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Books in Mathematics

The Mathematics collection presents a range of foundational and advanced research content across applied and discrete mathematics, including fields such as Computational Mathematics; Differential Equations; Linear Algebra; Modelling & Simulation; Numerical Analysis; Probability & Statistics.

BooksJournals

    • Perturbation Theory for Matrix Equations

      • 1st Edition
      • Volume 9
      • May 20, 2003
      • M. Konstantinov + 3 more
      • English
      • Hardback
        9 7 8 0 4 4 4 5 1 3 1 5 1
      • eBook
        9 7 8 0 0 8 0 5 3 8 6 7 9
      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

    • Mathematical Models of Hysteresis and their Applications

      • 1st Edition
      • August 15, 2003
      • Isaak D. Mayergoyz
      • English
      • Hardback
        9 7 8 0 1 2 4 8 0 8 7 3 7
      • Paperback
        9 7 8 0 1 2 3 9 9 2 4 4 4
      • eBook
        9 7 8 0 0 8 0 5 3 5 8 9 0
      This new edition has been significantly revised and updated to reflect advances in the field since the publication of the first edition, such as the systematic experimental testing of Preisach models of hysteresis. The author has, however, retained the two most salient features of the original, the emphasis on the universal nature of mathematical models of hysteresis and their applicability to the description of hysteresis phenomena in various areas of science, technology and economics and its accessibility to a broad audience of researchers, engineers, and students.

    • Foundations of Complex Analysis in Non Locally Convex Spaces

      • 1st Edition
      • Volume 193
      • November 11, 2003
      • A. Bayoumi
      • English
      • Hardback
        9 7 8 0 4 4 4 5 0 0 5 6 4
      • eBook
        9 7 8 0 0 8 0 5 3 1 9 2 2
      All the existing books in Infinite Dimensional Complex Analysis focus on the problems of locally convex spaces. However, the theory without convexity condition is covered for the first time in this book. This shows that we are really working with a new, important and interesting field.Theory of functions and nonlinear analysis problems are widespread in the mathematical modeling of real world systems in a very broad range of applications. During the past three decades many new results from the author have helped to solve multiextreme problems arising from important situations, non-convex and non linear cases, in function theory.Foundations of Complex Analysis in Non Locally Convex Spaces is a comprehensive book that covers the fundamental theorems in Complex and Functional Analysis and presents much new material.The book includes generalized new forms of: Hahn-Banach Theorem, Multilinear maps, theory of polynomials, Fixed Point Theorems, p-extreme points and applications in Operations Research, Krein-Milman Theorem, Quasi-differential Calculus, Lagrange Mean-Value Theorems, Taylor series, Quasi-holomorphic and Quasi-analytic maps, Quasi-Analytic continuations, Fundamental Theorem of Calculus, Bolzano's Theorem, Mean-Value Theorem for Definite Integral, Bounding and weakly-bounding (limited) sets, Holomorphic Completions, and Levi problem.Each chapter contains illustrative examples to help the student and researcher to enhance his knowledge of theory of functions.The new concept of Quasi-differentiabil... introduced by the author represents the backbone of the theory of Holomorphy for non-locally convex spaces. In fact it is different but much stronger than the Frechet one.The book is intended not only for Post-Graduate (M.Sc.& Ph.D.) students and researchers in Complex and Functional Analysis, but for all Scientists in various disciplines whom need nonlinear or non-convex analysis and holomorphy methods without convexity conditions to model and solve problems.bull; The book contains new generalized versions of:i) Fundamental Theorem of Calculus, Lagrange Mean-Value Theorem in real and complex cases, Hahn-Banach Theorems, Bolzano Theorem, Krein-Milman Theorem, Mean value Theorem for Definite Integral, and many others.ii) Fixed Point Theorems of Bruower, Schauder and Kakutani's. bull; The book contains some applications in Operations research and non convex analysis as a consequence of the new concept p-Extreme points given by the author.bull; The book contains a complete theory for Taylor Series representations of the different types of holomorphic maps in F-spaces without convexity conditions. bull; The book contains a general new concept of differentiability stronger than the Frechet one. This implies a new Differentiable Calculus called Quasi-differential (or Bayoumi differential) Calculus. It is due to the author's discovery in 1995.bull; The book contains the theory of polynomials and Banach Stienhaus theorem in non convex spaces.

    • Many-Dimensional Modal Logics: Theory and Applications

      • 1st Edition
      • Volume 148
      • October 21, 2003
      • A. Kurucz + 3 more
      • English
      • Hardback
        9 7 8 0 4 4 4 5 0 8 2 6 3
      • Paperback
        9 7 8 0 4 4 4 5 5 1 8 3 2
      • eBook
        9 7 8 0 0 8 0 5 3 5 7 8 4
      Modal logics, originally conceived in philosophy, have recently found many applications in computer science, artificial intelligence, the foundations of mathematics, linguistics and other disciplines. Celebrated for their good computational behaviour, modal logics are used as effective formalisms for talking about time, space, knowledge, beliefs, actions, obligations, provability, etc. However, the nice computational properties can drastically change if we combine some of these formalisms into a many-dimensional system, say, to reason about knowledge bases developing in time or moving objects.To study the computational behaviour of many-dimensional modal logics is the main aim of this book. On the one hand, it is concerned with providing a solid mathematical foundation for this discipline, while on the other hand, it shows that many seemingly different applied many-dimensional systems (e.g., multi-agent systems, description logics with epistemic, temporal and dynamic operators, spatio-temporal logics, etc.) fit in perfectly with this theoretical framework, and so their computational behaviour can be analyzed using the developed machinery.We start with concrete examples of applied one- and many-dimensional modal logics such as temporal, epistemic, dynamic, description, spatial logics, and various combinations of these. Then we develop a mathematical theory for handling a spectrum of 'abstract' combinations of modal logics - fusions and products of modal logics, fragments of first-order modal and temporal logics - focusing on three major problems: decidability, axiomatizability, and computational complexity. Besides the standard methods of modal logic, the technical toolkit includes the method of quasimodels, mosaics, tilings, reductions to monadic second-order logic, algebraic logic techniques. Finally, we apply the developed machinery and obtained results to three case studies from the field of knowledge representation and reasoning: temporal epistemic logics for reasoning about multi-agent systems, modalized description logics for dynamic ontologies, and spatio-temporal logics.The genre of the book can be defined as a research monograph. It brings the reader to the front line of current research in the field by showing both recent achievements and directions of future investigations (in particular, multiple open problems). On the other hand, well-known results from modal and first-order logic are formulated without proofs and supplied with references to accessible sources.The intended audience of this book is logicians as well as those researchers who use logic in computer science and artificial intelligence. More specific application areas are, e.g., knowledge representation and reasoning, in particular, terminological, temporal and spatial reasoning, or reasoning about agents. And we also believe that researchers from certain other disciplines, say, temporal and spatial databases or geographical information systems, will benefit from this book as well.Key Features:• Integrated approach to modern modal and temporal logics and their applications in artificial intelligence and computer science• Written by internationally leading researchers in the field of pure and applied logic• Combines mathematical theory of modal logic and applications in artificial intelligence and computer science• Numerous open problems for further research• Well illustrated with pictures and tables

    • Recent Advances and Trends in Nonparametric Statistics

      • 1st Edition
      • October 31, 2003
      • M.G. Akritas + 1 more
      • English
      • Hardback
        9 7 8 0 4 4 4 5 1 3 7 8 6
      • eBook
        9 7 8 0 0 8 0 5 4 0 3 7 5
      The advent of high-speed, affordable computers in the last two decades has given a new boost to the nonparametric way of thinking. Classical nonparametric procedures, such as function smoothing, suddenly lost their abstract flavour as they became practically implementable. In addition, many previously unthinkable possibilities became mainstream; prime examples include the bootstrap and resampling methods, wavelets and nonlinear smoothers, graphical methods, data mining, bioinformatics, as well as the more recent algorithmic approaches such as bagging and boosting. This volume is a collection of short articles - most of which having a review component - describing the state-of-the art of Nonparametric Statistics at the beginning of a new millennium.Key features:• algorithic approaches• wavelets and nonlinear smoothers• graphical methods and data mining• biostatistics and bioinformatics• bagging and boosting• support vector machines• resampling methods

    • Networks and Graphs

      • 1st Edition
      • January 1, 2003
      • D K Smith
      • English
      • Hardback
        9 7 8 1 8 9 8 5 6 3 9 1 4
      • eBook
        9 7 8 0 8 5 7 0 9 9 5 7 0
      Dr Smith here presents essential mathematical and computational ideas of network optimisation for senior undergraduate and postgraduate students in mathematics, computer science and operational research. He shows how algorithms can be used for finding optimal paths and flows, identifying trees in networks, and optimal matching. Later chapters discuss postman and salesperson tours, and demonstrate how many network problems are related to the ‘‘minimal-cost feasible-flow’’ problem. Techniques are presented both informally and with mathematical rigour and aspects of computation, especially of complexity, have been included. Numerous examples and diagrams illustrate the techniques and applications. The book also includes problem exercises with tutorial hints.

    • Mathematical Modelling in Education and Culture

      • 1st Edition
      • May 1, 2003
      • Q-X Ye + 3 more
      • English
      • Hardback
        9 7 8 1 9 0 4 2 7 5 0 5 3
      • eBook
        9 7 8 0 8 5 7 0 9 9 5 5 6
      The mathematical modelling movement in mathematics education at school and university level has been influencing curricula for about 25 years. Lecturers will find material to enhance their teaching and extracurricular activities and educators will find innovative ideas to inform their course design and focus their research, while students will find interesting problems to explore.

    • Calculations for Molecular Biology and Biotechnology

      • 1st Edition
      • June 30, 2003
      • Frank H. Stephenson
      • English
      • eBook
        9 7 8 0 0 8 0 5 0 0 6 1 4
      Calculations in Molecular Biology and Biotechnology: A Guide to Mathematics in the Laboratory is the first comprehensive guide devoted exclusively to calculations encountered in the genetic engineering laboratory. Mathematics, as a vital component of the successful design and interpretation of basic research, is used daily in laboratory work. This guide, written for students, technicians, and scientists, provides example calculations for the most frequently confronted problems encountered in gene discovery and analysis. The text and sample calculations are written in an easy-to-follow format. It is the perfect laboratory companion for anyone working in DNA manipulation and analysis.

    • Finite Element Method

      • 1st Edition
      • February 21, 2003
      • G.R. Liu + 1 more
      • English
      • Paperback
        9 7 8 0 7 5 0 6 5 8 6 6 9
      • eBook
        9 7 8 0 0 8 0 4 7 2 7 6 8
      The Finite Element Method (FEM) has become an indispensable technology for the modelling and simulation of engineering systems. Written for engineers and students alike, the aim of the book is to provide the necessary theories and techniques of the FEM for readers to be able to use a commercial FEM package to solve primarily linear problems in mechanical and civil engineering with the main focus on structural mechanics and heat transfer.Fundamental theories are introduced in a straightforward way, and state-of-the-art techniques for designing and analyzing engineering systems, including microstructural systems are explained in detail. Case studies are used to demonstrate these theories, methods, techniques and practical applications, and numerous diagrams and tables are used throughout.The case studies and examples use the commercial software package ABAQUS, but the techniques explained are equally applicable for readers using other applications including NASTRAN, ANSYS, MARC, etc.

Related subjects

Mathematics and applied mathematics

Statistics and probability