Books in Mathematics and applied mathematics

Nonmeasurable Sets and Functions

1st Edition
Volume 195
May 29, 2004
Alexander Kharazishvili
English
eBook
9 7 8 0 0 8 0 4 7 9 7 6 7

The book is devoted to various constructions of sets which are nonmeasurable with respect to invariant (more generally, quasi-invariant) measures. Our starting point is the classical Vitali theorem stating the existence of subsets of the real line which are not measurable in the Lebesgue sense. This theorem stimulated the development of the following interesting topics in mathematics:1. Paradoxical decompositions of sets in finite-dimensional Euclidean spaces;2. The theory of non-real-valued-meas... cardinals;3. The theory of invariant (quasi-invariant)ext... of invariant (quasi-invariant) measures.These topics are under consideration in the book. The role of nonmeasurable sets (functions) in point set theory and real analysis is underlined and various classes of such sets (functions) are investigated . Among them there are: Vitali sets, Bernstein sets, Sierpinski sets, nontrivial solutions of the Cauchy functional equation, absolutely nonmeasurable sets in uncountable groups, absolutely nonmeasurable additive functions, thick uniform subsets of the plane, small nonmeasurable sets, absolutely negligible sets, etc. The importance of properties of nonmeasurable sets for various aspects of the measure extension problem is shown. It is also demonstrated that there are close relationships between the existence of nonmeasurable sets and some deep questions of axiomatic set theory, infinite combinatorics, set-theoretical topology, general theory of commutative groups. Many open attractive problems are formulated concerning nonmeasurable sets and functions.

Advances in Computers

1st Edition
Volume 61
May 26, 2004
Marvin Zelkowitz
English
eBook
9 7 8 0 0 8 0 4 9 0 2 8 1

Advances in Computers covers new developments in computer technology. Most chapters present an overview of a current subfield within computer science, with many citations, and often include new developments in the field by the authors of the individual chapters. Topics include hardware, software, theoretical underpinnings of computing, and novel applications of computers. This current volume emphasizes architectural issues in the design of new hardware and software system. An architectural design evaluation process is described that allows developers to make sure that their source programs adhere to the architectural design of the specifications. This greatly aids in the maintenance of the system. Telecommunications issues are covered from the impact of new technology to security of wireless systems. Quantum computing, an exciting development that may greatly increase the speed of present computers, is described. The book series is a valuable addition to university courses that emphasize the topics under discussion in that particular volume as well as belonging on the bookshelf of industrial practitioners who need to implement many of the technologies that are described.

Parallel Computational Fluid Dynamics 2003

1st Edition
May 6, 2004
Boris Chetverushkin + 3 more
English
eBook
9 7 8 0 0 8 0 4 7 3 6 7 3

The book is devoted to using of parallel multiprocessor computer systems for numerical simulation of the problems which can be described by the equations of continuum mechanics. Parallel algorithms and software, the problems of meta-computing are discussed in details, some results of high performance simulation of modern gas dynamic problems, combustion phenomena, plasma physics etc are presented.

Infinitesimal Methods of Mathematical Analysis

1st Edition
May 1, 2004
J S Pinto
English
Paperback
9 7 8 1 8 9 8 5 6 3 9 9 0
eBook
9 7 8 0 8 5 7 0 9 9 5 0 1

This modern introduction to infinitesimal methods is a translation of the book Métodos Infinitesimais de Análise Matemática by José Sousa Pinto of the University of Aveiro, Portugal and is aimed at final year or graduate level students with a background in calculus. Surveying modern reformulations of the infinitesimal concept with a thoroughly comprehensive exposition of important and influential hyperreal numbers, the book includes previously unpublished material on the development of hyperfinite theory of Schwartz distributions and its application to generalised Fourier transforms and harmonic analysis. This translation by Roy Hoskins was also greatly assisted by the comments and constructive criticism of Professor Victor Neves, of the University of Aveiro.

Advances in Computers

1st Edition
Volume 60
April 30, 2004
Marvin Zelkowitz
English
eBook
9 7 8 0 0 8 0 4 7 1 8 9 1

Advances in Computers covers new developments in computer technology. Most chapters present an overview of a current subfield within computers, with many citations, and often include new developments in the field by the authors of the individual chapters. Topics include hardware, software, theoretical underpinnings of computing, and novel applications of computers. This current volume emphasizes information security issues and includes topics like certifying computer professionals, non-invasive attacks ("cognitive hacking"), computer files as legal evidence ("computer forensics") and the use of processors on plastic ("smartcards"). The book series is a valuable addition to university courses that emphasize the topics under discussion in that particular volume as well as belonging on the bookshelf of industrial practitioners who need to implement many of the technologies that are described.

The Rise of Modern Logic: from Leibniz to Frege

1st Edition
Volume 3
March 8, 2004
Dov M. Gabbay + 1 more
English
Hardback
9 7 8 0 4 4 4 5 1 6 1 1 4
eBook
9 7 8 0 0 8 0 5 3 2 8 7 5

With the publication of the present volume, the Handbook of the History of Logic turns its attention to the rise of modern logic. The period covered is 1685-1900, with this volume carving out the territory from Leibniz to Frege. What is striking about this period is the earliness and persistence of what could be called 'the mathematical turn in logic'. Virtually every working logician is aware that, after a centuries-long run, the logic that originated in antiquity came to be displaced by a new approach with a dominantly mathematical character. It is, however, a substantial error to suppose that the mathematization of logic was, in all essentials, Frege's accomplishment or, if not his alone, a development ensuing from the second half of the nineteenth century. The mathematical turn in logic, although given considerable torque by events of the nineteenth century, can with assurance be dated from the final quarter of the seventeenth century in the impressively prescient work of Leibniz. It is true that, in the three hundred year run-up to the Begriffsschrift, one does not see a smoothly continuous evolution of the mathematical turn, but the idea that logic is mathematics, albeit perhaps only the most general part of mathematics, is one that attracted some degree of support throughout the entire period in question. Still, as Alfred North Whitehead once noted, the relationship between mathematics and symbolic logic has been an "uneasy" one, as is the present-day association of mathematics with computing. Some of this unease has a philosophical texture. For example, those who equate mathematics and logic sometimes disagree about the directionality of the purported identity. Frege and Russell made themselves famous by insisting (though for different reasons) that logic was the senior partner. Indeed logicism is the view that mathematics can be re-expressed without relevant loss in a suitably framed symbolic logic. But for a number of thinkers who took an algebraic approach to logic, the dependency relation was reversed, with mathematics in some form emerging as the senior partner. This was the precursor of the modern view that, in its four main precincts (set theory, proof theory, model theory and recursion theory), logic is indeed a branch of pure mathematics. It would be a mistake to leave the impression that the mathematization of logic (or the logicization of mathematics) was the sole concern of the history of logic between 1665 and 1900. There are, in this long interval, aspects of the modern unfolding of logic that bear no stamp of the imperial designs of mathematicians, as the chapters on Kant and Hegcl make clear. Of the two, Hcgel's influence on logic is arguably the greater, serving as a spur to the unfolding of an idealist tradition in logic - a development that will be covered in a further volume, British Logic in the Nineteenth Century.

Mathematics of Optimization: Smooth and Nonsmooth Case

1st Edition
March 10, 2004
Giorgio Giorgi + 2 more
English
eBook
9 7 8 0 0 8 0 5 3 5 9 5 1

The book is intended for people (graduates, researchers, but also undergraduates with a good mathematical background) involved in the study of (static) optimization problems (in finite-dimensional spaces). It contains a lot of material, from basic tools of convex analysis to optimality conditions for smooth optimization problems, for non smooth optimization problems and for vector optimization problems.The development of the subjects are self-contained and the bibliographical references are usually treated in different books (only a few books on optimization theory deal also with vector problems), so the book can be a starting point for further readings in a more specialized literature.Assuming only a good (even if not advanced) knowledge of mathematical analysis and linear algebra, this book presents various aspects of the mathematical theory in optimization problems. The treatment is performed in finite-dimensional spaces and with no regard to algorithmic questions. After two chapters concerning, respectively, introductory subjects and basic tools and concepts of convex analysis, the book treats extensively mathematical programming problems in the smmoth case, in the nonsmooth case and finally vector optimization problems.

Actuaries' Survival Guide

1st Edition
February 23, 2004
Fred Szabo
English
eBook
9 7 8 0 0 8 0 5 2 4 2 4 5

This unique book is a guide for students and graduates of mathematics, statistics, economics, finance, and other number-based disciplines contemplating a career in actuarial science. Given the comprehensive range of the cases that are analyzed in the book, the Actuaries' Survival Guide can serve as a companion to existing study material for all courses designed to prepare students for actuarial examinations.

Stream Ciphers and Number Theory

1st Edition
Volume 66
February 17, 2004
Thomas W. Cusick + 2 more
English
Hardback
9 7 8 0 4 4 4 5 1 6 3 1 2
eBook
9 7 8 0 0 8 0 5 4 1 8 3 9

This is the unique book on cross-fertilisations between stream ciphers and number theory. It systematically and comprehensively covers known connections between the two areas that are available only in research papers. Some parts of this book consist of new research results that are not available elsewhere. In addition to exercises, over thirty research problems are presented in this book. In this revised edition almost every chapter was updated, and some chapters were completely rewritten. It is useful as a textbook for a graduate course on the subject, as well as a reference book for researchers in related fields.

Infinite Words

1st Edition
Volume 141
February 12, 2004
Dominique Perrin + 1 more
English
Hardback
9 7 8 0 1 2 5 3 2 1 1 1 2
eBook
9 7 8 0 0 8 0 5 2 5 6 4 8

Infinite Words is an important theory in both Mathematics and Computer Sciences. Many new developments have been made in the field, encouraged by its application to problems in computer science. Infinite Words is the first manual devoted to this topic.Infinite Words explores all aspects of the theory, including Automata, Semigroups, Topology, Games, Logic, Bi-infinite Words, Infinite Trees and Finite Words. The book also looks at the early pioneering work of Büchi, McNaughton and Schützenberger.

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Books in Mathematics and applied mathematics

Nonmeasurable Sets and Functions

Advances in Computers

Parallel Computational Fluid Dynamics 2003

Infinitesimal Methods of Mathematical Analysis

Advances in Computers

The Rise of Modern Logic: from Leibniz to Frege

Mathematics of Optimization: Smooth and Nonsmooth Case

Actuaries' Survival Guide

Stream Ciphers and Number Theory

Infinite Words

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