Books in Theory and mathematics

Computational Theory of Iterative Methods

1st Edition
Volume 15
September 4, 2007
Ioannis Argyros
English
eBook
9 7 8 0 0 8 0 5 6 0 7 0 0

The book is designed for researchers, students and practitioners interested in using fast and efficient iterative methods to approximate solutions of nonlinear equations. The following four major problems are addressed. Problem 1: Show that the iterates are well defined. Problem 2: concerns the convergence of the sequences generated by a process and the question of whether the limit points are, in fact solutions of the equation. Problem 3: concerns the economy of the entire operations. Problem 4: concerns with how to best choose a method, algorithm or software program to solve a specific type of problem and its description of when a given algorithm succeeds or fails. The book contains applications in several areas of applied sciences including mathematical programming and mathematical economics. There is also a huge number of exercises complementing the theory.

Handbook of Quantum Logic and Quantum Structures

1st Edition
August 1, 2007
Kurt Engesser + 2 more
English
eBook
9 7 8 0 0 8 0 5 5 0 3 8 1

Since its inception in the famous 1936 paper by Birkhoff and von Neumann entitled “The logic of quantum mechanics” quantum logic, i.e. the logical investigation of quantum mechanics, has undergone an enormous development. Various schools of thought and approaches have emerged and there are a variety of technical results.Quantum logic is a heterogeneous field of research ranging from investigations which may be termed logical in the traditional sense to studies focusing on structures which are on the border between algebra and logic. For the latter structures the term quantum structures is appropriate. The chapters of this Handbook, which are authored by the most eminent scholars in the field, constitute a comprehensive presentation of the main schools, approaches and results in the field of quantum logic and quantum structures. Much of the material presented is of recent origin representing the frontier of the subject. The present volume focuses on quantum structures. Among the structures studied extensively in this volume are, just to name a few, Hilbert lattices, D-posets, effect algebras MV algebras, partially ordered Abelian groups and those structures underlying quantum probability.

Network Routing

1st Edition
March 29, 2007
English
Hardback
9 7 8 0 1 2 0 8 8 5 8 8 6
eBook
9 7 8 0 0 8 0 4 7 4 9 7 7

Network routing can be broadly categorized into Internet routing, PSTN routing, and telecommunication transport network routing. This book systematically considers these routing paradigms, as well as their interoperability. The authors discuss how algorithms, protocols, analysis, and operational deployment impact these approaches. A unique feature of the book is consideration of both macro-state and micro-state in routing; that is, how routing is accomplished at the level of networks and how routers or switches are designed to enable efficient routing.In reading this book, one will learn about 1) the evolution of network routing, 2) the role of IP and E.164 addressing in routing, 3) the impact on router and switching architectures and their design, 4) deployment of network routing protocols, 5) the role of traffic engineering in routing, and 6) lessons learned from implementation and operational experience. This book explores the strengths and weaknesses that should be considered during deployment of future routing schemes as well as actual implementation of these schemes. It allows the reader to understand how different routing strategies work and are employed and the connection between them. This is accomplished in part by the authors' use of numerous real-world examples to bring the material alive.

Information Theory of Molecular Systems

1st Edition
February 22, 2006
Roman F Nalewajski
English
Hardback
9 7 8 0 4 4 4 5 1 9 6 6 5
eBook
9 7 8 0 0 8 0 4 5 9 7 4 5

As well as providing a unified outlook on physics, Information Theory (IT) has numerous applications in chemistry and biology owing to its ability to provide a measure of the entropy/information contained within probability distributions and criteria of their information "distance" (similarity) and independence. Information Theory of Molecular Systems applies standard IT to classical problems in the theory of electronic structure and chemical reactivity. The book starts by introducing the basic concepts of modern electronic structure/reactivity theory based upon the Density Functional Theory (DFT), followed by an outline of the main ideas and techniques of IT, including several illustrative applications to molecular systems. Coverage includes information origins of the chemical bond, unbiased definition of molecular fragments, adequate entropic measures of their internal (intra-fragment) and external (inter-fragment) bond-orders and valence-numbers, descriptors of their chemical reactivity, and information criteria of their similarity and independence. Information Theory of Molecular Systems is recommended to graduate students and researchers interested in fresh ideas in the theory of electronic structure and chemical reactivity.

Computational Error and Complexity in Science and Engineering

1st Edition
Volume 201
March 4, 2005
Vangipuram Lakshmikantham + 1 more
English
eBook
9 7 8 0 0 8 0 4 5 9 5 1 6

The book “Computational Error and Complexity in Science and Engineering” pervades all the science and engineering disciplines where computation occurs. Scientific and engineering computation happens to be the interface between the mathematical model/problem and the real world application. One needs to obtain good quality numerical values for any real-world implementation. Just mathematical quantities symbols are of no use to engineers/technologi... Computational complexity of the numerical method to solve the mathematical model, also computed along with the solution, on the other hand, will tell us how much computation/computat... effort has been spent to achieve that quality of result. Anyone who wants the specified physical problem to be solved has every right to know the quality of the solution as well as the resources spent for the solution. The computed error as well as the complexity provide the scientific convincing answer to these questions. Specifically some of the disciplines in which the book will be readily useful are (i) Computational Mathematics, (ii) Applied Mathematics/Computat... Engineering, Numerical and Computational Physics, Simulation and Modelling. Operations Research (both deterministic and stochastic), Computing Methodologies, Computer Applications, and Numerical Methods in Engineering.Key Features:- Describes precisely ready-to-use computational error and complexity- Includes simple easy-to-grasp examples wherever necessary.- Presents error and complexity in error-free, parallel, and probabilistic methods.- Discusses deterministic and probabilistic methods with error and complexity. - Points out the scope and limitation of mathematical error-bounds.- Provides a comprehensive up-to-date bibliography after each chapter.

Stochastic Local Search

1st Edition
September 16, 2004
Holger H. Hoos + 1 more
English
Hardback
9 7 8 1 5 5 8 6 0 8 7 2 6
eBook
9 7 8 0 0 8 0 4 9 8 2 4 9

Stochastic local search (SLS) algorithms are among the most prominent and successful techniques for solving computationally difficult problems in many areas of computer science and operations research, including propositional satisfiability, constraint satisfaction, routing, and scheduling. SLS algorithms have also become increasingly popular for solving challenging combinatorial problems in many application areas, such as e-commerce and bioinformatics.Hoos and Stützle offer the first systematic and unified treatment of SLS algorithms. In this groundbreaking new book, they examine the general concepts and specific instances of SLS algorithms and carefully consider their development, analysis and application. The discussion focuses on the most successful SLS methods and explores their underlying principles, properties, and features. This book gives hands-on experience with some of the most widely used search techniques, and provides readers with the necessary understanding and skills to use this powerful tool.

Computational Complexity: A Quantitative Perspective

1st Edition
Volume 196
July 7, 2004
Marius Zimand
English
eBook
9 7 8 0 0 8 0 4 7 6 6 6 7

There has been a common perception that computational complexity is a theory of "bad news" because its most typical results assert that various real-world and innocent-looking tasks are infeasible. In fact, "bad news" is a relative term, and, indeed, in some situations (e.g., in cryptography), we want an adversary to not be able to perform a certain task. However, a "bad news" result does not automatically become useful in such a scenario. For this to happen, its hardness features have to be quantitatively evaluated and shown to manifest extensively.The book undertakes a quantitative analysis of some of the major results in complexity that regard either classes of problems or individual concrete problems. The size of some important classes are studied using resource-bounded topological and measure-theoretical tools. In the case of individual problems, the book studies relevant quantitative attributes such as approximation properties or the number of hard inputs at each length.One chapter is dedicated to abstract complexity theory, an older field which, however, deserves attention because it lays out the foundations of complexity. The other chapters, on the other hand, focus on recent and important developments in complexity. The book presents in a fairly detailed manner concepts that have been at the centre of the main research lines in complexity in the last decade or so, such as: average-complexity, quantum computation, hardness amplification, resource-bounded measure, the relation between one-way functions and pseudo-random generators, the relation between hard predicates and pseudo-random generators, extractors, derandomization of bounded-error probabilistic algorithms, probabilistically checkable proofs, non-approximability of optimization problems, and others.The book should appeal to graduate computer science students, and to researchers who have an interest in computer science theory and need a good understanding of computational complexity, e.g., researchers in algorithms, AI, logic, and other disciplines.

Art and Complexity

1st Edition
February 19, 2003
J. Casti + 1 more
English
Hardback
9 7 8 0 4 4 4 5 0 9 4 4 4
eBook
9 7 8 0 0 8 0 5 2 7 5 8 1

This title is the result of a one-week workshop sponsored by the Swedish research agency, FRN, on the interface between complexity and art. Among others, it includes discussions on whether "good" art is "complex" art, how artists see the term "complex", and what poets try to convey in word about complex behavior in nature.

Mathematical Logic

1st Edition
Volume 4
December 5, 2001
R.O. Gandy + 1 more
English
eBook
9 7 8 0 0 8 0 5 3 5 9 2 0

Mathematical Logic is a collection of the works of one of the leading figures in 20th-century science. This collection of A.M. Turing's works is intended to include all his mature scientific writing, including a substantial quantity of unpublished material. His work in pure mathematics and mathematical logic extended considerably further; the work of his last years, on morphogenesis in plants, is also of the greatest originality and of permanent importance. This book is divided into three parts. The first part focuses on computability and ordinal logics and covers Turing's work between 1937 and 1938. The second part covers type theory; it provides a general introduction to Turing's work on type theory and covers his published and unpublished works between 1941 and 1948. Finally, the third part focuses on enigmas, mysteries, and loose ends. This concluding section of the book discusses Turing's Treatise on the Enigma, with excerpts from the Enigma Paper. It also delves into Turing's papers on programming and on minimum cost sequential analysis, featuring an excerpt from the unpublished manuscript. This book will be of interest to mathematicians, logicians, and computer scientists.

Handbook of Automated Reasoning

1st Edition
Volume 1
June 22, 2001
Alan J.A. Robinson + 1 more
English
eBook
9 7 8 0 0 8 0 5 3 2 7 9 0

Related subjects

Analysis of algorithms and problem complexity

Logics and meanings of programs

Mathematical logic and formal languages

Natural computation

Quantum computing

Theory and mathematics general

Life Sciences

Physical Sciences & Engineering

Social Sciences & Humanities

Health