Convex Sets and Their Applications

Author: Steven R. Lay

Publisher: Courier Corporation

ISBN: 0486458032

Category: Mathematics

Page: 244

View: 4780

Suitable for advanced undergraduates and graduate students, this text introduces the broad scope of convexity. It leads students to open questions and unsolved problems, and it highlights diverse applications. Author Steven R. Lay, Professor of Mathematics at Lee University in Tennessee, reinforces his teachings with numerous examples, plus exercises with hints and answers. The first three chapters form the foundation for all that follows, starting with a review of the fundamentals of linear algebra and topology. They also survey the development and applications of relationships between hyperplanes and convex sets. Subsequent chapters are relatively self-contained, each focusing on a particular aspect or application of convex sets. Topics include characterizations of convex sets, polytopes, duality, optimization, and convex functions. Hints, solutions, and references for the exercises appear at the back of the book.

Parameteridentifizierbarkeit in einem nichtlinearen Differentialgleichungssystem aus der Kontinuumsmechanik anhand von Randmessungen

Author: Arne Wöstehoff

Publisher: Logos Verlag Berlin GmbH

ISBN: 3832536078


Page: 283

View: 2988

Aufgrund vielfältiger Anwendungsmöglichkeiten wächst die Nachfrage nach zerstörungsfreien Prüfmethoden für hyperelastische Werkstoffe stark. Ein vielversprechendes Verfahren für den In-situ-Einsatz ist die Applikation eines Netzwerks von Piezosensoren und -aktuatoren. In dieser Arbeit wird als einfaches Modell eines Piezosensors ein Sensor angenommen, der gemittelte, gewichtete mechanische Spannungen an der Oberfläche misst. Ausgehend von diesem Szenario kann die kritische Frage, ob den Messungen solcher Sensoren eindeutig und stabil mechanische Eigenschaften des Körpers über die Identifikation der Verzerrungsenergiedichte zugeordnet werden können, dahingehend positiv beantwortet werden, als dass tatsächlich bei zulässigen Anfangszuständen und bei Darstellbarkeit der Verzerrungsenergiedichte als konische Kombination, die Abbildung des Quadrupels aus der Messung, den beiden Anfangswerten und der Massenkraftdichte auf die Verzerrungsenergiedichte stetig ist. Es wird gezeigt, dass kleine Fehler in den Messdaten oder leichte Abweichungen in den weiteren Ausgangsdaten des angesprochenen Quadrupels nur zu kleinen Änderungen der dadurch festgelegten mechanischen Eigenschaften führen. Dieses Charakteristikum ist eine unabdingbare Basisanforderung an jedes zuverlässig arbeitende System zur Schadenslokalisierung. Diese Aussagen werden im Wesentlichen in zwei Schritten erreicht: Zunächst erfolgt eine intensive Untersuchung des parameterabhängigen Vorwärtsproblems, welches sich als Anfangsrandwertproblem eines nichtlinearen partiellen Differentialgleichungssystems darstellt. Anschließend wird das inverse Problem der Parameteridentifizierung formuliert und analysiert.

Optimization Theory with Applications

Author: Donald A. Pierre

Publisher: Courier Corporation

ISBN: 0486136957

Category: Mathematics

Page: 640

View: 2805

Broad-spectrum approach to important topic. Explores the classic theory of minima and maxima, classical calculus of variations, simplex technique and linear programming, optimality and dynamic programming, more. 1969 edition.

Elements of the Theory of Functions and Functional Analysis

Author: Andre? Nikolaevich Kolmogorov,Serge? Vasil?evich Fomin,S. V. Fomin

Publisher: Courier Corporation

ISBN: 9780486406831

Category: Mathematics

Page: 288

View: 3015

Advanced-level text, now available in a single volume, discusses metric and normed spaces, continuous curves in metric spaces, measure theory, Lebesque intervals, Hilbert space, more. Exercises. 1957 edition.

A Course in Functional Analysis and Measure Theory

Author: Vladimir Kadets

Publisher: Springer

ISBN: 3319920049

Category: Mathematics

Page: 539

View: 1537

Written by an expert on the topic and experienced lecturer, this textbook provides an elegant, self-contained introduction to functional analysis, including several advanced topics and applications to harmonic analysis. Starting from basic topics before proceeding to more advanced material, the book covers measure and integration theory, classical Banach and Hilbert space theory, spectral theory for bounded operators, fixed point theory, Schauder bases, the Riesz-Thorin interpolation theorem for operators, as well as topics in duality and convexity theory. Aimed at advanced undergraduate and graduate students, this book is suitable for both introductory and more advanced courses in functional analysis. Including over 1500 exercises of varying difficulty and various motivational and historical remarks, the book can be used for self-study and alongside lecture courses.

Constructive Real Analysis

Author: Allen A. Goldstein

Publisher: Courier Corporation

ISBN: 0486286606

Category: Mathematics

Page: 192

View: 8954

This text introduces students of mathematics, science, and technology to the methods of applied functional analysis and applied convexity. Topics include iterations and fixed points, metric spaces, nonlinear programming, applications to integral equations, and more. 1967 edition.

Mathematical Foundations of Image Processing and Analysis

Author: Jean-Charles Pinoli

Publisher: John Wiley & Sons

ISBN: 1118984552

Category: Technology & Engineering

Page: 496

View: 5397

Mathematical Imaging is currently a rapidly growing field inapplied mathematics, with an increasing need for theoreticalmathematics. This book, the second of two volumes, emphasizes the role ofmathematics as a rigorous basis for imaging sciences. It provides acomprehensive and convenient overview of the key mathematicalconcepts, notions, tools and frameworks involved in the variousfields of gray-tone and binary image processing and analysis, byproposing a large, but coherent, set of symbols and notations, acomplete list of subjects and a detailed bibliography. Itestablishes a bridge between the pure and applied mathematicaldisciplines, and the processing and analysis of gray-tone andbinary images. It is accessible to readers who have neitherextensive mathematical training, nor peer knowledge in ImageProcessing and Analysis. It is a self-contained book focusing on the mathematicalnotions, concepts, operations, structures, and frameworks that arebeyond or involved in Image Processing and Analysis. The notationsare simplified as far as possible in order to be more explicativeand consistent throughout the book and the mathematical aspects aresystematically discussed in the image processing and analysiscontext, through practical examples or concrete illustrations.Conversely, the discussed applicative issues allow the role ofmathematics to be highlighted. Written for a broad audience – students, mathematicians,image processing and analysis specialists, as well as otherscientists and practitioners – the author hopes that readerswill find their own way of using the book, thus providing amathematical companion that can help mathematicians become morefamiliar with image processing and analysis, and likewise, imageprocessing and image analysis scientists, researchers and engineersgain a deeper understanding of mathematical notions andconcepts.

Convex Surfaces

Author: Herbert Busemann

Publisher: Courier Corporation

ISBN: 0486154998

Category: Mathematics

Page: 208

View: 2769

This exploration of convex surfaces focuses on extrinsic geometry and applications of the Brunn-Minkowski theory. It also examines intrinsic geometry and the realization of intrinsic metrics. 1958 edition.

Geometric Applications of Fourier Series and Spherical Harmonics

Author: H. Groemer

Publisher: Cambridge University Press

ISBN: 9780521473187

Category: Mathematics

Page: 329

View: 8588

This book provides a comprehensive presentation of geometric results, primarily from the theory of convex sets, that have been proved by the use of Fourier series or spherical harmonics. An important feature of the book is that all necessary tools from the classical theory of spherical harmonics are presented with full proofs. These tools are used to prove geometric inequalities, stability results, uniqueness results for projections and intersections by hyperplanes or half-spaces and characterisations of rotors in convex polytopes. Again, full proofs are given. To make the treatment as self-contained as possible the book begins with background material in analysis and the geometry of convex sets. This treatise will be welcomed both as an introduction to the subject and as a reference book for pure and applied mathematics.

Complex Analysis in Banach Spaces

Author: Jorge Mujica

Publisher: Courier Corporation

ISBN: 0486474666

Category: Mathematics

Page: 440

View: 5287

The development of complex analysis is based on issues related to holomorphic continuation and holomorphic approximation. This volume presents a unified view of these topics in finite and infinite dimensions. A high-level tutorial in pure and applied mathematics, its prerequisites include a familiarity with the basic properties of holomorphic functions, the principles of Banach and Hilbert spaces, and the theory of Lebesgue integration. The four-part treatment begins with an overview of the basic properties of holomorphic mappings and holomorphic domains in Banach spaces. The second section explores differentiable mappings, differentiable forms, and polynomially convex compact sets, in which the results are applied to the study of Banach and Fréchet algebras. Subsequent sections examine plurisubharmonic functions and pseudoconvex domains in Banach spaces, along with Riemann domains and envelopes of holomorphy. In addition to its value as a text for advanced graduate students of mathematics, this volume also functions as a reference for researchers and professionals.

The Mathematics of Games of Strategy

Author: Melvin Dresher

Publisher: Courier Corporation

ISBN: 0486150062

Category: Mathematics

Page: 208

View: 3967

This text offers an exceptionally clear presentation of the mathematical theory of games of strategy and its applications to many fields including economics, military, business, and operations research.

Problems in Euclidean Space

Application of Convexity

Author: Harold Gordon Eggleston

Publisher: Courier Corporation

ISBN: 0486458466

Category: Mathematics

Page: 165

View: 7864

This text for advanced undergraduates and graduate students examines problems concerning convex sets in real Euclidean spaces of two or three dimensions. It illustrates the different ways in which convexity can enter into the formulation as the solution to different problems in these spaces. Problems in Euclidean Space features four chapters that develop an increasingly dominant influence of convexity. In the first chapter, convexity plays a minor role; the second chapter considers problems originally stated in a wider context that can be reduced to problems concerning convex sets. In the third chapter, the problems are defined strictly for convex sets and not for more general sets, and the final chapter discusses properties of subclasses of the class of convex sets.

Theory of Functions of a Real Variable

Author: I.P. Natanson

Publisher: Courier Dover Publications

ISBN: 048680643X

Category: Mathematics

Page: 560

View: 8152

Long out-of-print volume by a prominent Soviet mathematician presents a thorough examination of the theory of functions of a real variable. Intended for advanced undergraduates and graduate students of mathematics. 1955 and 1960 editions.

Functional Analysis

Theory and Applications

Author: R.E. Edwards

Publisher: Courier Corporation

ISBN: 0486145107

Category: Mathematics

Page: 800

View: 3426

Massive compilation offers detailed, in-depth discussions of vector spaces, Hahn-Banach theorem, fixed-point theorems, duality theory, Krein-Milman theorem, theory of compact operators, much more. Many examples and exercises. 32-page bibliography. 1965 edition.

Introduction to the Theory of Games

Author: J. C. C. McKinsey

Publisher: Courier Corporation

ISBN: 0486154424

Category: Mathematics

Page: 384

View: 1421

This comprehensive overview of the mathematical theory of games illustrates applications to situations involving conflicts of interest, including economic, social, political, and military contexts. Advanced calculus a prerequisite. Includes 51 figures and 8 tables. 1952 edition.

Differential Forms with Applications to the Physical Sciences

Author: Harley Flanders

Publisher: Courier Corporation

ISBN: 0486139611

Category: Mathematics

Page: 240

View: 3020

A graduate-level text utilizing exterior differential forms in the analysis of a variety of mathematical problems in the physical and engineering sciences. Includes 45 illustrations. Index.

Mathematics for Operations Research

Author: W. H. Marlow

Publisher: Courier Corporation

ISBN: 0486677230

Category: Mathematics

Page: 483

View: 9015

Practical and applications-oriented, this text explains effective procedures for performing mathematical tasks that arise in many fields, including operations research, engineering, systems sciences, statistics, and economics. Most of the examples and many of the 1,300 problems illustrate techniques, and nearly all of the tables display reference material for procedures. 1978 edition.

Pursuit Games

An Introduction to the Theory and Applications of Differential Games of Pursuit and Evasion

Author: Otomar Hajek

Publisher: Courier Corporation

ISBN: 0486462838

Category: Mathematics

Page: 266

View: 6769

A presentation of systematic methods for winning differential games of pursuit and evasion, this volume explores the procedures' scope and applications. Numerous examples illustrate basic and advanced concepts, including capture, strategy, and algebraic theory. Detailed proofs appear throughout the text, along with 200 exercises that further clarify each subject. 1975 edition.