Books in Mathematics and applied mathematics

Contributions to Algebra

1st Edition
May 10, 2014
Hyman Bass + 2 more
English
eBook
9 7 8 1 4 8 3 2 6 8 0 6 4

Contributions to Algebra: A Collection of Papers Dedicated to Ellis Kolchin provides information pertinent to commutative algebra, linear algebraic group theory, and differential algebra. This book covers a variety of topics, including complex analysis, logic, K-theory, stochastic matrices, and differential geometry. Organized into 29 chapters, this book begins with an overview of the influence that Ellis Kolchin's work on the Galois theory of differential fields has had on the development of differential equations. This text then discusses the background model theoretic work in differential algebra and discusses the notion of model completions. Other chapters consider some properties of differential closures and some immediate consequences and include extensive notes with proofs. This book discusses as well the problems in finite group theory in finding the complex finite projective groups of a given degree. The final chapter deals with the finite forms of quasi-simple algebraic groups. This book is a valuable resource for students.

Computers in Nonassociative Rings and Algebras

1st Edition
May 10, 2014
Robert E. Beck + 1 more
English
eBook
9 7 8 1 4 8 3 2 6 7 9 5 1

Computers in Nonassociative Rings and Algebras provides information pertinent to the computational aspects of nonassociative rings and algebras. This book describes the algorithmic approaches for solving problems using a computer. Organized into 10 chapters, this book begins with an overview of the concept of a symmetrized power of a group representation. This text then presents data structures and other computational methods that may be useful in the field of computational algebra. Other chapters consider several mathematical ideas, including identity processing in nonassociative algebras, structure theory of Lie algebra, and representation theory. This book presents as well an historical survey of the use of computers in Lie algebra theory, with specific reference to computing the coupling and recoupling coefficients for the irreducible representations of simple Lie algebras. The final chapter deals with how representations of semi-simple Lie algebras can be symmetrized in a straightforward manner. This book is a valuable resource for mathematicians.

Vector Analysis and Cartesian Tensors

2nd Edition
May 10, 2014
D. E. Bourne + 1 more
English
eBook
9 7 8 1 4 8 3 2 6 0 7 0 9

Vector Analysis and Cartesian Tensors, Second Edition focuses on the processes, methodologies, and approaches involved in vector analysis and Cartesian tensors, including volume integrals, coordinates, curves, and vector functions. The publication first elaborates on rectangular Cartesian coordinates and rotation of axes, scalar and vector algebra, and differential geometry of curves. Discussions focus on differentiation rules, vector functions and their geometrical representation, scalar and vector products, multiplication of a vector by a scalar, and angles between lines through the origin. The text then elaborates on scalar and vector fields and line, surface, and volume integrals, including surface, volume, and repeated integrals, general orthogonal curvilinear coordinates, and vector components in orthogonal curvilinear coordinates. The manuscript ponders on representation theorems for isotropic tensor functions, Cartesian tensors, applications in potential theory, and integral theorems. Topics include geometrical and physical significance of divergence and curl, Poisson's equation in vector form, isotropic scalar functions of symmetrical second order tensors, and diagonalization of second-order symmetrical tensors. The publication is a valuable reference for mathematicians and researchers interested in vector analysis and Cartesian tensors.

Functional Analysis in Modern Applied Mathematics

1st Edition
Volume 132
August 24, 1977
Ruth F. Curtain + 1 more
English
eBook
9 7 8 0 0 8 0 9 5 6 4 1 1

In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; andmethods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.As a result, the book represents a blend of new methods in general computational analysis,and specific, but also generic, techniques for study of systems theory ant its particularbranches, such as optimal filtering and information compression.

Multivariate Statistical Inference

1st Edition
July 10, 2014
Narayan C. Giri
Z. W. Birnbaum + 1 more
English
eBook
9 7 8 1 4 8 3 2 6 3 3 3 5

Multivariate Statistical Inference is a 10-chapter text that covers the theoretical and applied aspects of multivariate analysis, specifically the multivariate normal distribution using the invariance approach. Chapter I contains some special results regarding characteristic roots and vectors, and partitioned submatrices of real and complex matrices, as well as some special theorems on real and complex matrices useful in multivariate analysis. Chapter II deals with the theory of groups and related results that are useful for the development of invariant statistical test procedures, including the Jacobians of some specific transformations that are useful for deriving multivariate sampling distributions. Chapter III is devoted to basic notions of multivariate distributions and the principle of invariance in statistical testing of hypotheses. Chapters IV and V deal with the study of the real multivariate normal distribution through the probability density function and through a simple characterization and the maximum likelihood estimators of the parameters of the multivariate normal distribution and their optimum properties. Chapter VI tackles a systematic derivation of basic multivariate sampling distributions for the real case, while Chapter VII explores the tests and confidence regions of mean vectors of multivariate normal populations with known and unknown covariance matrices and their optimum properties. Chapter VIII is devoted to a systematic derivation of tests concerning covariance matrices and mean vectors of multivariate normal populations and to the study of their optimum properties. Chapters IX and X look into a treatment of discriminant analysis and the different covariance models and their analysis for the multivariate normal distribution. These chapters also deal with the principal components, factor models, canonical correlations, and time series. This book will prove useful to statisticians, mathematicians, and advance mathematics students.

Extensions of Linear-Quadratic Control, Optimization and Matrix Theory

1st Edition
Volume 133
April 1, 2000
David H. JACOBSON
English
eBook
9 7 8 0 0 8 0 9 5 6 4 2 8

Perspectives on Computer Science

1st Edition
June 17, 2014
Anita K. Jones
English
eBook
9 7 8 1 4 8 3 2 1 8 4 6 5

Perspectives on Computer Science provides information pertinent to the fundamental aspects of computer science. This book discusses the weaknesses frequently found in minicomputers. Organized into 12 chapters, this book begins with an overview of the technological, economic, and human aspects of the environment in which PDP–11 was designed and built. This text then examines the set of techniques for tree searching. Other chapters consider a tutorial on automatic planning systems, with emphasis given to knowledge representation issues. This book discusses as well the classical least-fixedpoint approach toward recursive programs and examines the interplay between time and space determined by a variety of machine models. The final chapter deals with some of the primary influences in contemporary programming language design, namely, programming methodology, program specification, verification, and formal semantic definition techniques. This book is a valuable resource for students and teachers. Computer science theoreticians and mathematicians will also find this book useful.

Fixed Points

1st Edition
May 10, 2014
Stepan Karamardian
English
eBook
9 7 8 1 4 8 3 2 6 1 1 3 3

Fixed Points: Algorithms and Applications covers the proceedings of the First International Conference on Computing Fixed Points with Applications, held in the Department of Mathematical Sciences at Clemson University, Clemson, South Carolina on June 26-28, 1974. This book is composed of 21 chapters and starts with reviews of finding roots of polynomials by pivoting procedures and the relations between convergence and labeling in approximation algorithm. The next chapters deal with the principles of complementary pivot theory and the Markovian decision chains; the method of continuation for Brouwer fixed point calculation; a fixed point approach to stability in cooperative games; and computation of fixed points in a nonconvex region. Other chapters discuss a computational comparison of fixed point algorithms, the fundamentals of union jack triangulations, and some aspects of Mann’s iterative method for approximating fixed points. The final chapters consider the application of fixed point algorithms to the analysis of tax policies and the pricing for congestion in telephone networks. This book will prove useful to mathematicians, computer scientists, and advance mathematics students.

Data Structures, Computer Graphics, and Pattern Recognition

1st Edition
May 10, 2014
A. Klinger + 2 more
English
eBook
9 7 8 1 4 8 3 2 6 7 2 5 8

Data Structures, Computer Graphics, and Pattern Recognition focuses on the computer graphics and pattern recognition applications of data structures methodology. This book presents design related principles and research aspects of the computer graphics, system design, data management, and pattern recognition tasks. The topics include the data structure design, concise structuring of geometric data for computer aided design, and data structures for pattern recognition algorithms. The survey of data structures for computer graphics systems, application of relational data structures in computer graphics, and observations on linguistics for scene analysis are also elaborated. This text likewise covers the design of satellite graphics systems, interactive image segmentation, surface representation for computer aided design, and error-correcting parsing for syntactic pattern recognition. This publication is valuable to practitioners in data structures, particularly those who are applying real computer systems to problems involving image, speech, and medical data.

Set-Theoretic Topology

1st Edition
May 10, 2014
George M. Reed
English
eBook
9 7 8 1 4 8 3 2 6 3 9 2 2

Set-Theoretic Topology deals with results concerning set theoretic topology and indicates directions for further investigations. Topics covered include normality and conditions in abstract spaces, compactifications, cardinal invariance, mapping theory, product spaces, and metrization. Comprised of 29 chapters, this volume begins with an example concerning the preservation of the Lindelöf property in product spaces, followed by a discussion on closed-completeness in spaces with a quasi-G? diagonal and with weak covering properties. The reader is then introduced to countably compact extensions of normal locally compact M-spaces; continuously semi-metrizable spaces; and closed discrete collections of singular cardinality. Subsequent chapters focus on open mapping theory; a selection-theoretic approach to certain extension theorems; semicompletable Moore spaces; and non-normal spaces. The book also considers complete mappings in base of countable order theory before concluding with an analysis of locally separable Moore spaces. This monograph should be of value to students, researchers, and specialists in the field of mathematics.

Related subjects

Abstract harmonic analysis

Algebra and number theory

Algebraic geometry

Algebraic topology

Analysis

Applied mathematics

Approximations and expansions

Associative rings and algebras

Biomathematics

Calculus of variations and optimal control optimization

Category theory homological algebra

Commutative rings and algebras

Computer science

Convex sets and related geometric topics

Differential geometry

Discrete mathematics combinatorics

Field theory and polynomials

Finite differences and functional equations

Fourier analysis

Functional analysis

Functions of a complex variable

General mathematical systems

General topology

Geometry

Global analysis analysis of manifolds

Group theory and generalizations

Integral equations

Integral transforms operational calculus

Linear and multilinear algebra matrix theory

Logic

Manifolds and cell complexes

Mathematical economics and game theory

Mathematical logic and foundations

Mathematical programming

Mathematics general

Mathematics history and biography

Measure and integration

Number theory

Numerical analysis

Operator theory

Order lattices ordered algebraic structures

Ordinary differential equations

Partial differential equations

Real functions

Sequences series summability

Set theory

Several complex variables and analytic spaces

Special functions

Systems theory control

Topological groups lie groups

Life Sciences

Physical Sciences & Engineering

Social Sciences & Humanities

Health