Convex Sets and Their Applications

Author: Steven R. Lay

Publisher: Courier Corporation

ISBN: 0486458032

Category: Mathematics

Page: 244

View: 8643

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: 9504

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.

A Course in Functional Analysis and Measure Theory

Author: Vladimir Kadets

Publisher: Springer

ISBN: 3319920049

Category: Mathematics

Page: 539

View: 3841

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.

Mathematical Foundations of Image Processing and Analysis

Author: Jean-Charles Pinoli

Publisher: John Wiley & Sons

ISBN: 1118984552

Category: Technology & Engineering

Page: 496

View: 4564

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.

Geometric Applications of Fourier Series and Spherical Harmonics

Author: H. Groemer

Publisher: Cambridge University Press

ISBN: 9780521473187

Category: Mathematics

Page: 329

View: 5771

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.

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: 4954

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.

Optimization Theory with Applications

Author: Donald A. Pierre

Publisher: Courier Corporation

ISBN: 0486136957

Category: Mathematics

Page: 640

View: 706

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.

Constructive Real Analysis

Author: Allen A. Goldstein

Publisher: Courier Corporation

ISBN: 0486286606

Category: Mathematics

Page: 192

View: 9110

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.

The Mathematics of Games of Strategy

Author: Melvin Dresher

Publisher: Courier Corporation

ISBN: 0486150062

Category: Mathematics

Page: 208

View: 4854

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.

Functional Analysis

Theory and Applications

Author: R.E. Edwards

Publisher: Courier Corporation

ISBN: 0486145107

Category: Mathematics

Page: 800

View: 1492

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.

Problems in Euclidean Space

Application of Convexity

Author: Harold Gordon Eggleston

Publisher: Courier Corporation

ISBN: 0486458466

Category: Mathematics

Page: 165

View: 6118

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.

Mathematics for Operations Research

Author: W. H. Marlow

Publisher: Courier Corporation

ISBN: 0486677230

Category: Mathematics

Page: 483

View: 2431

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.

Convex Surfaces

Author: Herbert Busemann

Publisher: Courier Corporation

ISBN: 0486154998

Category: Mathematics

Page: 208

View: 3816

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.

Introduction to the Theory of Games

Author: J. C. C. McKinsey

Publisher: Courier Corporation

ISBN: 0486154424

Category: Mathematics

Page: 384

View: 8811

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.

Complex Analysis in Banach Spaces

Author: Jorge Mujica

Publisher: Courier Corporation

ISBN: 0486474666

Category: Mathematics

Page: 440

View: 4889

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.

An Introduction to Lebesgue Integration and Fourier Series

Author: Howard J. Wilcox,David L. Myers

Publisher: Courier Corporation

ISBN: 9780486682938

Category: Mathematics

Page: 159

View: 2677

This book arose out of the authors' desire to present Lebesgue integration and Fourier series on an undergraduate level, since most undergraduate texts do not cover this material or do so in a cursory way. The result is a clear, concise, well-organized introduction to such topics as the Riemann integral, measurable sets, properties of measurable sets, measurable functions, the Lebesgue integral, convergence and the Lebesgue integral, pointwise convergence of Fourier series and other subjects. The authors not only cover these topics in a useful and thorough way, they have taken pains to motivate the student by keeping the goals of the theory always in sight, justifying each step of the development in terms of those goals. In addition, whenever possible, new concepts are related to concepts already in the student's repertoire. Finally, to enable readers to test their grasp of the material, the text is supplemented by numerous examples and exercises. Mathematics students as well as students of engineering and science will find here a superb treatment, carefully thought out and well presented , that is ideal for a one semester course. The only prerequisite is a basic knowledge of advanced calculus, including the notions of compactness, continuity, uniform convergence and Riemann integration.

Theory of Functions of a Real Variable

Author: I.P. Natanson

Publisher: Courier Dover Publications

ISBN: 048680643X

Category: Mathematics

Page: 560

View: 9605

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.

The Convolution Transform

Author: Isidore Isaac Hirschman,David V. Widder

Publisher: Courier Corporation

ISBN: 0486154564

Category: Mathematics

Page: 288

View: 3379

The relation between differential operators and integral transforms is the theme of this work. Discusses finite and non-finite kernels, variation diminishing transforms, asymptotic behavior of kernels, real inversion theory, representation theory, the Weierstrass transform, more.