This book presents what in our opinion constitutes the basis of the theory of the mu-calculus, considered as an algebraic system rather than a logic. We have wished to present the subject in a unified way, and in a form as general as possible. Therefore, our emphasis is on the generality of the fixed-point notation, and on the connections between mu-calculus, games, and automata, which we also explain in an algebraic way.
This book should be accessible for graduate or advanced undergraduate students both in mathematics and computer science. We have designed this book especially for researchers and students interested in logic in computer science, comuter aided verification, and general aspects of automata theory. We have aimed at gathering in a single place the fundamental results of the theory, that are currently very scattered in the literature, and often hardly accessible for interested readers.
The presentation is self-contained, except for the proof of the Mc-Naughton's Determinization Theorem (see, e.g., 97]. However, we suppose that the reader is already familiar with some basic automata theory and universal algebra. The references, credits, and suggestions for further reading are given at the end of each chapter.

This Proceedings Volume contains 32 articles on various interesting areas of
present-day functional analysis and its applications: Banach spaces and
their geometry, operator ideals, Banach and operator algebras, operator and
spectral theory, Frechet spaces and algebras, function and sequence spaces.
The authors have taken much care with their articles and many papers present
important results and methods in active fields of research. Several survey
type articles (at the beginning and the end of the book) will be very useful
for mathematicians who want to learn "what is going on" in some particular
field of research.

"Materials Science in Manufacturing" focuses on materials science and materials processing primarily for engineering and technology students preparing for careers in manufacturing. The text also serves as a useful reference on materials science for the practitioner engaged in manufacturing as well as the beginning graduate student.
Integrates theoretical understanding and current practices to provide a resource for students preparing for advanced study or career in industry. Also serves as a useful resource to the practitioner who works with diverse materials and processes, but is not a specialist in materials science. This book covers a wider range of materials and processes than is customary in the elementary materials science books.
This book covers a wider range of materials and processes than is customary in the elementary materials science books.
* Detailed explanations of theories, concepts, principles and practices of materials and processes of manufacturing through richly illustrated text
* Includes new topics such as nanomaterials and nanomanufacturing, not covered in most similar works
* Focuses on the interrelationship between Materials Science, Processing Science, and Manufacturing Technology

The book is devoted to the perturbation analysis of matrix equations. The importance of perturbation analysis is that it gives a way to estimate the influence of measurement and/or parametric errors in mathematical models together with the rounding errors done in the computational process. The perturbation bounds may further be incorporated in accuracy estimates for the solution computed in finite arithmetic. This is necessary for the development of reliable computational methods, algorithms and software from the viewpoint of modern numerical analysis.

In this book a general perturbation theory for matrix algebraic equations is presented. Local and non-local perturbation bounds are derived for general types of matrix equations as well as for the most important equations arising in linear algebra and control theory. A large number of examples, tables and figures is included in order to illustrate the perturbation techniques and bounds.

Key features:

The first book in this field
Can be used by a variety of specialists
Material is self-contained
Results can be used in the development of reliable computational algorithms
A large number of examples and graphical illustrations are given
Written by prominent specialists in the field
"

The aim of the present work is two-fold. Firstly it aims at a giving an account of many existing algorithms for calculating with finite-dimensional Lie algebras. Secondly, the book provides an introduction into the theory of finite-dimensional Lie algebras. These two subject areas are intimately related. First of all, the algorithmic perspective often invites a different approach to the theoretical material than the one taken in various other monographs (e.g., 42], 48], 77], 86]). Indeed, on various occasions the knowledge of certain algorithms allows us to obtain a straightforward proof of theoretical results (we mention the proof of the Poincare-Birkhoff-Witt theorem and the proof of Iwasawa's theorem as examples). Also proofs that contain algorithmic constructions are explicitly formulated as algorithms (an example is the isomorphism theorem for semisimple Lie algebras that constructs an isomorphism in case it exists). Secondly, the algorithms can be used to arrive at a better understanding of the theory. Performing the algorithms in concrete examples, calculating with the concepts involved, really brings the theory of life.

The modern theory of algebras of binary relations, reformulated by Tarski as an abstract, algebraic, equational theory of relation algebras, has considerable mathematical significance, with applications in various fields: e.g., in computer science---databases, specification theory, AI---and in anthropology, economics, physics, and philosophical logic.
This comprehensive treatment of the theory of relation algebras and the calculus of relations is the first devoted to a systematic development of the subject.
Key Features:
- Presents historical milestones from a modern perspective
- Careful, thorough, detailed guide to understanding relation algebras
- Provides a framework and unified perspective of the subject

This volume gives a state of the art of triangular norms which can be used for the generalization of several mathematical concepts, such as conjunction, metric, measure, etc. 16 chapters written by leading experts provide a state of the art overview of theory and applications of triangular norms and related operators in fuzzy logic, measure theory, probability theory, and probabilistic metric spaces.
Key Features:
- Complete state of the art of the importance of triangular norms in various mathematical fields
- 16 self-contained chapters with extensive bibliographies cover both the theoretical background and many applications
- Chapter authors are leading authorities in their fields
- Triangular norms on different domains (including discrete, partially ordered) are described
- Not only triangular norms but also related operators (aggregation operators, copulas) are covered
- Book contains many enlightening illustrations
- Complete state of the art of the importance of triangular norms in various mathematical fields
- 16 self-contained chapters with extensive bibliographies cover both the theoretical background and many applications
- Chapter authors are leading authorities in their fields
- Triangular norms on different domains (including discrete, partially ordered) are described
- Not only triangular norms but also related operators (aggregation operators, copulas) are covered
- Book contains many enlightening illustrations

Many problems for partial difference and integro-difference equations can be written as difference equations in a normed space. This book is devoted to linear and nonlinear difference equations in a normed space. Our aim in this monograph is to initiate systematic investigations of the global behavior of solutions of difference equations in a normed space. Our primary concern is to study the asymptotic stability of the equilibrium solution. We are also interested in the existence of periodic and positive solutions. There are many books dealing with the theory of ordinary difference equations. However there are no books dealing systematically with difference equations in a normed space. It is our hope that this book will stimulate interest among mathematicians to develop the stability theory of abstract difference equations.
Note that even for ordinary difference equations, the problem of stability analysis continues to attract the attention of many specialists despite its long history. It is still one of the most burning problems, because of the absence of its complete solution,
but many general results available for ordinary difference equations
(for example, stability by linear approximation) may be easily proved for abstract difference equations.
The main methodology presented in this publication is based on a combined use of recent norm estimates for operator-valued functions with the following
methods and results:
a) the freezing method;
b) the Liapunov type equation;
c) the method of majorants;
d) the multiplicative representation of solutions.
In addition, we present stability results for abstract Volterra discrete equations.
The bookconsists of 22 chapters and an appendix. In Chapter 1, some definitions and preliminary results are collected. They are systematically used in the next chapters.
In, particular, we recall very briefly some basic notions and results of the theory of operators in Banach and ordered spaces. In addition, stability concepts are presented and Liapunov's functions are introduced. In Chapter 2 we review various classes of linear operators and their spectral properties. As examples, infinite matrices are considered. In Chapters 3 and 4, estimates for the norms of operator-valued and matrix-valued functions are suggested. In particular, we consider Hilbert-Schmidt, Neumann-Schatten, quasi-Hermitian and quasiunitary operators. These classes contain numerous infinite matrices arising in applications. In Chapter 5, some perturbation results for linear operators in a Hilbert space are presented. These results are then used in the next chapters to derive bounds for the spectral radiuses. Chapters 6-14 are devoted to asymptotic and exponential stabilities, as well as boundedness of solutions of linear and nonlinear difference equations. In Chapter 6 we investigate the linear equation with a bounded constant operator acting in a Banach space. Chapter 7 is concerned with the Liapunov type operator equation. Chapter 8 deals with estimates for the spectral radiuses of concrete operators, in particular, for infinite matrices. These bounds enable the formulation of explicit stability conditions. In Chapters 9 and 10 we consider nonautonomous (time-variant) linear equations. An essential role in this chapter is played by the evolution operator. In addition, we use the "freezing" method and multiplicativerepresentations of solutions to construct the majorants for linear equations. Chapters 11 and 12 are devoted to semilinear autonomous and nonautonomous equations. Chapters 13 and 14 are concerned with linear and nonlinear higher order difference equations. Chapter 15 is devoted to the input-to-state stability. In Chapter 16 we study periodic solutions of linear and nonlinear difference equations in a Banach space, as well as the global orbital stability of solutions of vector difference equations. Chapters 17 and 18 deal with linear and nonlinear Volterra discrete equations in a Banach space. An important role in these chapter is played by operator pencils. Chapter 19 deals with a class of the Stieltjes differential equations.
These equations generalize difference and differential equations. We apply estimates for norms of operator valued functions and properties of the multiplicative integral to certain classes of linear and nonlinear Stieltjes differential equations to obtain solution estimates that allow us to study the stability and boundedness of solutions. We also show the existence and uniqueness of solutions as well as the continuous dependence of the solutions on the time integrator. Chapter 20 provides some results regarding the Volterra--Stieltjes equations. The Volterra--Stieltjes equations include Volterra difference and Volterra integral equations. We obtain estimates for the norms of solutions of the Volterra--Stieltjes equation. Chapter 21 is devoted to difference equations with continuous time. In Chapter 22, we suggest some conditions for the existence of nontrivial and positive steady states of difference equations, as well as bounds for the stationary solutions.
- Deals systematically with difference equations in normed spaces
- Considers new classes of equations that could not be studied in the frameworks of ordinary and partial difference equations
- Develops the freezing method and presents recent results on Volterra discrete equations
- Contains an approach based on the estimates for norms of operator functions

The book contains a systematic treatment of the qualitative theory of elliptic boundary value problems for linear and quasilinear second order equations in non-smooth domains. The authors concentrate on the following fundamental results: sharp estimates for strong and weak solutions, solvability of the boundary value problems, regularity assertions for solutions near singular points.

Key features:

* New the Hardy - Friedrichs - Wirtinger type inequalities as well as new integral inequalities related to the Cauchy problem for a differential equation.
* Precise exponents of the solution decreasing rate near boundary singular points and best possible conditions for this.
* The question about the influence of the coefficients smoothness on the regularity of solutions.
* New existence theorems for the Dirichlet problem for linear and quasilinear equations in domains with conical points.
* The precise power modulus of continuity at singular boundary point for solutions of the Dirichlet, mixed and the Robin problems.
* The behaviour of weak solutions near conical point for the Dirichlet problem for m - Laplacian.
* The behaviour of weak solutions near a boundary edge for the Dirichlet and mixed problem for elliptic quasilinear equations with triple degeneration.
* Precise exponents of the solution decreasing rate near boundary singular points and best possible conditions for this.
* The question about the influence of the coefficients smoothness on the regularity of solutions.
* New existence theorems for the Dirichlet problem for linear and quasilinear equations in domains with conical points.
* The precise power modulus of continuity atsingular boundary point for solutions of the Dirichlet, mixed and the Robin problems.
* The behaviour of weak solutions near conical point for the Dirichlet problem for m - Laplacian.
* The behaviour of weak solutions near a boundary edge for the Dirichlet and mixed problem for elliptic quasilinear equations with triple degeneration.

The problems of constructing covering codes and of estimating their parameters are the main concern of this book. It provides a unified account of the most recent theory of covering codes and shows how a number of mathematical and engineering issues are related to covering problems.

Scientists involved in discrete mathematics, combinatorics, computer science, information theory, geometry, algebra or number theory will find the book of particular significance. It is designed both as an introductory textbook for the beginner and as a reference book for the expert mathematician and engineer.

A number of unsolved problems suitable for research projects are also discussed.

This volume is a collection of surveys of research problems in topology and its applications. The topics covered include general topology, set-theoretic topology, continuum theory, topological algebra, dynamical systems, computational topology and functional analysis.
* New surveys of research problems in topology
* New perspectives on classic problems
* Representative surveys of research groups from all around the world

Corrosion is a huge issue for materials, mechanical, civil and petrochemical engineers. With comprehensive coverage of the principles of corrosion engineering, this book is a one-stop text and reference for students and practicing corrosion engineers. Highly illustrated, with worked examples and definitions, it covers basic corrosion principles, and more advanced information for postgraduate students and professionals. Basic principles of electrochemistry and chemical thermodynamics are incorporated to make the book accessible for students and engineers who do not have prior knowledge of this area. Each form of corrosion covered in the book has a definition, description, mechanism, examples and preventative methods. Case histories of failure are cited for each form. End of chapter questions are accompanied by an online solutions manual.
* Comprehensively covers the principles of corrosion engineering, methods of corrosion protection and corrosion processes and control in selected engineering environments
* Structured for corrosion science and engineering classes at senior undergraduate and graduate level, and is an ideal reference that readers will want to use in their professional work
* Worked examples, extensive end of chapter exercises and accompanying online solutions and written by an expert from a key pretochemical university

A uniquely practical DSP text, this book gives a thorough understanding of the principles and applications of DSP with a minimum of mathematics, and provides the reader with an introduction to DSP applications in telecoms, control engineering and measurement and data analysis systems.
The new edition contains:
- Expanded coverage of the basic concepts to aid understanding
- New sections on filter sysnthesis, control theory and contemporary topics of speech and image recognition
- Full solutions to all questions and exercises in the book
- A complete on-line resource
The on-line resource offers instructors and students complete lecture notes, lecture videos, PowerPoint slides for presentations, final exams and solutions, project exercises, URLs to DSP applet experiment animations and e-meeting software for direct communication with the authors.
Assuming the reader already has some prior knowledge of signal theory, this textbook will be highly suitable for undergraduate and postgraduate students in electrical and electronic engineering taking introductory and advanced courses in DSP, as well as courses in communications and control systems engineering. It will also prove an invaluable introduction to DSP and its applications for the professional engineer.
- Expanded coverage of the basic concepts to aid understanding, along with a wide range of DSP applications
- New textbook features included throughout, including learning objectives, summary
sections, exercises and worked examples to increase accessibility of the text
- Full solutions to all questions and exercises included in the book, with extra resources on-line

Infinite Words is an important theory in both Mathematics and Computer Sciences. Many new developments have been made in the field, encouraged by its application to problems in computer science. Infinite Words is the first manual devoted to this topic.
Infinite Words explores "all" aspects of the theory, including Automata, Semigroups, Topology, Games, Logic, Bi-infinite Words, Infinite Trees and Finite Words. The book also looks at the early pioneering work of Buchi, McNaughton and Schutzenberger.
Serves as both an introduction to the field and as a reference book.
Contains numerous exercises desgined to aid students and readers.
Self-contained chapters provide helpful guidance for lectures.

The definitive practical guide to choosing the optimum manufacturing process, written for students and engineers.
Process Selection provides engineers with the essential technological and economic data to guide the selection of manufacturing processes. This fully revised second edition covers a wide range of important manufacturing processes and will ensure design decisions are made to achieve optimal cost and quality objectives.
Expanded and updated to include contemporary manufacturing, fabrication and assembly technologies, the book puts process selection and costing into the context of modern product development and manufacturing, based on parameters such as materials requirements, design considerations, quality and economic factors. Key features of the book include: manufacturing process information maps (PRIMAs) provide detailed information on the characteristics and capabilities of 65 processes and their variants in a standard format; process capability charts detailing the processing tolerance ranges for key material types; strategies to facilitate process selection; detailed methods for estimating costs, both at the component and assemby level.
The approach enables an engineer to understand the consequences of design decisions on the technological and economic aspects of component manufacturing, fabrication and assembly.
This comprehensive book provides both a definitive guide to the subject for students and an invaluable source of reference for practising engineers.
* manufacturing process information maps (PRIMAs) provide detailed information on the characteristics and capabilities of 65 processes in a standard format
* process capability charts detail the processing tolerance ranges for key material types
* detailed methods for estimating costs, both at the component and assembly level

This title is the result of a one-week workshop sponsored by the Swedish research agency, FRN, on the interface between complexity and art. Among others, it includes discussions on whether "good" art is "complex" art, how artists see the term "complex," and what poets try to convey in word about complex behavior in nature.

This book is carefully designed to be used on a wide range of introductory courses at first degree and HND level in the U.K., with content matched to a variety of first year degree modules from IEng and other BSc Engineering and Technology courses. Lecturers will find the breadth of material covered gears the book towards a flexible style of use, which can be tailored to their syllabus, and used along side the other IIE Core Textbooks to bring first year students up to speed on the mathematics they require for their engineering degree.
*Features real-world examples, case studies, assignments and knowledge-check questions throughout
*Introduces key mathematical methods in practical engineering contexts
*Bridges the gap between theory and practice

Essential Java serves as an introduction to the programming language, Java, for scientists and engineers, and can also be used by experienced programmers wishing to learn Java as an additional language. The book focuses on how Java, and object-oriented programming, can be used to solve science and engineering problems.
Many examples are included from a number of different scientific and engineering areas, as well as from business and everyday life. Pre-written packages of code are provided to help in such areas as input/output, matrix manipulation and scientific graphing.
Java source code and solutions to selected exercises are available at: www.bh.com/companions/0750659912
A free solutions manual is available to lecturers at: http: //textbooks.elsevier.com
* Takes a 'dive-in' approach, getting the reader writing and running programs immediately
* Teaches object-oriented programming for problem-solving in engineering and science
* Fully supported with online resources and listings to download

Working through this student-centred text readers will be brought up to speed with the modelling of control systems using Laplace, and given a solid grounding of the pivotal role of control systems across the spectrum of modern engineering. A clear, readable text is supported by numerous worked example and problems.
* Key concepts and techniques introduced through applications
* Introduces mathematical techniques without assuming prior knowledge
* Written for the latest vocational and undergraduate courses

This book describes the use of models in process engineering. Process engineering is all about manufacturing--of just about anything! To manage processing and manufacturing systematically, the engineer has to bring together many different techniques and analyses of the interaction between various aspects of the process. For example, process engineers would apply models to perform feasibility analyses of novel process designs, assess environmental impact, and detect potential hazards or accidents.
To manage complex systems and enable process design, the behavior of systems is reduced to simple mathematical forms. This book provides a systematic approach to the mathematical development of process models and explains how to analyze those models. Additionally, there is a comprehensive bibliography for further reading, a question and answer section, and an accompanying Web site developed by the authors with additional data and exercises.
* Introduces a structured modeling methodology emphasizing the importance of the modeling goal and including key steps such as model verification, calibration, and validation.
* Focuses on novel and advanced modeling techniques such as discrete, hybrid, hierarchical, and empirical modeling
* Illustrates the notions, tools, and techniques of process modeling with examples and advances applications

Multigrid presents both an elementary introduction to multigrid methods for solving partial differential equations and a contemporary survey of advanced multigrid techniques and real-life applications.
Multigrid methods are invaluable to researchers in scientific disciplines including physics, chemistry, meteorology, fluid and continuum mechanics, geology, biology, and all engineering disciplines. They are also becoming increasingly important in economics and financial mathematics.
Readers are presented with an invaluable summary covering 25 years of practical experience acquired by the multigrid research group at the Germany National Research Center for Information Technology. The book presents both practical and theoretical points of view.
* Covers the whole field of multigrid methods from its elements up to the most advanced applications
* Style is essentially elementary but mathematically rigorous
* No other book is so comprehensive and written for both practitioners and students

Foundations of Engineering Acoustics takes the reader on a journey from a qualitative introduction to the physical nature of sound, explained in terms of common experience, to mathematical models and analytical results which underlie the techniques applied by the engineering industry to improve the acoustic performance of their products. The book is distinguished by extensive descriptions and explanations of audio-frequency acoustic phenomena and their relevance to engineering, supported by a wealth of diagrams, and by a guide for teachers of tried and tested class demonstrations and laboratory-based experiments.
Foundations of Engineering Acoustics is a textbook suitable for both senior undergraduate and postgraduate courses in mechanical, aerospace, marine, and possibly electrical and civil engineering schools at universities. It will be a valuable reference for academic teachers and researchers and will also assist Industrial Acoustic Group staff and Consultants.
Comprehensive and up-to-date: broad coverage, many illustrations, questions, elaborated answers, references and a bibliography
Introductory chapter on the importance of sound in technology and the role of the engineering acoustician
Deals with the fundamental concepts, principles, theories and forms of mathematical representation, rather than methodology
Frequent reference to practical applications and contemporary technology
Emphasizes qualitative, physical introductions to each principal as an entree to mathematical analysis for the less theoretically oriented readers and courses
Provides a 'cook book' of demonstrations and laboratory-based experiments for teachers
Useful for discussing acoustical problems with non-expert clients/managers because the descriptive sections are couched in largely non-technical language and any jargon is explained
Draws on the vast pedagogic experience of the writer"

'Introduction to Digital Signal Processing' covers the basic theory and practice of digital signal processing (DSP) at an introductory level. As with all volumes in the Essential Electronics Series, this book retains the unique formula of minimal mathematics and straightforward explanations. The author has included examples throughout of the standard software design package, MATLAB and screen dumps are used widely throughout to illustrate the text.
Ideal for students on degree and diploma level courses in electric and electronic engineering, 'Introduction to Digital Signal Processing' contains numerous worked examples throughout as well as further problems with solutions to enable students to work both independently and in conjunction with their course.
Assumes only minimum knowledge of mathematics and electronics.
Concise and written in a straightforward and accessible style.
Packed with worked examples, exercises and self-assesment questions.

Engineers need to be familiar with the fundamental principles and concepts in materials and structures in order to be able to design structurers to resist failures. For 4 decades, this book has provided engineers with these fundamentals.

Thoroughly updated, the book has been expanded to cover everything on materials and structures that engineering students are likely to need. Starting with basic mechanics, the book goes on to cover modern numerical techniques such as matrix and finite element methods. There is also additional material on composite materials, thick shells, flat plates and the vibrations of complex structures. Illustrated throughout with worked examples, the book also provides numerous problems for students to attempt.
New edition introducing modern numerical techniques, such as matrix and finite element methods
Covers requirements for an engineering undergraduate course on strength of materials and structures