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Module theory over commutative asociative rings is usually extended to noncommutative associative rings by introducing the category of left (or right) modules.An alternative to this procedure is suggested by considering bimodules.A refined module theory for associative rings is used to investigate the bimodule structure of arbitary algebras and group actions on these algebras. ... Read more

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A continuation of the authors’ previous book, Isometries on Banach Spaces: Vector-valued Function Spaces and Operator Spaces, Volume Two covers much of the work that has been done on characterizing isometries on various Banach spaces.

Picking up where the first volume left off, the book begins with a chapter on the Banach–Stone property. The authors consider the case where the isometry is from C₀(Q, X) to C₀(K, Y) so that the property involves pairs (X, Y) of spaces. The next chapter examines spaces X for which the isometries on L^P(μ, X) can be described as a generalization of the form given by Lamperti in the scalar case. The book then studies isometries on direct sums of Banach and Hilbert spaces, isometries on spaces of matrices with a variety of norms, and isometries on Schatten classes. It subsequently highlights spaces on which the group of isometries is maximal or minimal. The final chapter addresses more peripheral topics, such as adjoint abelian operators and spectral isometries.

Essentially self-contained, this reference explores a fundamental aspect of Banach space theory. Suitable for both experts and newcomers to the field, it offers many references to provide solid coverage of the literature on isometries. ... Read more

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Dynamic programming is a powerful method for solving optimization problems, but has a number of drawbacks that limit its use to solving problems of very low dimension. To overcome these limitations, author Rein Luus suggested using it in an iterative fashion. Although this method required vast computer resources, modifications to his original scheme have made the computational procedure feasible. With iteration, dynamic programming becomes an effective optimization procedure for very high-dimensional optimal control problems and has demonstrated applicability to singular control problems. Recently, iterative dynamic programming (IDP)has been refined to handle inequality state constraints and noncontinuous functions.Iterative Dynamic Programming offers a comprehensive presentation of this powerful tool. It brings together the results of work carried out by the author and others - previously available only in scattered journal articles - along with the insight that led to its development. The author provides the necessary background, examines the effects of the parameters involved, and clearly illustrates IDP's advantages. ... Read more

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Singular Partial Differential Equations provides an analytical, constructive, and elementary approach to non-elementary problems. In the first monograph to consider such equations, the author investigates the solvability of partial differential equations and systems in a class of bounded functions with complex coefficients having singularities at the inner points or boundary of the domain. Using complex variable techniques, the author considers a variety of problems, including the Dirichlet, Neumann, and other problems for first order systems. He also explores applications to singular equations, degenerate, high-dimensional Beltrami systems in Cn,, and others. Singular Partial Differential Equations fills a gap in the literature on degenerate and singular partial differential equations and significantly contributes to the theory of boundary value problems for these equations and systems. It will undoubtedly stimulate further research in the field. Practical applications in analysis and physics make this important reading for researchers and students in physics and engineering, along with mathematicians. ... Read more

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'Applied Maths for Engineering' covers all the necessary theory required for the maths units in the Advanced GNVQ in engineering, including all the recent changes in the syllabus. This textbook begins with fundamentals such as indices, roots and fractions before going on to algebra, trigonometry and calculus. The author demonstrates the use of maths as an engineering tool in a series of assignments based on practical engineering situations.

As well as being ideal for the Advanced GNVQ scheme, 'Applied Maths for Engineering' can be used for national certificates and diplomas, and higher education modules in engineering. Students entering engineering degree courses without sufficient proficiency in maths will find this book very useful.

Plenty of practical exercises and solutions
Comprehensive glossary of important engineering and mathematical terms
Detailed appendices

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Incorporating substantial developments from the last thirty years into one resource, Asymptotics and Borel Summability provides a self-contained introduction to asymptotic analysis with special emphasis on topics not covered in traditional asymptotics books. The author explains basic ideas, concepts, and methods of generalized Borel summability, transseries, and exponential asymptotics. He provides complete mathematical rigor while supplementing it with heuristic material and examples, so that some proofs may be omitted by applications-oriented readers.

To give a sense of how new methods are used in a systematic way, the book analyzes in detail general nonlinear ordinary differential equations (ODEs) near a generic irregular singular point. It enables readers to master basic techniques, supplying a firm foundation for further study at more advanced levels. The book also examines difference equations, partial differential equations (PDEs), and other types of problems.

Chronicling the progress made in recent decades, this book shows how Borel summability can recover exact solutions from formal expansions, analyze singular behavior, and vastly improve accuracy in asymptotic approximations.

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Filled with practical examples, Quasilinear Hyperbolic Systems, Compressible Flows, and Waves presents a self-contained discussion of quasilinear hyperbolic equations and systems with applications. It emphasizes nonlinear theory and introduces some of the most active research in the field.

After linking continuum mechanics and quasilinear partial differential equations, the book discusses the scalar conservation laws and hyperbolic systems in two independent variables. Using the method of characteristics and singular surface theory, the author then presents the evolutionary behavior of weak and mild discontinuities in a quasilinear hyperbolic system. He also explains how to apply weakly nonlinear geometrical optics in nonequilibrium and stratified gas flows and demonstrates the power, generality, and elegance of group theoretic methods for solving Euler equations of gasdynamics involving shocks. The final chapter deals with the kinematics of a shock of arbitrary strength in three dimensions.

With a focus on physical applications, this text takes readers on a journey through this fascinating area of applied mathematics. It provides the essential mathematical concepts and techniques to understand the phenomena from a theoretical standpoint and to solve a variety of physical problems.

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This volume encompasses both the automatic transformation of computer programs as well as the methodologies for the efficient exploitation of mathematical underpinnings or program structure. ... Read more

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DEFFERENTIAL EQN'S
math methods in egineering, statics of rigid bodies ... Read more

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Despite decades of research and progress in the theory of generalized solutions to first-order nonlinear partial differential equations, a gap between the local and the global theories remains: The Cauchy characteristic method yields the local theory of classical solutions. Historically, the global theory has principally depended on the vanishing viscosity method. The authors of this volume help bridge the gap between the local and global theories by using the characteristic method as a basis for setting a theoretical framework for the study of global generalized solutions. That is, they extend the smooth solutions obtained by the characteristic method. The authors offer material previously unpublished in book form, including treatments of the life span of classical solutions, the construction of singularities of generalized solutions, new existence and uniqueness theorems on minimax solutions, differential inequalities of Haar type and their application to the uniqueness of global, semi-classical solutions, and Hopf-type explicit formulas for global solutions. These subjects yield interesting relations between purely mathematical theory and the applications of first-order nonlinear PDEs.The Characteristic Method and Its Generalizations for First-Order Nonlinear Partial Differential Equations represents a comprehensive exposition of the authors' works over the last decade. The book is self-contained and assumes only basic measure theory, topology, and ordinary differential equations as prerequisites. With its innovative approach, new results, and many applications, it will prove valuable to mathematicians, physicists, and engineers and especially interesting to researchers in nonlinear PDEs, differential inequalities, multivalued analysis, differential games, and related topics in applied analysis. ... Read more

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Linear and nonlinear systems of equations are the basis for many, if not most, of the models of phenomena in science and engineering, and their efficient numerical solution is critical to progress in these areas. This is the first book to be published on nonlinear equations since the mid-1980s. Although it stresses recent developments in this area, such as Newton-Krylov methods, considerable material on linear equations has been incorporated. This book focuses on a small number of methods and treats them in depth. The author provides a complete analysis of the conjugate gradient and generalized minimum residual iterations as well as recent advances including Newton-Krylov methods, incorporation of inexactness and noise into the analysis, new proofs and implementations of Broyden's method, and globalization of inexact Newton methods. ... Read more

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Iterative Methods for Linear and Nonlinear Equations (Frontiers inApplied Mathematics, Vol. 16)
I recommend this book as a jump start to the arena. This is a comprehenshive book, that includes examples of the subjects discussed and script files in Matlab that are provided online. ... Read more

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Full coverage of 12 different math topics in just one volume! Statistis, plane trigonometry, calculus, boolean algebra--most likely your mathematics needs don't fit neatly into books on single math topics. That's why we created the new Handbook of Applied Mathematics for Engineers and Scientists--the first math problemsolver to solve tough daily problems in 13 different math fields. put this new Hnadbook at your fingertips, and you'll be able to review essential math principles and definitions in seconds, and use its data as a springboard for creative problems-solving. Each math area features definitions, principles and equations, and all applications are cross-indexed for maximum convenience. Algebra; Plane and Spherical Trigonometry; Plane and Solid Analytic Geometry; Permutations and Combinations; Matrix Algebra; Boolean Algebra; Transformation of Space in Computer Graphics; Statistics; Probability; Regression Analysis; Cybernetics; Calculus. ... Read more

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The computational power currently available means that practitioners can find extremely accurate approximations to the solutions of more and more sophisticated mathematical models-providing they know the right analytical techniques. In relatively simple terms, this book describes a class of techniques that fulfill this need by providing closed-form solutions to many boundary value problems that arise in science and engineering. Boundary integral equation methods (BIEM's) have certain advantages over other procedures for solving such problems: BIEM's are powerful, applicable to a wide variety of situations, elegant, and ideal for numerical treatment. Certain fundamental constructs in BIEM's are also essential ingredients in boundary element methods, often used by scientists and engineers.However, BIEM's are also sometimes more difficult to use in plane cases than in their three-dimensional counterparts. Consequently, the full, detailed BIEM treatment of two-dimensional problems has been largely neglected in the literature-even when it is more than marginally different from that applied to the corresponding three-dimensional versions.This volume discusses three typical cases where such differences are clear: the Laplace equation (one unknown function), plane strain (two unknown functions), and the bending of plates with transverse shear deformation (three unknown functions). The author considers each of these with Dirichlet, Neumann, and Robin boundary conditions. He subjects each to a thorough investigation-with respect to the existence and uniqueness of regular solutions-through several BIEM's. He proposes suitable generalizations of the concept of logarithmic capacity for plane strain and bending of plates, then uses these to identify contours where non-uniqueness may occur. In the final section, the author compares and contrasts the various solution representations, links them by means of boundary operators, and evaluates them for their suitability for numeric computation. ... Read more

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Mathematics Major
I am utilizing it for an independent study as an undergraduate. It is concise and well written. I do not recommend it as a primary text. It serves as a great supplemental text for my Boundary Elements Method investigations. ... Read more

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This volume on invariant imbedding and inverse problems is based on a conference held in Alberquerque, New Mexico, in April 1990. ... Read more

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This volume contains selected papers that focus on the use of linear algebra, computational statistics, and computer science in the development of algorithms and software systems for text retrieval. Experts in information modeling and retrieval share their perspectives on the design of scalable but precise text retrieval systems, revealing many of the challenges and obstacles that mathematical and statistical models must overcome to be viable for automated text processing. This very useful proceedings is an excellent companion for courses in information retrieval, applied linear algebra, and applied statistics.

Computational Information Retrieval provides background material on vector space models for text retrieval that applied mathematicians, statisticians, and computer scientists may not be familiar with. For graduate students in these areas, several research questions in information modeling are exposed. In addition, several case studies concerning the efficacy of the popular Latent Semantic Analysis (or Indexing) approach are provided. ... Read more

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This text examines the power of ideas from dynamical systems that are being adapted and developed in the context of shock waves. ... Read more

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This volume begins with processing in biological organisms, moves through interactions between processing in biology and computer science, and ends with massively parallel computing. ... Read more

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This text on domain decomposition focuses on the notion that by breaking the domain of the original problem into subdomains, such an approach can, if properly implemented, lead to considerable speedup. the methods are suited for parallel computers. ... Read more

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These papers focus on issues related to modelling (including design), parameter estimation and system identification, and feedback control for problems described by partial differential equations. It includes applications of flow control, as well as control of structures. ... Read more

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Conference held in Arcata, California, May 1989.

This carefully edited survey volume introduces the reader to important problems for partial differential equations, including such diverse applications as quantum scattering, electric impedencee tomography, and identification of coefficients in partial differential equations.

Each article carefully outlines key concepts and uses well chosen examples to illustrate its main points.The extensive primary and secondary references provide access to the literature in this rapidly expanding area.This volume can introduce the novice to an area of challenging mathematical research and significant applications.At the same time, it is an authoritative reference for the specialist. ... Read more

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This volume contains selected papers from a conference held at the Johns Hopkins University, Maryland, in 1995, which was organized to bring together researchers in the mathematical programming aspects of complementarity in a variety of application areas. ... Read more