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Elsevier

Books in Theory and mathematics

Our portfolio includes foundational theories, algorithms, formal methods, and computational complexity. Featuring rigorous research, mathematical frameworks, and practical applications, these titles support theorists, mathematicians, and computer scientists in advancing the theoretical underpinnings of computing. Addressing emerging areas like quantum algorithms and formal verification, the collection fuels innovation and scientific discovery.

  • Logic Colloquium 76, Proceedings of a conference

    • 1st Edition
    • Volume 87
    • Lev D. Beklemishev
    • English

  • Logic, Methodology and Philosophy of Science, Proceeding of the 1960 International Congress

    • 1st Edition
    • Volume 44
    • Lev D. Beklemishev
    • English

  • Enveloping Algebras

    • 1st Edition
    • Volume 14
    • Diximier
    • English

  • Multiparametric Statistics

    • 1st Edition
    • Vadim Ivanovich Serdobolskii
    • English
    This monograph presents mathematical theory of statistical models described by the essentially large number of unknown parameters, comparable with sample size but can also be much larger. In this meaning, the proposed theory can be called "essentially multiparametric". It is developed on the basis of the Kolmogorov asymptotic approach in which sample size increases along with the number of unknown parameters.This theory opens a way for solution of central problems of multivariate statistics, which up until now have not been solved. Traditional statistical methods based on the idea of an infinite sampling often break down in the solution of real problems, and, dependent on data, can be inefficient, unstable and even not applicable. In this situation, practical statisticians are forced to use various heuristic methods in the hope the will find a satisfactory solution.Mathematica... theory developed in this book presents a regular technique for implementing new, more efficient versions of statistical procedures. Near exact solutions are constructed for a number of concrete multi-dimensional problems: estimation of expectation vectors, regression and discriminant analysis, and for the solution to large systems of empiric linear algebraic equations. It is remarkable that these solutions prove to be not only non-degenerating and always stable, but also near exact within a wide class of populations.In the conventional situation of small dimension and large sample size these new solutions far surpass the classical, commonly used consistent ones. It can be expected in the near future, for the most part, traditional multivariate statistical software will be replaced by the always reliable and more efficient versions of statistical procedures implemented by the technology described in this book.This monograph will be of interest to a variety of specialists working with the theory of statistical methods and its applications. Mathematicians would find new classes of urgent problems to be solved in their own regions. Specialists in applied statistics creating statistical packages will be interested in more efficient methods proposed in the book. Advantages of these methods are obvious: the user is liberated from the permanent uncertainty of possible instability and inefficiency and gets algorithms with unimprovable accuracy and guaranteed for a wide class of distributions.A large community of specialists applying statistical methods to real data will find a number of always stable highly accurate versions of algorithms that will help them to better solve their scientific or economic problems. Students and postgraduates will be interested in this book as it will help them get at the foremost frontier of modern statistical science.

  • Computational Theory of Iterative Methods

    • 1st Edition
    • Volume 15
    • Ioannis Argyros
    • English
    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

    Quantum Structures
    • 1st Edition
    • Kurt Engesser + 2 more
    • English
    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

    Algorithms, Protocols, and Architectures
    • 1st Edition
    • English
    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
    • Roman F Nalewajski
    • English
    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

    Computational Error and Complexity
    • 1st Edition
    • Volume 201
    • Vangipuram Lakshmikantham + 1 more
    • English
    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.

  • Computational Complexity: A Quantitative Perspective

    • 1st Edition
    • Volume 196
    • Marius Zimand
    • English
    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.

  • Resolving Conflicts with Mathematica

    Algorithms for Two-Person Games
    • 1st Edition
    • Morton John Canty
    • English
    The revised and updated edition of this popular German textbook is unique in its emphasis on algorithmic methods and in its original use of Mathematica as a tool to obtain solutions to game-theoretical models.Resolving Conflicts with Mathematica begins with the basic theory of extensive and normal form games, as well as introducing the fundamental concept of Nash equilibria. The restriction to two-person games helps to make the material more digestible for the beginner. In later chapters the subtleties of degenerate games are discussed thoroughly. Many aspects of equilibrium selection theory are treated, including algorithms for determining evolutionary stable equilibria in biology. Finally, the book looks at the wide-scale application of game theory to practical conflict situations.Resolving Conflicts with Mathematica includes a set of Mathematica programs which implement all of the algorithms described in the text. Exercises are closely integrated with the book's material and Mathematica 'notebooks' are supplied with each of the chapters.

  • Art and Complexity

    • 1st Edition
    • J. Casti + 1 more
    • English
    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
    • R.O. Gandy + 1 more
    • English
    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
    • Alan J.A. Robinson + 1 more
    • English
    Handbook of Automated Reasoning presents overviews of the fundamental notations, techniques, ideas and methods developed and used in automated reasoning and its practical applications, which are used in many areas of computer science, including software and hardware, logic and functional programming, formal methods, knowledge representation, deductive databases, and artificial intelligence.

  • Handbook of Automated Reasoning

    • 1st Edition
    • Volume II
    • Alan J.A. Robinson + 1 more
    • English

  • CAFE: An Industrial-Strength Algebraic Formal Method

    • 1st Edition
    • K. Futatsugi + 2 more
    • English
    This book contains selected papers on the language, applications, and environments of CafeOBJ, which is a state-of -the-art algebraic specification language. The authors are speakers at a workshop held in 1998 to commemorate a large industrial/academic project dedicated to CafeOBJ. The project involved more than 40 people from more than 10 organisations, of which 6 are industrial. The workshop attracted about 30 talks and more than 70 attendees.The papers in the book however, are either heavily revised versions presented at the workshop, to reflect recent advancements or research; or completely new ones, written especially for this book. In this regard, the book is not a usual postpublication after a workshop. Also, although it is a compendium of papers that are related to CafeOBJ, the book is not a manual, reference, or tutorial of CafeOBJ. Probably the best description is that it is a collection of papers that investigate how to use, or to make it easy to use, CafeOBJ. Reflecting the diverse nature of the project and its participants (most of the authors are participants to the project), the papers, put together, offer a comprehensive picture from this methodological perspective.Some papers deal with various advanced aspects of the language, such as rewriting logic and behavioural logic. For rewriting logic, a couple of significant applications were reported. In particular, UML, now considered de facto standard language for modelling systems, is the subject of one paper. For behavioural logic, new methodological guidelines are presented. Some papers shed new light on a more traditional paradigm in the language; order-sorted equational specifications. One paper, in particular, deal with a way to associate CafeOBJ with object-oriented programming. The other papers deal with environments for writing and vertifying specifications written in CafeOBJ. Underlying those papers are two major considerations: user interfaces for manipulating specifications, and systematic supports for proofs. All the environments explained in the papers assume and support distributed computing, and de facto standard network technologies, such as WWW and http, are incorporated.

  • Provability, Computability and Reflection

    • 1st Edition
    • Volume 24
    • Lev D. Beklemishev
    • English

  • Foundational Studies Selected Works

    • 1st Edition
    • Volume 93A
    • Lev D. Beklemishev
    • English

  • Computer Programming and Formal Systems

    • 1st Edition
    • Volume 35
    • Lev D. Beklemishev
    • English

  • Provability, Computability and Reflection

    • 1st Edition
    • Volume 12
    • Lev D. Beklemishev
    • English

  • Model Theory For Infinitary Logic

    • 1st Edition
    • Volume 62
    • Lev D. Beklemishev
    • English

  • Lincos

    Design of a Language for Cosmic Intercourse
    • 1st Edition
    • Volume 28
    • Lev D. Beklemishev
    • English

  • Provability, Computability and Reflection

    • 1st Edition
    • Volume 34
    • Lev D. Beklemishev
    • English
    The book consists of a selection of the forms of the axiom of choice which appeared in the literature together with additional forms which were obtained in the process of writing the book. Forms which were either used often in practice, unusual, relatively unknown, or particularly weak or strong were chosen for inclusion. The book assumes a knowledge of logic and elementary set theory (von Neumann-Bemays-Godel set theory), but does include a list of definitions of set theoretical symbols and terms in the section entitled "Preliminary Definitions and Theorems".

  • Word Problems

    • 1st Edition
    • Volume 71
    • Lev D. Beklemishev
    • English

  • Provability, Computability and Reflection

    • 1st Edition
    • Volume 4
    • Lev D. Beklemishev
    • English

  • Constructible Sets with Applications

    • 1st Edition
    • Volume 57
    • Lev D. Beklemishev
    • English

  • Provability, Computability and Reflection

    • 1st Edition
    • Volume 7
    • Lev D. Beklemishev
    • English

  • Algebra of Proofs

    • 1st Edition
    • Volume 88
    • Lev D. Beklemishev
    • English

  • Provability, Computability and Reflection

    • 1st Edition
    • Volume 15
    • Lev D. Beklemishev
    • English

  • An Algebraic Approach to Non-Classical Logics

    • 1st Edition
    • Volume 78
    • Lev D. Beklemishev
    • English

  • Proceedings of the Second Scandinavian Logic Symposium

    • 1st Edition
    • Volume 63
    • Lev D. Beklemishev
    • English

  • Set Theory

    • 1st Edition
    • Volume 76
    • Lev D. Beklemishev
    • English

  • A Transfinite Type Theory with Type Variables

    • 1st Edition
    • Volume 37
    • Lev D. Beklemishev
    • English

  • Provability, Computability and Reflection

    • 1st Edition
    • Volume 30
    • Lev D. Beklemishev
    • English

  • Sets and Classes on The Work by Paul Bernays

    • 1st Edition
    • Volume 84
    • Lev D. Beklemishev
    • English

  • Generalized Recursion Theory

    • 1st Edition
    • Volume 79
    • Lev D. Beklemishev
    • English

  • Studies in Logic and the Foundations of Mathematics

    • 1st Edition
    • Volume 42
    • Lev D. Beklemishev
    • English

  • Proof Theory

    • 1st Edition
    • Volume 81
    • Lev D. Beklemishev
    • English

  • The Theory of Semisets

    • 1st Edition
    • Volume 70
    • Lev D. Beklemishev
    • English

  • SET THEORY

    • 1st Edition
    • Volume 86
    • Lev D. Beklemishev
    • English

  • Constructive Order Types

    • 1st Edition
    • Volume 56
    • Lev D. Beklemishev
    • English

  • Computer Programming and Formal Systems

    • 1st Edition
    • Volume 26
    • Lev D. Beklemishev
    • English

  • WORD PROBLEMS II

    • 1st Edition
    • Volume 95
    • Lev D. Beklemishev
    • English

  • Provability, Computability and Reflection

    • 1st Edition
    • Volume 18
    • Lev D. Beklemishev
    • English

  • Mathematical Logic in Latin America, Proceedings of the IV Latin American Symposium on Mathematical Logic

    • 1st Edition
    • Volume 99
    • Lev D. Beklemishev
    • English

  • Intuitionistic Logic Model Theory and Forcing

    • 1st Edition
    • Volume 54
    • Lev D. Beklemishev
    • English

  • Sets, Models and Recursion Theory

    • 1st Edition
    • Volume 46
    • Lev D. Beklemishev
    • English

  • Provability, Computability and Reflection

    • 1st Edition
    • Volume 17
    • Lev D. Beklemishev
    • English

  • Provability, Computability and Reflection

    • 1st Edition
    • Volume 20
    • Lev D. Beklemishev
    • English
    Studies in Logic publishes monographs and occasionally edited volumes in the area of mathematical logic and its applications.

  • Provability, Computability and Reflection

    • 1st Edition
    • Volume 29
    • Lev D. Beklemishev
    • English

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