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Books > Academic & Education > Professional & Technical > Mathematics

Computational Materials Engineering - An Introduction to Microstructure Evolution (Hardcover): Koenraad George Frans Janssens,... Computational Materials Engineering - An Introduction to Microstructure Evolution (Hardcover)
Koenraad George Frans Janssens, Dierk Raabe, Ernest Kozeschnik, Mark A Miodownik, Britta Nestler
R3,293 Discovery Miles 32 930 Ships in 10 - 15 working days

Computational Materials Engineering is an advanced introduction to the computer-aided modeling of essential material properties and behavior, including the physical, thermal and chemical parameters, as well as the mathematical tools used to perform simulations. Its emphasis will be on crystalline materials, which includes all metals. The basis of Computational Materials Engineering allows scientists and engineers to create virtual simulations of material behavior and properties, to better understand how a particular material works and performs and then use that knowledge to design improvements for particular material applications. The text displays knowledge of software designers, materials scientists and engineers, and those involved in materials applications like mechanical engineers, civil engineers, electrical engineers, and chemical engineers.
Readers from students to practicing engineers to materials research scientists will find in this book a single source of the major elements that make up contemporary computer modeling of materials characteristics and behavior. The reader will gain an understanding of the underlying statistical and analytical tools that are the basis for modeling complex material interactions, including an understanding of computational thermodynamics and molecular kinetics; as well as various modeling systems. Finally, the book will offer the reader a variety of algorithms to use in solving typical modeling problems so that the theory presented herein can be put to real-world use.
Balanced coverage of fundamentals of materials modeling, as well as more advanced aspects of modeling, such as modeling at all scales from the atomic to the molecular to the macro-material
Concise, yet rigorous mathematical coverage of such analytical tools as the Potts type Monte Carlo method, cellular automata, phase field, dislocation dynamics and Finite Element Analysis in statistical and analytical modeling
Companion web site will offer ample workable programs, along with suggested projects, resources for further reading, and useful classroom exercises"

Computational Theory of Iterative Methods, Volume 15 (Hardcover, 15th edition): Ioannis Argyros Computational Theory of Iterative Methods, Volume 15 (Hardcover, 15th edition)
Ioannis Argyros
R6,212 Discovery Miles 62 120 Ships in 10 - 15 working days

The book is designed for researchers, students and practitioners interested in using fast and efficient iterative methods to approximate solutions of nonlinear equations. The following four major problems are addressed. Problem 1: Show that the iterates are well defined. Problem 2: concerns the convergence of the sequences generated by a process and the question of whether the limit points are, in fact solutions of the equation. Problem 3: concerns the economy of the entire operations. Problem 4: concerns with how to best choose a method, algorithm or software program to solve a specific type of problem and its description of when a given algorithm succeeds or fails. The book contains applications in several areas of applied sciences including mathematical programming and mathematical economics. There is also a huge number of exercises complementing the theory.
- Latest convergence results for the iterative methods
- Iterative methods with the least computational cost
- Iterative methods with the weakest convergence conditions
- Open problems on iterative methods

Handbook of Quantum Logic and Quantum Structures - Quantum Structures (Hardcover): Kurt Engesser, Dov M. Gabbay, Daniel Lehmann Handbook of Quantum Logic and Quantum Structures - Quantum Structures (Hardcover)
Kurt Engesser, Dov M. Gabbay, Daniel Lehmann
R7,306 Discovery Miles 73 060 Ships in 10 - 15 working days

Since its inception in the famous 1936 paper by Birkhoff and von Neumann entitled "The logic of quantum mechanics" quantum logic, i.e. the logical investigation of quantum mechanics, has undergone an enormous development. Various schools of thought and approaches have emerged and there are a variety of technical results.
Quantum logic is a heterogeneous field of research ranging from investigations which may be termed logical in the traditional sense to studies focusing on structures which are on the border between algebra and logic. For the latter structures the term quantum structures is appropriate.
The chapters of this Handbook, which are authored by the most eminent scholars in the field, constitute a comprehensive presentation of the main schools, approaches and results in the field of quantum logic and quantum structures. Much of the material presented is of recent origin representing the frontier of the subject.
The present volume focuses on quantum structures. Among the structures studied extensively in this volume are, just to name a few, Hilbert lattices, D-posets, effect algebras MV algebras, partially ordered Abelian groups and those structures underlying quantum probability.
- Written by eminent scholars in the field of logic
- A comprehensive presentation of the theory, approaches and results in the field of quantum logic
- Volume focuses on quantum structures

Numerical Methods for Roots of Polynomials - Part I, Volume 14 (Hardcover, 14th edition): J. M. McNamee Numerical Methods for Roots of Polynomials - Part I, Volume 14 (Hardcover, 14th edition)
J. M. McNamee
R5,052 Discovery Miles 50 520 Ships in 10 - 15 working days

This book (along with volume 2 covers most of the traditional methods for polynomial root-finding such as Newton s, as well as numerous variations on them invented in the last few decades. Perhaps more importantly it covers recent developments such as Vincent s method, simultaneous iterations, and matrix methods. There is an extensive chapter on evaluation of polynomials, including parallel methods and errors. There are pointers to robust and efficient programs. In short, it could be entitled A Handbook of Methods for Polynomial Root-finding . This book will be invaluable to anyone doing research in polynomial roots, or teaching a graduate course on that topic.


- First comprehensive treatment of Root-Finding in several decades.
- Gives description of high-grade software and where it can be down-loaded.
- Very up-to-date in mid-2006; long chapter on matrix methods.
- Includes Parallel methods, errors where appropriate.
- Invaluable for research or graduate course.

"

Viability, Invariance and Applications, Volume 207 (Hardcover, 207th edition): Ovidiu Carja, Mihai Necula, Ioan I. Vrabie Viability, Invariance and Applications, Volume 207 (Hardcover, 207th edition)
Ovidiu Carja, Mihai Necula, Ioan I. Vrabie
R4,086 Discovery Miles 40 860 Ships in 10 - 15 working days

The book is an almost self-contained presentation of the most important concepts and results in viability and invariance. The viability of a set K with respect to a given function (or multi-function) F, defined on it, describes the property that, for each initial data in K, the differential equation (or inclusion) driven by that function or multi-function) to have at least one solution. The invariance of a set K with respect to a function (or multi-function) F, defined on a larger set D, is that property which says that each solution of the differential equation (or inclusion) driven by F and issuing in K remains in K, at least for a short time.
The book includes the most important necessary and sufficient conditions for viability starting with Nagumo's Viability Theorem for ordinary differential equations with continuous right-hand sides and continuing with the corresponding extensions either to differential inclusions or to semilinear or even fully nonlinear evolution equations, systems and inclusions. In the latter (i.e. multi-valued) cases, the results (based on two completely new tangency concepts), all due to the authors, are original and extend significantly, in several directions, their well-known classical counterparts.
- New concepts for multi-functions as the classical tangent vectors for functions
- Provides the very general and necessary conditions for viability in the case of differential inclusions, semilinear and fully nonlinear evolution inclusions
- Clarifying examples, illustrations and numerous problems, completely and carefully solved
- Illustrates the applications from theory into practice
- Very clear and elegant style

Residuated Lattices: An Algebraic Glimpse at Substructural Logics, Volume 151 (Hardcover, 151st edition): Nikolaos Galatos,... Residuated Lattices: An Algebraic Glimpse at Substructural Logics, Volume 151 (Hardcover, 151st edition)
Nikolaos Galatos, Peter Jipsen, Tomasz Kowalski, Hiroakira Ono
R4,125 Discovery Miles 41 250 Ships in 10 - 15 working days

The book is meant to serve two purposes. The first and more obvious one is to present state of the art results in algebraic research into residuated structures related to substructural logics. The second, less obvious but equally important, is to provide a reasonably gentle introduction to algebraic logic. At the beginning, the second objective is predominant. Thus, in the first few chapters the reader will find a primer of universal algebra for logicians, a crash course in nonclassical logics for algebraists, an introduction to residuated structures, an outline of Gentzen-style calculi as well as some titbits of proof theory - the celebrated Hauptsatz, or cut elimination theorem, among them. These lead naturally to a discussion of interconnections between logic and algebra, where we try to demonstrate how they form two sides of the same coin. We envisage that the initial chapters could be used as a textbook for a graduate course, perhaps entitled Algebra and Substructural Logics.
As the book progresses the first objective gains predominance over the second. Although the precise point of equilibrium would be difficult to specify, it is safe to say that we enter the technical part with the discussion of various completions of residuated structures. These include Dedekind-McNeille completions and canonical extensions. Completions are used later in investigating several finiteness properties such as the finite model property, generation of varieties by their finite members, and finite embeddability. The algebraic analysis of cut elimination that follows, also takes recourse to completions. Decidability of logics, equational and quasi-equational theories comes next, where we show how proof theoretical methods like cut elimination are preferable for small logics/theories, but semantic tools like Rabin's theorem work better for big ones. Then we turn to Glivenko's theorem, which says that a formula is an intuitionistic tautology if and only if its double negation is a classical one. We generalise it to the substructural setting, identifying for each substructural logic its Glivenko equivalence class with smallest and largest element. This is also where we begin investigating lattices of logics and varieties, rather than particular examples. We continue in this vein by presenting a number of results concerning minimal varieties/maximal logics. A typical theorem there says that for some given well-known variety its subvariety lattice has precisely such-and-such number of minimal members (where values for such-and-such include, but are not limited to, continuum, countably many and two). In the last two chapters we focus on the lattice of varieties corresponding to logics without contraction. In one we prove a negative result: that there are no nontrivial splittings in that variety. In the other, we prove a positive one: that semisimple varieties coincide with discriminator ones.
Within the second, more technical part of the book another transition process may be traced. Namely, we begin with logically inclined technicalities and end with algebraically inclined ones. Here, perhaps, algebraic rendering of Glivenko theorems marks the equilibrium point, at least in the sense that finiteness properties, decidability and Glivenko theorems are of clear interest to logicians, whereas semisimplicity and discriminator varieties are universal algebra par exellence. It is for the reader to judge whether we succeeded in weaving these threads into a seamless fabric.
- Considers both the algebraic and logical perspective within a common framework.
- Written by experts in the area.
- Easily accessible to graduate students and researchers from other fields.
- Results summarized in tables and diagrams to provide an overview of the area.
- Useful as a textbook for a course in algebraic logic, with exercises and suggested research directions.
- Provides a concise introduction to the subject and leads directly to research topics.
- The ideas from algebra and logic are developed hand-in-hand and the connections are shown in every level.

Open Problems in Topology II (Hardcover, 2nd edition): Elliott M. Pearl Open Problems in Topology II (Hardcover, 2nd edition)
Elliott M. Pearl
R3,311 Discovery Miles 33 110 Ships in 10 - 15 working days

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

Handbook of Latent Variable and Related Models, Volume 1 (Hardcover): Sik--Yum Lee Handbook of Latent Variable and Related Models, Volume 1 (Hardcover)
Sik--Yum Lee
R4,950 Discovery Miles 49 500 Ships in 10 - 15 working days

This Handbook covers latent variable models, which are a flexible class of models for modeling multivariate data to explore relationships among observed and latent variables.
- Covers a wide class of important models
- Models and statistical methods described provide tools for analyzing a wide spectrum of complicated data
- Includes illustrative examples with real data sets from business, education, medicine, public health and sociology.
- Demonstrates the use of a wide variety of statistical, computational, and mathematical techniques.

Leonhard Euler, Volume 5 - Life, Work and Legacy (Hardcover, 5th edition): Robert E. Bradley, Ed Sandifer Leonhard Euler, Volume 5 - Life, Work and Legacy (Hardcover, 5th edition)
Robert E. Bradley, Ed Sandifer
R5,364 Discovery Miles 53 640 Ships in 10 - 15 working days

The year 2007 marks the 300th anniversary of the birth of one of the Enlightenment's most important mathematicians and scientists, Leonhard Euler. This volume is a collection of 24 essays by some of the world's best Eulerian scholars from seven different countries about Euler, his life and his work.
Some of the essays are historical, including much previously unknown information about Euler's life, his activities in the St. Petersburg Academy, the influence of the Russian Princess Dashkova, and Euler's philosophy. Others describe his influence on the subsequent growth of European mathematics and physics in the 19th century. Still others give technical details of Euler's innovations in probability, number theory, geometry, analysis, astronomy, mechanics and other fields of mathematics and science.
- Over 20 essays by some of the best historians of mathematics and science, including Ronald Calinger, Peter Hoffmann, Curtis Wilson, Kim Plofker, Victor Katz, Ruediger Thiele, David Richeson, Robin Wilson, Ivor Grattan-Guinness and Karin Reich
- New details of Euler's life in two essays, one by Ronald Calinger and one he co-authored with Elena Polyakhova
- New information on Euler's work in differential geometry, series, mechanics, and other important topics including his influence in the early 19th century

Difference Equations in Normed Spaces, Volume 206 - Stability and Oscillations (Hardcover, 206th edition): Michael Gil Difference Equations in Normed Spaces, Volume 206 - Stability and Oscillations (Hardcover, 206th edition)
Michael Gil
R4,096 Discovery Miles 40 960 Ships in 10 - 15 working days

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

Handbook of Differential Equations: Ordinary Differential Equations, Volume 3 (Hardcover, 3rd edition): A Canada, P. Drabek, A... Handbook of Differential Equations: Ordinary Differential Equations, Volume 3 (Hardcover, 3rd edition)
A Canada, P. Drabek, A Fonda
R6,849 Discovery Miles 68 490 Ships in 10 - 15 working days

This handbook is the third volume in a series of volumes devoted to self contained and up-to-date surveys in the tehory of ordinary differential equations, written by leading researchers in the area. All contributors have made an additional effort to achieve readability for mathematicians and scientists from other related fields so that the chapters have been made accessible to a wide audience.
These ideas faithfully reflect the spirit of this multi-volume and hopefully it becomes a very useful tool for reseach, learing and teaching. This volumes consists of seven chapters covering a variety of problems in ordinary differential equations. Both pure mathematical research and real word applications are reflected by the contributions to this volume.
- Covers a variety of problems in ordinary differential equations
- Pure mathematical and real world applications
- Written for mathematicians and scientists of many related fields

Integral and Finite Difference Inequalities and Applications, Volume 205 (Hardcover): B.G. Pachpatte Integral and Finite Difference Inequalities and Applications, Volume 205 (Hardcover)
B.G. Pachpatte
R5,037 Discovery Miles 50 370 Ships in 10 - 15 working days

The monograph is written with a view to provide basic tools for researchers working in Mathematical Analysis and Applications, concentrating on differential, integral and finite difference equations. It contains many inequalities which have only recently appeared in the literature and which can be used as powerful tools and will be a valuable source for a long time to come. It is self-contained and thus should be useful for those who are interested in learning or applying the inequalities with explicit estimates in their studies.
- Contains a variety of inequalities discovered which find numerous applications in various branches of differential, integral and finite difference equations.
- Many inequalities which have only recently discovered in the literature and can not yet be found in bother book.
- A valuable reference for someone requiring results about inequalities for use in some applications in various other branches of mathematics.
- Will be of interest to researchers working both in pure and applied mathematics and other areas of science and technology, and it could also be used as a text for an advanced graduate course.
- Contains a variety of inequalities discovered which find numerous applications in various branches of differential, integral and finite difference equations
- Valuable reference for someone requiring results about inequalities for use in some applications in various other branches of mathematics
- Highlights pure and applied mathematics and other areas of science and technology

Relation Algebras, Volume 150 (Hardcover): Roger Duncan Maddux Relation Algebras, Volume 150 (Hardcover)
Roger Duncan Maddux
R7,227 Discovery Miles 72 270 Ships in 10 - 15 working days

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

Topics in Multivariate Approximation and Interpolation, Volume 12 (Hardcover): Kurt Jetter, Martin Buhmann, Werner Haussmann,... Topics in Multivariate Approximation and Interpolation, Volume 12 (Hardcover)
Kurt Jetter, Martin Buhmann, Werner Haussmann, Robert Schaback, Joachim Stoeckler
R6,018 Discovery Miles 60 180 Ships in 10 - 15 working days

This book is a collection of eleven articles, written by leading experts and dealing with special topics in Multivariate Approximation and Interpolation. The material discussed here has far-reaching applications in many areas of Applied Mathematics, such as in Computer Aided Geometric Design, in Mathematical Modelling, in Signal and Image Processing and in Machine Learning, to mention a few. The book aims at giving a comprehensive information leading the reader from the fundamental notions and results of each field to the forefront of research. It is an ideal and up-to-date introduction for graduate students specializing in these topics, and for researchers in universities and in industry.


- A collection of articles of highest scientific standard.
- An excellent introduction and overview of recent topics from multivariate approximation.
- A valuable source of references for specialists in the field.
- A representation of the state-of-the-art in selected areas of multivariate approximation.
- A rigorous mathematical introduction to special topics of interdisciplinary research.

Materials Processing and Manufacturing Science (Hardcover): Rajiv Asthana, Ashok Kumar, Narendra B. Dahotre Materials Processing and Manufacturing Science (Hardcover)
Rajiv Asthana, Ashok Kumar, Narendra B. Dahotre
R3,719 Discovery Miles 37 190 Ships in 10 - 15 working days

"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

Elliptic Boundary Value Problems of Second Order in Piecewise Smooth Domains, Volume 69 (Hardcover, 69th edition): Michail... Elliptic Boundary Value Problems of Second Order in Piecewise Smooth Domains, Volume 69 (Hardcover, 69th edition)
Michail Borsuk, Vladimir Kondratiev
R6,189 Discovery Miles 61 890 Ships in 10 - 15 working days

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.

Linear Discrete Parabolic Problems, Volume 203 (Hardcover, 203rd edition): Nikolai Bakaev Linear Discrete Parabolic Problems, Volume 203 (Hardcover, 203rd edition)
Nikolai Bakaev
R4,755 Discovery Miles 47 550 Ships in 10 - 15 working days

This volume introduces a unified, self-contained study of linear discrete parabolic problems through reducing the starting discrete problem to the Cauchy problem for an evolution equation in discrete time. Accessible to beginning graduate students, the book contains a general stability theory of discrete evolution equations in Banach space and gives applications of this theory to the analysis of various classes of modern discretization methods, among others, Runge-Kutta and linear multistep methods as well as operator splitting methods.


Key features:


* Presents a unified approach to examining discretization methods for parabolic equations.
* Highlights a stability theory of discrete evolution equations (discrete semigroups) in Banach space.
* Deals with both autonomous and non-autonomous equations as well as with equations with memory.
* Offers a series of numerous well-posedness and convergence results for various discretization methods as applied to abstract parabolic equations; among others, Runge-Kutta and linear multistep methods as well as certain operator splitting methods.
* Provides comments of results and historical remarks after each chapter.
. Presents a unified approach to examining discretization methods for parabolic equations.
. Highlights a stability theory of discrete evolution equations (discrete semigroups) in Banach space.
. Deals with both autonomous and non-autonomous equations as well as with equations with memory.
. Offers a series of numerous well-posedness and convergence results for various discretization methods as applied to abstract parabolic equations; among others, Runge-Kutta and linear multistep methods as well as certain operator splitting methods as well as certain operator splitting methods are studied in detail.
.Provides comments of results and historical remarks after each chapter."

Handbook of Differential Equations: Evolutionary Equations, Volume 2 (Hardcover, New): C.M. Dafermos, Eduard Feireisl Handbook of Differential Equations: Evolutionary Equations, Volume 2 (Hardcover, New)
C.M. Dafermos, Eduard Feireisl
R6,962 Discovery Miles 69 620 Ships in 10 - 15 working days

The aim of this Handbook is to acquaint the reader with the current status of the theory of evolutionary partial differential equations, and with some of its applications. Evolutionary partial differential equations made their first appearance in the 18th century, in the endeavor to understand the motion of fluids and other continuous media. The active research effort over the span of two centuries, combined with the wide variety of physical phenomena that had to be explained, has resulted in an enormous body of literature. Any attempt to produce a comprehensive survey would be futile. The aim here is to collect review articles, written by leading experts, which will highlight the present and expected future directions of development of the field. The emphasis will be on nonlinear equations, which pose the most challenging problems today.
. Volume I of this Handbook does focus on the abstract theory of evolutionary equations.
. Volume 2 considers more concrete problems relating to specific applications.
. Together they provide a panorama of this amazingly complex and rapidly developing branch of mathematics.

Handbook of Differential Equations: Ordinary Differential Equations, Volume 2 (Hardcover, 2nd edition): A Canada, P. Drabek, A... Handbook of Differential Equations: Ordinary Differential Equations, Volume 2 (Hardcover, 2nd edition)
A Canada, P. Drabek, A Fonda
R6,795 Discovery Miles 67 950 Ships in 10 - 15 working days

This handbook is the second volume in a series devoted to self contained and up-to-date surveys in the theory of ordinary differential equations, written
by leading researchers in the area. All contributors have made an additional effort to achieve readability for mathematicians and scientists from other related fields, in order to make the chapters of the volume accessible to a wide audience.
. Six chapters covering a variety of problems in ordinary differential equations.
. Both, pure mathematical research and real word applications are reflected
. Written by leading researchers in the area.

Topological Algebras with Involution, Volume 200 (Hardcover): M Fragoulopoulou Topological Algebras with Involution, Volume 200 (Hardcover)
M Fragoulopoulou
R5,664 Discovery Miles 56 640 Ships in 10 - 15 working days

This book familiarizes both popular and fundamental notions and techniques from the theory of non-normed topological algebras with involution, demonstrating with examples and basic results the necessity of this perspective. The main body of the book is focussed on the Hilbert-space (bounded) representation theory of topological *-algebras and their topological tensor products, since in our physical world, apart from the majority of the existing unbounded operators, we often meet operators that are forced to be bounded, like in the case of symmetric *-algebras. So, one gets an account of how things behave, when the mathematical structures are far from being algebras endowed with a complete or non-complete algebra norm. In problems related with mathematical physics, such instances are, indeed, quite common.


Key features:


- Lucid presentation
- Smooth in reading
- Informative
- Illustrated by examples
- Familiarizes the reader with the non-normed *-world
- Encourages the hesitant
- Welcomes new comers.
- Well written and lucid presentation.
- Informative and illustrated by examples.
- Familiarizes the reader with the non-normed *-world.

Infinite Dimensional Linear Control Systems, Volume 201 - The Time Optimal and Norm Optimal Problems (Hardcover): H.O. Fattorini Infinite Dimensional Linear Control Systems, Volume 201 - The Time Optimal and Norm Optimal Problems (Hardcover)
H.O. Fattorini
R4,770 Discovery Miles 47 700 Ships in 10 - 15 working days

For more than forty years, the equation y (t) = Ay(t) + u(t) in Banach spaces has been used as model for optimal control processes described by partial differential equations, in particular heat and diffusion processes. Many of the outstanding open problems, however, have remained open until recently, and some have never been solved. This book is a survey of all results know to the author, with emphasis on very recent results (1999 to date).


The book is restricted to linear equations and two particular problems (the time optimal problem, the norm optimal problem) which results in a more focused and concrete treatment. As experience shows, results on linear equations are the basis for the treatment of their semilinear counterparts, and techniques for the time and norm optimal problems can often be generalized to more general cost functionals.


The main object of this book is to be a state-of-the-art monograph on the theory of the time and norm optimal controls for y (t) = Ay(t) + u(t) that ends at the very latest frontier of research, with open problems and indications for future research.


Key features:


. Applications to optimal diffusion processes.
. Applications to optimal heat propagation processes.
. Modelling of optimal processes governed by partial
differential equations.
. Complete bibliography.
. Includes the latest research on the subject.
. Does not assume anything from the reader except
basic functional analysis.
. Accessible to researchers and advanced graduate
students alike
. Applications to optimal diffusion processes.
. Applications to optimal heat propagation processes.
. Modelling of optimal processes governed by partial
differential equations.
. Complete bibliography.
. Includes the latest research on the subject.
. Does not assume anything from the reader except
basic functional analysis.
. Accessible to researchers and advanced graduate
students alike"

Half-Linear Differential Equations, Volume 202 (Hardcover, New): Ondrej Dosly, Pavel Reh ak Half-Linear Differential Equations, Volume 202 (Hardcover, New)
Ondrej Dosly, Pavel Reh ak
R5,484 Discovery Miles 54 840 Ships in 10 - 15 working days

The book presents a systematic and compact treatment of the qualitative theory of half-linear
differential equations. It contains the most updated and comprehensive material and represents the first attempt to present the results of the rapidly developing theory of half-linear differential equations in a unified form. The main topics covered by the book are oscillation and asymptotic theory and the theory of boundary value problems associated with half-linear equations, but the book also contains a treatment of related topics like PDE s with p-Laplacian, half-linear difference equations and various more general nonlinear differential equations.
- The first complete treatment of the qualitative theory of half-linear differential equations.
- Comparison of linear and half-linear theory.
- Systematic approach to half-linear oscillation and asymptotic theory.
- Comprehensive bibliography and index.
- Useful as a reference book in the topic.

A Practical Logic of Cognitive Systems - The Reach of Abduction: Insight and Trial (Hardcover): Dov M. Gabbay, John Woods A Practical Logic of Cognitive Systems - The Reach of Abduction: Insight and Trial (Hardcover)
Dov M. Gabbay, John Woods
R6,041 Discovery Miles 60 410 Ships in 10 - 15 working days

The present work is a continuation of the authors' acclaimed multi-volume A
Practical Logic of Cognitive Systems. After having investigated the notion of
relevance in their previous volume, Gabbay and Woods now turn to abduction. In
this highly original approach, abduction is construed as ignorance-preserving
inference, in which conjecture plays a pivotal role. Abduction is a response to a
cognitive target that cannot be hit on the basis of what the agent currently knows.
The abducer selects a hypothesis which were it true would enable the reasoner to attain his target. He concludes from this fact that the hypothesis may be conjectured. In allowing conjecture to stand in for the knowledge he fails to have, the abducer reveals himself to be a satisficer, since an abductive solution is not a solution from knowledge. Key to the authors' analysis is the requirement that a conjectured proposition is not just what a reasoner might allow himself to assume, but a proposition he must defeasibly release as a premiss for further inferences in the domain of enquiry in which the original abduction problem has arisen.


The coverage of the book is extensive, from the philosophy of science to
computer science and AI, from diagnostics to the law, from historical explanation to linguistic interpretation. One of the volume's strongest contributions is its exploration of the abductive character of criminal trials, with special attention given to the standard of proof beyond a reasonable doubt.


Underlying their analysis of abductive reasoning is the authors' conception of
practical agency. In this approach, practical agency is dominantly a matter of the
comparativemodesty of an agent's cognitive agendas, together with comparatively scant resources available for their advancement. Seen in these ways, abduction has a significantly practical character, precisely because it is a form of inference that satisfices rather than maximizes its response to the agent's cognitive target.


The Reach of Abduction will be necessary reading for researchers, graduate
students and senior undergraduates in logic, computer science, AI, belief dynamics, argumentation theory, cognitive psychology and neuroscience, linguistics, forensic science, legal reasoning and related areas.


Key features:


- Reach of Abduction is fully integrated with a background logic of cognitive systems.

- The most extensive coverage compared to competitive works.

- Demonstrates not only that abduction is a form of ignorance preserving
inference but that it is a mode of inference that is wholly rational.

- Demonstrates the satisficing rather than maximizing character of
abduction.

- The development of formal models of abduction is considerably more extensive than one finds in existing literature. It is an especially impressive amalgam of sophisticated
conceptual analysis and extensive logical modelling.
- Reach of Abduction is fully integrated with a background logic of cognitive systems.
- The most extensive coverage compared to competitive works
- Demonstrates not only that abduction is a form of ignorance preserving
inference but that it is a mode of inference that is wholly rational.
- Demonstrates the satisficing rather than maximizing character of
abduction.
- The development of formal models of abduction isconsiderably more extensive than one finds in existing literature. It is an especially impressive amalgam of sophisticated
conceptual analysis and extensive logical modelling.

Mathematical Inequalities, Volume 67 (Hardcover, New): B.G. Pachpatte Mathematical Inequalities, Volume 67 (Hardcover, New)
B.G. Pachpatte
R7,314 Discovery Miles 73 140 Ships in 10 - 15 working days

The book addresses many important new developments in the field. All the topics covered are of great interest to the readers because such inequalities have become a major tool in the analysis of various branches of mathematics.
* It contains a variety of inequalities which find numerous applications in various branches of mathematics.
* It contains many inequalities which have only recently appeared in the literature and cannot yet be found in other books.
* It will be a valuable reference for someone requiring a result about inequalities for use in some applications in various other branches of mathematics.
* Each chapter ends with some miscellaneous inequalities for futher study.
* The work will be of interest to researchers working both in pure and applied mathematics, and it could also be used as the text for an advanced graduate course.

Ten Mathematical Essays on Approximation in Analysis and Topology - Ten Mathematical Essays (Hardcover): J. Ferrera, J.... Ten Mathematical Essays on Approximation in Analysis and Topology - Ten Mathematical Essays (Hardcover)
J. Ferrera, J. Lopez-Gomez, F. R. Ruiz del Portal
R5,855 Discovery Miles 58 550 Ships in 10 - 15 working days

This book collects 10 mathematical essays on approximation in Analysis and Topology by some of the most influent mathematicians of the last third of the 20th Century. Besides the papers contain the very ultimate results in each of their respective fields, many of them also include a series of historical remarks about the state of mathematics at the time they found their most celebrated results, as well as some of their personal circumstances originating them, which makes particularly attractive the book for all scientist interested in these fields, from beginners to experts. These gem pieces of mathematical intra-history should delight to many forthcoming generations of mathematicians, who will enjoy some of the most fruitful mathematics of the last third of 20th century presented by their own authors.


This book covers a wide range of new mathematical results. Among them, the most advanced characterisations of very weak versions of the classical maximum principle, the very last results on global bifurcation theory, algebraic multiplicities, general dependencies of solutions of boundary value problems with respect to variations of the underlying domains, the deepest available results in rapid monotone schemes applied to the resolution of non-linear boundary value problems, the intra-history of the the genesis of the first general global continuation results in the context of periodic solutions of nonlinear periodic systems, as well as the genesis of the coincidence degree, some novel applications of the topological degree for ascertaining the stability of the periodic solutions of some classical families of periodic second order equations,
the resolution of a number of conjectures related to some very celebrated approximation problems in topology and inverse problems, as well as a number of applications to engineering, an extremely sharp discussion of the problem of approximating topological spaces by polyhedra using various techniques based on inverse systems, as well as homotopy expansions, and the Bishop-Phelps theorem.


Key features:


- It contains a number of seminal contributions by some of the most world leading mathematicians of the second half of the 20th Century.


- The papers cover a complete range of topics, from the intra-history of the involved mathematics to the very last developments in Differential Equations, Inverse Problems, Analysis, Nonlinear Analysis and Topology.


- All contributed papers are self-contained works containing rather complete list of references on each of the subjects covered.


- The book contains some of the very last findings concerning the maximum principle, the theory of monotone schemes in nonlinear problems, the theory of algebraic multiplicities, global bifurcation theory, dynamics of periodic equations and systems, inverse problems and approximation in topology.


- The papers are extremely well written and directed to a wide audience, from beginners to experts. An excellent occasion to become engaged with some of the most fruitful mathematics developed during the last decades.
. It contains a number of seminal contributions by some of the most world leading mathematicians of the second half of the 20th Century.
. The papers cover a complete range of topics, from the intra-history of the involved mathematics to the very last developments in Differential Equations, Inverse Problems, Analysis, Nonlinear Analysis and Topology.
. All contributed papers are self-contained works containing rather complete list of references on each of the subjects covered.
. The book contains some of the very last findings concerning the maximum principle, the theory of monotone schemes in nonlinear problems, the theory of algebraic multiplicities, global bifurcation theory, dynamics of periodic equations and systems, inverse problems and approximation in topology.
. The papers are extremely well written and directed to a wide audience, from beginners to experts. An excellent occasion to become engaged with some of the most fruitful mathematics developed during the last decades."

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