Books in Mathematics and applied mathematics

Representations of Commonsense Knowledge

1st Edition
July 10, 2014
Ernest Davis
Ronald J. Brachman
English
eBook
9 7 8 1 4 8 3 2 2 1 1 3 7

Representations of Commonsense Knowledge provides a rich language for expressing commonsense knowledge and inference techniques for carrying out commonsense knowledge. This book provides a survey of the research on commonsense knowledge. Organized into 10 chapters, this book begins with an overview of the basic ideas on artificial intelligence commonsense reasoning. This text then examines the structure of logic, which is roughly analogous to that of a programming language. Other chapters describe how rules of universal validity can be applied to facts known with absolute certainty to deduce other facts known with absolute certainty. This book discusses as well some prominent issues in plausible inference. The final chapter deals with commonsense knowledge about the interrelations and interactions among agents and discusses some issues in human and social interactions that have been studied in the artificial intelligence literature. This book is a valuable resource for students on a graduate course on knowledge representation.

Computational Geometry

1st Edition
May 10, 2014
Su Bu-qing + 1 more
English
eBook
9 7 8 1 4 8 3 2 7 2 2 8 3

Computational Geometry: Curve and Surface Modeling provides information pertinent to the fundamental aspects of computational geometry. This book discusses the geometric properties of parametric polynomial curves by using the theory of affine invariants for algebraic curves. Organized into eight chapters, this book begins with an overview of the objects studies in computational geometry, namely surfaces and curves. This text then explores the developments in the theory and application of spline functions, which began with cubic spline functions. Other chapters consider the mechanical background of the cubic spline functions, which is the wooden spline with small deflection. This book discusses as well that in mathematical lofting the information of a geometric shape is given by a set of data points, while in geometric design other ways of representations are available. The final chapter deals with the concepts in the theory of algebraic curves. This book is a valuable resource for mathematicians.

Asymptotic Approximations of Integrals

1st Edition
May 10, 2014
R. Wong
Werner Rheinboldt + 1 more
English
eBook
9 7 8 1 4 8 3 2 2 0 7 1 0

Asymptotic Approximations of Integrals deals with the methods used in the asymptotic approximation of integrals. Topics covered range from logarithmic singularities and the summability method to the distributional approach and the Mellin transform technique for multiple integrals. Uniform asymptotic expansions via a rational transformation are also discussed, along with double integrals with a curve of stationary points. For completeness, classical methods are examined as well. Comprised of nine chapters, this volume begins with an introduction to the fundamental concepts of asymptotics, followed by a discussion on classical techniques used in the asymptotic evaluation of integrals, including Laplace's method, Mellin transform techniques, and the summability method. Subsequent chapters focus on the elementary theory of distributions; the distributional approach; uniform asymptotic expansions; and integrals which depend on auxiliary parameters in addition to the asymptotic variable. The book concludes by considering double integrals and higher-dimensional integrals. This monograph is intended for graduate students and research workers in mathematics, physics, and engineering.

Geometry of Manifolds

1st Edition
August 28, 1989
K. Shiohama
English
eBook
9 7 8 0 0 8 0 9 2 5 7 8 3

This volume contains the papers presented at a symposium on differential geometry at Shinshu University in July of 1988. Carefully reviewed by a panel of experts, the papers pertain to the following areas of research: dynamical systems, geometry of submanifolds and tensor geometry, lie sphere geometry, Riemannian geometry, Yang-Mills Connections, and geometry of the Laplace operator.

Rewriting Techniques

1st Edition
May 10, 2014
Hassan Aït-Kaci + 1 more
English
eBook
9 7 8 1 4 8 3 2 5 9 6 7 3

Resolution of Equations in Algebraic Structures: Volume 2, Rewriting Techniques is a collection of papers dealing with the construction of canonical rewrite systems, constraint handling in logic programming, and completion algorithms for conditional rewriting systems. Papers discuss the Knuth-Bendix completion method which constructs a complete system for a given set of equations, including extensions of the method dealing with termination, unfailing completion, and associative-communic... completion. One paper examines the various practical techniques that can be used to extend Prolog as a constraint solver, particularly on techniques that solve boolean equations, imposing inequality, disequality, and finitary domain constraints on variables. Another paper presents a sufficient condition for confluence of conditional rewriting, and a practical unification algorithm modulo conditional rewriting through the notion of conditional narrowing. One paper analyzes the possibility of using completion for inductive proofs in the initial algebra of an equational variety without explicit induction. Another papers discusses solving systems of word equations in the free monoid and the free group, where a solution is defined as a word homomorphism. Programmers, mathematicians, students, and instructors involved in computer science and computer logic will find this collection valuable.

The Desktop Fractal Design Handbook

1st Edition
May 10, 2014
Michael F. Barnsley
English
eBook
9 7 8 1 4 8 3 2 6 5 4 8 3

The Desktop Fractal Design Handbook is a four-chapter introductory text to fractal geometry. The underlying algorithms are derived from mathematics, which is reflected in the images they produce. Chapter 1 provides an overview of the products of the desktop fractal design system. Chapter 2 describes the installation and operation of hardware and operating system of the design system, along with its maintenance. Chapter 3 outlines the use of the desktop fractal design system, specifically on hot to design fractals on the fractal design screen, maps, paintings, and help screens. Chapter 4 focuses on the many practical applications of fractals. This book will be of value to mathematicians, engineers, graphic artists, teachers, and students.

Rational Politics

1st Edition
May 10, 2014
Steven J. Brams
English
eBook
9 7 8 1 4 8 3 2 5 8 5 7 7

Rational Politics: Decisions, Games, and Strategy focuses on the unified presentation of politics as a rational human activity, including the paradox of voting and proportional representation. The publication first offers information on the study of rational politics, political intrigue in the Bible, and candidate strategies. Topics include the factor of timing in presidential primaries, rational positions in a multicandidate race, primacy of issues and their spatial representation, and politics in the story of Esther. The text then elaborates on voting paradoxes and the problems of representation, voting power, and threats and deterrence. Discussions focus on a sequential view of the Cuban missile crisis, use of threat power in Poland, power anomalies in the European Community Council of Ministers, probability of the paradox of voting, empirical examples of the paradox of voting, and problems in achieving proportional representation. The book is a valuable reference for researchers interested in rational politics.

VLSI and Computer Architecture

1st Edition
Volume 20
December 1, 2014
Ravi Shankar + 1 more
Norman G. Einspruch
English
eBook
9 7 8 1 4 8 3 2 1 7 8 4 0

VLSI Electronics Microstructure Science, Volume 20: VLSI and Computer Architecture reviews the approaches in design principles and techniques and the architecture for computer systems implemented in VLSI. This volume is divided into two parts. The first section is concerned with system design. Chapters under this section focus on the discussion of such topics as the evolution of VLSI; system performance and processor design considerations; and VLSI system design and processing tools. Part II of the book focuses on the architectural possibilities that have become cost effective with the development of VLSI circuits. Topics on architectural requirements and various architectures such as the Reduced Instruction Set, Extended Von Neumann, Language-Oriented, and Microprogrammable architectures are elaborated in detail. Also included are chapters that discuss the evaluation of architecture, multiprocessing configurations, and the future of VLSI. Computer designers, those evaluating computer systems, researchers, and students of computer architecture will find the book very useful.

System-Theoretic Methods in Economic Modelling II

1st Edition
Volume 22
June 28, 2014
S. Mittnik
English
eBook
9 7 8 1 4 8 3 2 9 6 2 3 4

System-Theoretic Methods in Economic Modelling II complements the editor's earlier volume, bringing together current research efforts integrating system-theoretic concepts with economic modelling processes. The range of papers presented here goes beyond the long-accepted control-theoretic contributions in dynamic optimization and focuses on system-theoretic methods in the construction as well as the application stages of economic modelling. This volume initiates new and intensifies existing debate between researchers and practitioners within and across the disciplines involved, with the objective of encouraging interdisciplinary research. The papers are split into four sections - estimation, filtering and smoothing problems in the context of state space modelling; applying the state space concept to financial modelling; modelling rational expectation; and a miscellaneous section including a follow-up case study by Tse and Khilnani on their integrated system model for a fishery management process, which featured in the first volume.

Logic, Methodology and Philosophy of Science VIII

1st Edition
Volume 126
August 16, 1989
J.E. Fenstad + 2 more
English
eBook
9 7 8 0 0 8 0 8 7 9 8 9 5

Logic, Methodology and Philosophy of Science VIII presents the results of recent research into the foundations of science. The volume contains 37 invited papers presented at the Congress, covering the areas of Logic, Mathematics, Physical Sciences, Biological Sciences and the Humanities.

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