of EDS and TDS treated in this book can be considered as further developments of the results presented in the highly respected books of the Russian mathematician A. A. Samarskii. It is shown that the new Samarskii-like techniques open the horizon for the numerical treatment of more complicated problems. The book contains exercises and the corresponding solutions enabling the use as a course text or for self-study. Researchers and students from numerical methods, engineering and other sciences will find this book provides an accessible and self-contained introduction to numerical methods for solving boundary value ODEs.

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247

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Springer Science & Business Media

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ISBN 10

3034801076

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9783034801072

Numerical Approximations of Stochastic Differential Equations with Non-Globally Lipschitz Continuous Coefficients

By: Martin Hutzenthaler,Arnulf Jentzen

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Numerical Approximations of Stochastic Differential Equations with Non-Globally Lipschitz Continuous Coefficients

By: Martin Hutzenthaler,Arnulf Jentzen

Many stochastic differential equations (SDEs) in the literature have a superlinearly growing nonlinearity in their drift or diffusion coefficient. Unfortunately, moments of the computationally efficient Euler-Maruyama approximation method diverge for these SDEs in finite time. This article develops a general theory based on rare events for studying integrability properties such as moment bounds for discrete-time stochastic processes. Using this approach, the authors establish moment bounds for fully and partially drift-implicit Euler methods and for a class of new explicit approximation methods which require only a few more arithmetical operations than the Euler-Maruyama method. These moment bounds are then used to prove strong convergence of the proposed schemes. Finally, the authors illustrate their results for several SDEs from finance, physics, biology and chemistry.

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112

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American Mathematical Soc.

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ISBN 10

1470409844

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9781470409845

Computational Methods for Physicists

Compendium for Students

By: Simon Sirca,Martin Horvat

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Computational Methods for Physicists

Compendium for Students

By: Simon Sirca,Martin Horvat

This book helps advanced undergraduate, graduate and postdoctoral students in their daily work by offering them a compendium of numerical methods. The choice of methods pays significant attention to error estimates, stability and convergence issues as well as to the ways to optimize program execution speeds. Many examples are given throughout the chapters, and each chapter is followed by at least a handful of more comprehensive problems which may be dealt with, for example, on a weekly basis in a one- or two-semester course. In these end-of-chapter problems the physics background is pronounced, and the main text preceding them is intended as an introduction or as a later reference. Less stress is given to the explanation of individual algorithms. It is tried to induce in the reader an own independent thinking and a certain amount of scepticism and scrutiny instead of blindly following readily available commercial tools.

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724

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Springer Science & Business Media

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ISBN 10

3642324789

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9783642324789

Numerical Treatment of Partial Differential Equations

By: Christian Grossmann,Hans-G. Roos,Martin Stynes

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Numerical Treatment of Partial Differential Equations

By: Christian Grossmann,Hans-G. Roos,Martin Stynes

This book deals with discretization techniques for partial differential equations of elliptic, parabolic and hyperbolic type. It provides an introduction to the main principles of discretization and gives a presentation of the ideas and analysis of advanced numerical methods in the area. The book is mainly dedicated to finite element methods, but it also discusses difference methods and finite volume techniques. Coverage offers analytical tools, properties of discretization techniques and hints to algorithmic aspects. It also guides readers to current developments in research.

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601

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Springer Science & Business Media

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ISBN 10

3540715827

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9783540715825

Numerical Methods for Singularly Perturbed Differential Equations

Convection-Diffusion and Flow Problems

By: Hans-Görg Roos,Martin Stynes,Lutz Tobiska

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Numerical Methods for Singularly Perturbed Differential Equations

Convection-Diffusion and Flow Problems

By: Hans-Görg Roos,Martin Stynes,Lutz Tobiska

The analysis of singular perturbed differential equations began early in this century, when approximate solutions were constructed from asymptotic ex pansions. (Preliminary attempts appear in the nineteenth century [vD94].) This technique has flourished since the mid-1960s. Its principal ideas and methods are described in several textbooks. Nevertheless, asymptotic ex pansions may be impossible to construct or may fail to simplify the given problem; then numerical approximations are often the only option. The systematic study of numerical methods for singular perturbation problems started somewhat later - in the 1970s. While the research frontier has been steadily pushed back, the exposition of new developments in the analysis of numerical methods has been neglected. Perhaps the only example of a textbook that concentrates on this analysis is [DMS80], which collects various results for ordinary differential equations, but many methods and techniques that are relevant today (especially for partial differential equa tions) were developed after 1980.Thus contemporary researchers must comb the literature to acquaint themselves with earlier work. Our purposes in writing this introductory book are twofold. First, we aim to present a structured account of recent ideas in the numerical analysis of singularly perturbed differential equations. Second, this important area has many open problems and we hope that our book will stimulate further investigations.Our choice of topics is inevitably personal and reflects our own main interests.

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364

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Springer Science & Business Media

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ISBN 10

3662032066

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9783662032060

Time-Domain Scattering

By: P. A. Martin

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Time-Domain Scattering

By: P. A. Martin

The first thorough synthesis of methods for solving time-domain scattering problems, covering both theoretical and computational aspects.

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265

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Cambridge University Press

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ISBN 10

1108835597

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9781108835596

Counting: The Art of Enumerative Combinatorics

By: George E. Martin

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Counting: The Art of Enumerative Combinatorics

By: George E. Martin

This book provides an introduction to discrete mathematics. At the end of the book the reader should be able to answer counting questions such as: How many ways are there to stack n poker chips, each of which can be red, white, blue, or green, such that each red chip is adjacent to at least 1 green chip? The book can be used as a textbook for a semester course at the sophomore level. The first five chapters can also serve as a basis for a graduate course for in-service teachers.

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263

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Springer Science & Business Media

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ISBN 10

1475748787

ISBN 13

9781475748789

Bridging the Gap to University Mathematics

By: Edward Hurst,Martin Gould

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Bridging the Gap to University Mathematics

By: Edward Hurst,Martin Gould

Helps to ease the transition between school/college and university mathematics by (re)introducing readers to a range of topics that they will meet in the first year of a degree course in the mathematical sciences, refreshing their knowledge of basic techniques and focussing on areas that are often perceived as the most challenging. Each chapter starts with a "Test Yourself" section so that readers can monitor their progress and readily identify areas where their understanding is incomplete. A range of exercises, complete with full solutions, makes the book ideal for self-study.

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347

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Springer Science & Business Media

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ISBN 10

1848002904

ISBN 13

9781848002906

Adaptive Numerical Solution of PDEs

By: Peter Deuflhard,Martin Weiser

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Adaptive Numerical Solution of PDEs

By: Peter Deuflhard,Martin Weiser

This book deals with the general topic “Numerical solution of partial differential equations (PDEs)” with a focus on adaptivity of discretizations in space and time. By and large, introductory textbooks like “Numerical Analysis in Modern Scientific Computing” by Deuflhard and Hohmann should suffice as a prerequisite. The emphasis lies on elliptic and parabolic systems. Hyperbolic conservation laws are treated only on an elementary level excluding turbulence. Numerical Analysis is clearly understood as part of Scientific Computing. The focus is on the efficiency of algorithms, i.e. speed, reliability, and robustness, which directly leads to the concept of adaptivity in algorithms. The theoretical derivation and analysis is kept as elementary as possible. Nevertheless required somewhat more sophisticated mathematical theory is summarized in comprehensive form in an appendix. Complex relations are explained by numerous figures and illustrating examples. Non-trivial problems from regenerative energy, nanotechnology, surgery, and physiology are inserted. The text will appeal to graduate students and researchers on the job in mathematics, science, and technology. Conceptually, it has been written as a textbook including exercises and a software list, but at the same time it should be well-suited for self-study.

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436

Publisher

Walter de Gruyter

Published Date

ISBN 10

3110283115

ISBN 13

9783110283112

Analyzable Functions and Applications

International Workshop on Analyzable Functions and Applications, June 17-21, 2002, International Centre for Mathematical Sciences, Edinburgh, Scotland

By: Ovidiu Costin,Martin David Kruskal,Angus Macintyre

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Analyzable Functions and Applications

International Workshop on Analyzable Functions and Applications, June 17-21, 2002, International Centre for Mathematical Sciences, Edinburgh, Scotland

By: Ovidiu Costin,Martin David Kruskal,Angus Macintyre

The theory of analyzable functions is a technique used to study a wide class of asymptotic expansion methods and their applications in analysis, difference and differential equations, partial differential equations and other areas of mathematics. Key ideas in the theory of analyzable functions were laid out by Euler, Cauchy, Stokes, Hardy, E. Borel, and others. Then in the early 1980s, this theory took a great leap forward with the work of J. Ecalle. Similar techniques and conceptsin analysis, logic, applied mathematics and surreal number theory emerged at essentially the same time and developed rapidly through the 1990s. The links among various approaches soon became apparent and this body of ideas is now recognized as a field of its own with numerous applications. Thisvolume stemmed from the International Workshop on Analyzable Functions and Applications held in Edinburgh (Scotland). The contributed articles, written by many leading experts, are suitable for graduate students and researchers interested in asymptotic methods.

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384

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American Mathematical Soc.

Published Date

ISBN 10

0821834193

ISBN 13

9780821834190

Signal Processing for Communications

By: Paolo Prandoni,Martin Vetterli

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Signal Processing for Communications

By: Paolo Prandoni,Martin Vetterli

Taking a novel, less classical approach to the subject, the authors have written this book with the conviction that signal processing should be fun. Their treatment is less focused on the mathematics and more on the conceptual aspects, allowing students to think about the subject at a higher conceptual level, thus building the foundations for more advanced topics and helping students solve real-world problems. The last chapter pulls together the individual topics into an in-depth look at the development of an end-to-end communication system. Richly illustrated with examples and exercises in each chapter, the book offers a fresh approach to the teaching of signal processing to upper-level undergraduates.

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400

Publisher

EPFL Press

Published Date

ISBN 10

1420070460

ISBN 13

9781420070460

Nonlinear Ordinary Differential Equations

Analytical Approximation and Numerical Methods

By: Martin Hermann,Masoud Saravi

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Nonlinear Ordinary Differential Equations

Analytical Approximation and Numerical Methods

By: Martin Hermann,Masoud Saravi

The book discusses the solutions to nonlinear ordinary differential equations (ODEs) using analytical and numerical approximation methods. Recently, analytical approximation methods have been largely used in solving linear and nonlinear lower-order ODEs. It also discusses using these methods to solve some strong nonlinear ODEs. There are two chapters devoted to solving nonlinear ODEs using numerical methods, as in practice high-dimensional systems of nonlinear ODEs that cannot be solved by analytical approximate methods are common. Moreover, it studies analytical and numerical techniques for the treatment of parameter-depending ODEs. The book explains various methods for solving nonlinear-oscillator and structural-system problems, including the energy balance method, harmonic balance method, amplitude frequency formulation, variational iteration method, homotopy perturbation method, iteration perturbation method, homotopy analysis method, simple and multiple shooting method, and the nonlinear stabilized march method. This book comprehensively investigates various new analytical and numerical approximation techniques that are used in solving nonlinear-oscillator and structural-system problems. Students often rely on the finite element method to such an extent that on graduation they have little or no knowledge of alternative methods of solving problems. To rectify this, the book introduces several new approximation techniques.

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320

Publisher

Springer

Published Date

ISBN 10

813222812X

ISBN 13

9788132228127

Transformation Geometry

An Introduction to Symmetry

By: George E. Martin

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Transformation Geometry

An Introduction to Symmetry

By: George E. Martin

Transformation Geometry: An Introduction to Symmetry offers a modern approach to Euclidean Geometry. This study of the automorphism groups of the plane and space gives the classical concrete examples that serve as a meaningful preparation for the standard undergraduate course in abstract algebra. The detailed development of the isometries of the plane is based on only the most elementary geometry and is appropriate for graduate courses for secondary teachers.

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251

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Springer Science & Business Media

Published Date

ISBN 10

1461256801

ISBN 13

9781461256809

Formulation and Numerical Solution of Quantum Control Problems

By: Alfio Borzi,Gabriele Ciaramella,Martin Sprengel

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Formulation and Numerical Solution of Quantum Control Problems

By: Alfio Borzi,Gabriele Ciaramella,Martin Sprengel

This book provides an introduction to representative nonrelativistic quantum control problems and their theoretical analysis and solution via modern computational techniques. The quantum theory framework is based on the Schr?dinger picture, and the optimization theory, which focuses on functional spaces, is based on the Lagrange formalism. The computational techniques represent recent developments that have resulted from combining modern numerical techniques for quantum evolutionary equations with sophisticated optimization schemes. Both finite and infinite-dimensional models are discussed, including the three-level Lambda system arising in quantum optics, multispin systems in NMR, a charged particle in a well potential, Bose?Einstein condensates, multiparticle spin systems, and multiparticle models in the time-dependent density functional framework. This self-contained book covers the formulation, analysis, and numerical solution of quantum control problems and bridges scientific computing, optimal control and exact controllability, optimization with differential models, and the sciences and engineering that require quantum control methods.

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396

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SIAM

Published Date

ISBN 10

1611974844

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9781611974843

Wave Propagation in Viscoelastic and Poroelastic Continua

A Boundary Element Approach

By: Martin Schanz

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Wave Propagation in Viscoelastic and Poroelastic Continua

A Boundary Element Approach

By: Martin Schanz

Wave propagation is an important topic in engineering sciences, especially, in the field of solid mechanics. A description of wave propagation phenomena is given by Graff [98]: The effect of a sharply applied, localized disturbance in a medium soon transmits or 'spreads' to other parts of the medium. These effects are familiar to everyone, e.g., transmission of sound in air, the spreading of ripples on a pond of water, or the transmission of radio waves. From all wave types in nature, here, attention is focused only on waves in solids. Thus, solely mechanical disturbances in contrast to electro-magnetic or acoustic disturbances are considered. of waves - the compression wave similar to the In solids, there are two types pressure wave in fluids and, additionally, the shear wave. Due to continual reflec tions at boundaries and propagation of waves in bounded solids after some time a steady state is reached. Depending on the influence of the inertia terms, this state is governed by a static or dynamic equilibrium in frequency domain. However, if the rate of onset of the load is high compared to the time needed to reach this steady state, wave propagation phenomena have to be considered.

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176

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Springer Science & Business Media

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ISBN 10

3540445757

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9783540445753

Geometric Singular Perturbation Theory Beyond the Standard Form

By: Martin Wechselberger

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Geometric Singular Perturbation Theory Beyond the Standard Form

By: Martin Wechselberger

This volume provides a comprehensive review of multiple-scale dynamical systems. Mathematical models of such multiple-scale systems are considered singular perturbation problems, and this volume focuses on the geometric approach known as Geometric Singular Perturbation Theory (GSPT). It is the first of its kind that introduces the GSPT in a coordinate-independent manner. This is motivated by specific examples of biochemical reaction networks, electronic circuit and mechanic oscillator models and advection-reaction-diffusion models, all with an inherent non-uniform scale splitting, which identifies these examples as singular perturbation problems beyond the standard form. The contents cover a general framework for this GSPT beyond the standard form including canard theory, concrete applications, and instructive qualitative models. It contains many illustrations and key pointers to the existing literature. The target audience are senior undergraduates, graduate students and researchers interested in using the GSPT toolbox in nonlinear science, either from a theoretical or an application point of view. Martin Wechselberger is Professor at the School of Mathematics & Statistics, University of Sydney, Australia. He received the J.D. Crawford Prize in 2017 by the Society for Industrial and Applied Mathematics (SIAM) for achievements in the field of dynamical systems with multiple time-scales.

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143

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Springer Nature

Published Date

ISBN 10

3030363996

ISBN 13

9783030363994

Nonautonomous Bifurcation Theory

Concepts and Tools

By: Vasso Anagnostopoulou,Christian Pötzsche,Martin Rasmussen

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Nonautonomous Bifurcation Theory

Concepts and Tools

By: Vasso Anagnostopoulou,Christian Pötzsche,Martin Rasmussen

Bifurcation theory is a major topic in dynamical systems theory with profound applications. However, in contrast to autonomous dynamical systems, it is not clear what a bifurcation of a nonautonomous dynamical system actually is, and so far, various different approaches to describe qualitative changes have been suggested in the literature. The aim of this book is to provide a concise survey of the area and equip the reader with suitable tools to tackle nonautonomous problems. A review, discussion and comparison of several concepts of bifurcation is provided, and these are formulated in a unified notation and illustrated by means of comprehensible examples. Additionally, certain relevant tools needed in a corresponding analysis are presented.

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159

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Springer Nature

Published Date

ISBN 10

303129842X

ISBN 13

9783031298424

Hydro-Environmental Analysis

Freshwater Environments

By: James L. Martin

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Hydro-Environmental Analysis

Freshwater Environments

By: James L. Martin

Focusing on fundamental principles, Hydro-Environmental Analysis: Freshwater Environments presents in-depth information about freshwater environments and how they are influenced by regulation. It provides a holistic approach, exploring the factors that impact water quality and quantity, and the regulations, policy and management methods that are necessary to maintain this vital resource. It offers a historical viewpoint as well as an overview and foundation of the physical, chemical, and biological characteristics affecting the management of freshwater environments. The book concentrates on broad and general concepts, providing an interdisciplinary foundation. The author covers the methods of measurement and classification; chemical, physical, and biological characteristics; indicators of ecological health; and management and restoration. He also considers common indicators of environmental health; characteristics and operations of regulatory control structures; applicable laws and regulations; and restoration methods. The text delves into rivers and streams in the first half and lakes and reservoirs in the second half. Each section centers on the characteristics of those systems and methods of classification, and then moves on to discuss the physical, chemical, and biological characteristics of each. In the section on lakes and reservoirs, it examines the characteristics and operations of regulatory structures, and presents the methods commonly used to assess the environmental health or integrity of these water bodies. It also introduces considerations for restoration, and presents two unique aquatic environments: wetlands and reservoir tailwaters. Written from an engineering perspective, the book is an ideal introduction to the aquatic and limnological sciences for students of environmental science, as well as students of environmental engineering. It also serves as a reference for engineers and scientists involved in the management, regulation, or restoration of freshwater environments.

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5742

Publisher

CRC Press

Published Date

ISBN 10

1138000868

ISBN 13

9781138000865

Geometric Constructions

By: George E. Martin

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Geometric Constructions

By: George E. Martin

Geometric constructions have been a popular part of mathematics throughout history. The first chapter here is informal and starts from scratch, introducing all the geometric constructions from high school that have been forgotten or were never learned. The second chapter formalises Plato's game, and examines problems from antiquity such as the impossibility of trisecting an arbitrary angle. After that, variations on Plato's theme are explored: using only a ruler, a compass, toothpicks, a ruler and dividers, a marked rule, or a tomahawk, ending in a chapter on geometric constructions by paperfolding. The author writes in a charming style and nicely intersperses history and philosophy within the mathematics, teaching a little geometry and a little algebra along the way. This is as much an algebra book as it is a geometry book, yet since all the algebra and geometry needed is developed within the text, very little mathematical background is required. This text has been class tested for several semesters with a master's level class for secondary teachers.

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210

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Springer Science & Business Media

Published Date

ISBN 10

1461206294

ISBN 13

9781461206293

The Foundations of Geometry and the Non-Euclidean Plane

By: G.E. Martin

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The Foundations of Geometry and the Non-Euclidean Plane

By: G.E. Martin

This book is a text for junior, senior, or first-year graduate courses traditionally titled Foundations of Geometry and/or Non Euclidean Geometry. The first 29 chapters are for a semester or year course on the foundations of geometry. The remaining chap ters may then be used for either a regular course or independent study courses. Another possibility, which is also especially suited for in-service teachers of high school geometry, is to survey the the fundamentals of absolute geometry (Chapters 1 -20) very quickly and begin earnest study with the theory of parallels and isometries (Chapters 21 -30). The text is self-contained, except that the elementary calculus is assumed for some parts of the material on advanced hyperbolic geometry (Chapters 31 -34). There are over 650 exercises, 30 of which are 10-part true-or-false questions. A rigorous ruler-and-protractor axiomatic development of the Euclidean and hyperbolic planes, including the classification of the isometries of these planes, is balanced by the discussion about this development. Models, such as Taxicab Geometry, are used exten sively to illustrate theory. Historical aspects and alternatives to the selected axioms are prominent. The classical axiom systems of Euclid and Hilbert are discussed, as are axiom systems for three and four-dimensional absolute geometry and Pieri's system based on rigid motions. The text is divided into three parts. The Introduction (Chapters 1 -4) is to be read as quickly as possible and then used for ref erence if necessary.

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525

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Springer Science & Business Media

Published Date

ISBN 10

1461257255

ISBN 13

9781461257257

Mathematical Analysis of Complex Cellular Activity

By: Richard Bertram,Joel Tabak,Wondimu Teka,Theodore Vo,Martin Wechselberger,Vivien Kirk,James Sneyd

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Mathematical Analysis of Complex Cellular Activity

By: Richard Bertram,Joel Tabak,Wondimu Teka,Theodore Vo,Martin Wechselberger,Vivien Kirk,James Sneyd

This book contains two review articles on mathematical physiology that deal with closely related topics but were written and can be read independently. The first article reviews the basic theory of calcium oscillations (common to almost all cell types), including spatio-temporal behaviors such as waves. The second article uses, and expands on, much of this basic theory to show how the interaction of cytosolic calcium oscillators with membrane ion channels can result in highly complex patterns of electrical spiking. Through these examples one can see clearly how multiple oscillatory processes interact within a cell, and how mathematical methods can be used to understand such interactions better. The two reviews provide excellent examples of how mathematics and physiology can learn from each other, and work jointly towards a better understanding of complex cellular processes. Review 1: Richard Bertram, Joel Tabak, Wondimu Teka, Theodore Vo, Martin Wechselberger: Geometric Singular Perturbation Analysis of Bursting Oscillations in Pituitary Cells Review 2: Vivien Kirk, James Sneyd: Nonlinear Dynamics of Calcium

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Page Count

120

Publisher

Springer

Published Date

ISBN 10

3319181149

ISBN 13

9783319181141

Store Windows 12 INTL

By: Martin M. Pegler

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Store Windows 12 INTL

By: Martin M. Pegler

Over 300 dazzling examples of store windows created by expert designers worldwide. Clever themes, outrageous props, and head-turning arrangements make this tour of store windows a fascinating journey for merchandisers everywhere.

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Page Count

184

Publisher

Visual Reference Publications

Published Date

ISBN 10

1584710675

ISBN 13

9781584710677

Random Walks and Heat Kernels on Graphs

By: Martin T. Barlow

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Random Walks and Heat Kernels on Graphs

By: Martin T. Barlow

This introduction to random walks on infinite graphs gives particular emphasis to graphs with polynomial volume growth. It offers an overview of analytic methods, starting with the connection between random walks and electrical resistance, and then proceeding to study the use of isoperimetric and Poincaré inequalities. The book presents rough isometries and looks at the properties of a graph that are stable under these transformations. Applications include the 'type problem': determining whether a graph is transient or recurrent. The final chapters show how geometric properties of the graph can be used to establish heat kernel bounds, that is, bounds on the transition probabilities of the random walk, and it is proved that Gaussian bounds hold for graphs that are roughly isometric to Euclidean space. Aimed at graduate students in mathematics, the book is also useful for researchers as a reference for results that are hard to find elsewhere.

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Page Count

239

Publisher

Cambridge University Press

Published Date

ISBN 10

1108124593

ISBN 13

9781108124591

Geometric and Cohomological Methods in Group Theory

By: Martin R. Bridson

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Geometric and Cohomological Methods in Group Theory

By: Martin R. Bridson

An extended tour through a selection of the most important trends in modern geometric group theory.

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Page Count

331

Publisher

Cambridge University Press

Published Date

ISBN 10

052175724X

ISBN 13

9780521757249

Numerical Analysis of Partial Differential Equations Using Maple and MATLAB

By: Martin J. Gander,Felix Kwok

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Numerical Analysis of Partial Differential Equations Using Maple and MATLAB

By: Martin J. Gander,Felix Kwok

This book provides an elementary yet comprehensive introduction to the numerical solution of partial differential equations (PDEs). Used to model important phenomena, such as the heating of apartments and the behavior of electromagnetic waves, these equations have applications in engineering and the life sciences, and most can only be solved approximately using computers. Numerical Analysis of Partial Differential Equations Using Maple and MATLAB provides detailed descriptions of the four major classes of discretization methods for PDEs (finite difference method, finite volume method, spectral method, and finite element method) and runnable MATLAB? code for each of the discretization methods and exercises. It also gives self-contained convergence proofs for each method using the tools and techniques required for the general convergence analysis but adapted to the simplest setting to keep the presentation clear and complete. This book is intended for advanced undergraduate and early graduate students in numerical analysis and scientific computing and researchers in related fields. It is appropriate for a course on numerical methods for partial differential equations.

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Page Count

163

Publisher

SIAM

Published Date

ISBN 10

1611975301

ISBN 13

9781611975307

Book's by Martin Hairer

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