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1000年

作者： Gerald E. Bergum Andreas N. Philippou Alwyn F. Horadam

ISBN: (数字)9789400902237

ISBN: (纸本)9780792339564;9789401065832

This book contains 43 papers form among the 55 papers presented at the Sixth International Conference on Fibonacci numbers and Their applications which was held at Washington State University, Pullman, Washington, from July 18-22, 1994. These papers have been selected after a careful review by well known referees in the field, and they range from elementary number theory to probability and statistics. The Fibonacci numbers and recurrence relations are their unifying bond. It is anticipated that this book, like its five predecessors, will be useful to research workers and graduate students interested in the Fibonacci numbers and their applications. October 30, 1995 The Editors Gerald E. Bergum South Dakota State University Brookings, South Dakota, U.S.A. Alwyn F. Horadam University of New England Armidale, N.S.W., Australia Andreas N. Philippou 26 Atlantis Street Aglangia, Nicosia Cyprus xxi THE ORGANIZING COMMITTEES LOCAL COMMITTEE INTERNATIONAL COMMITTEE Long, Calvin T., Co-Chair Horadam, A.F. (Australia), Co-Chair Webb, William A., Co-Chair Philippou, A.N. (Cyprus), Co-Chair Burke, John Ando, S. (Japan) DeTemple, Duane W.

关键词： number theory algebra Statistics, general Computational Mathematics and Numerical Analysis Group theory and Generalizations

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Logical Methods 1

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丛书名： Progress in computer Science and Applied Logic

1000年

作者： John N. Crossley Jeffrey B. Remmel Richard A. Shore Moss E. Sweedler

ISBN: (数字)9781461203254

ISBN: (纸本)9780817636906;9781461267089

The twenty-six papers in this volume reflect the wide and still expanding range of Anil Nerode's work. A conference on Logical Methods was held in honor of Nerode's sixtieth birthday (4 June 1992) at the Mathematical Sciences Institute, Cornell University, 1-3 June 1992. Some of the conference papers are here, but others are from students, co-workers and other colleagues. The intention of the conference was to look forward, and to see the directions currently being pursued, in the development of work by, or with, Nerode. Here is a brief summary of the contents of this book. We give a retrospective view of Nerode's work. A number of specific areas are readily discerned: recursive equivalence types, recursive algebra and model theory, the theory of Turing degrees and r.e. sets, polynomial-time computability and computer science. Nerode began with automata theory and has also taken a keen interest in the history of mathematics. All these areas are represented. The one area missing is Nerode's applied mathematical work relating to the environment. Kozen's paper builds on Nerode's early work on automata. Recursive equivalence types are covered by Dekker and Barback, the latter using directly a fundamental metatheorem of Nerode. Recursive algebra is treated by Ge & Richards (group representations). Recursive model theory is the subject of papers by Hird, Moses, and Khoussainov & Dadajanov, while a combinatorial problem in recursive model theory is discussed in Cherlin & Martin's paper. Cenzer presents a paper on recursive dynamics.

关键词： Math applications in computer Science applications of Mathematics Mathematical Logic and Foundations Mathematical Logic and Formal Languages Logics and Meanings of Programs

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Structured Matrices and polynomials 1

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1000年

作者： Victor Y. Pan

ISBN: (数字)9781461201298

ISBN: (纸本)9780817642402;9781461266259

Structured matrices serve as a natural bridge between the areas of algebraic computations with polynomials and numerical matrix computations, allowing cross-fertilization of both fields. This book covers most fundamental numerical and algebraic computations with Toeplitz, Hankel, Vandermonde, Cauchy, and other popular structured matrices. Throughout the computations, the matrices are represented by their compressed images, called displacements, enabling both a unified treatment of various matrix structures and dramatic saving of computer time and memory. The resulting superfast algorithms allow further dramatic parallel acceleration using FFT and fast sine and cosine transforms. Included are specific applications to other fields, in particular, superfast solutions to: various fundamental problems of computer algebra; the tangential Nevanlinna--Pick and matrix Nehari problems The primary intended readership for this work includes researchers, algorithm designers, and advanced graduate students in the fields of computations with structured matrices, computer algebra, and numerical rational interpolation. The book goes beyond research frontiers and, apart from very recent research articles, includes yet unpublished results. To serve a wider audience, the presentation unfolds systematically and is written in a user-friendly engaging style. Only some preliminary knowledge of the fundamentals of linear algebra is required. This makes the material accessible to graduate students and new researchers who wish to study the rapidly exploding area of computations with structured matrices and polynomials. Examples, tables, figures, exercises, extensive bibliography, and index lend this text to classroom use or self-study.

关键词： algebra Linear and Multilinear algebras, Matrix theory theory of Computation Mathematics of Computing Computational Mathematics and Numerical Analysis

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Monte Carlo and Quasi-Monte Carlo Methods 1996 1

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丛书名： Lecture Notes in Statistics

1000年

作者： Harald Niederreiter Peter Hellekalek Gerhard Larcher Peter Zinterhof

ISBN: (数字)9781461216902

ISBN: (纸本)9780387983356

Monte Carlo methods are numerical methods based on random sampling and quasi-Monte Carlo methods are their deterministic versions. This volume contains the refereed proceedings of the Second International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing which was held at the University of Salzburg (Austria) from July 9--12, 1996. The conference was a forum for recent progress in the theory and the applications of these methods. The topics covered in this volume range from theoretical issues in Monte Carlo and simulation methods, low-discrepancy point sets and sequences, lattice rules, and pseudorandom number generation to applications such as numerical integration, numerical linear algebra, integral equations, binary search, global optimization, computational physics, mathematical finance, and computer graphics. These proceedings will be of interest to graduate students and researchers in Monte Carlo and quasi-Monte Carlo methods, to numerical analysts, and to practitioners of simulation methods.

关键词： applications of Mathematics

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Performance Engineering of computer and Telecommunications Systems 1

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1000年

作者： Madjid Merabti Michael Carew Frank Ball

ISBN: (数字)9781447110071

ISBN: (纸本)9783540760085

This book is the proceedings of the Workshop on the Performance Engineering of computer and Telecommunications Systems. The workshop Was held at Liverpool John Moores University, England on the 5th and 6th September 1995. The workshop follows a series organised by the British computer Society (BCS) Special Interest Group on Performance Engineering. The workshop addressed most techniques and experieI1ces in the Engineering of computer and Telecommunications Systems that provide a guaranteed quality of service. Techniques such as measurements, simulation, and analytical models and their applications to ATM networks, Multimedia Systems, Distributed Systems, Access and Wide Area Networks were presented. In addition a number of papers dealt with advances in the development of analytical models, simulation architectures and the application of formal methods, stich as Process algebra, to the specification and building of performance biased computer systems. The book is suitable for systems designers, engineers, researchers and postgraduate students interested in the design and implementation of computer Systems, Networks and Telecommunications. Many people assisted in the arrangements and success of this workshop. I would like to thank them all and in particular the reviewers. I would also like to particularly thank our industrial sponsors GPT Public Networks Group, Liverpool and BICC Cables, Chester, England for their generous financial and material support.

关键词： theory of Computation computer Engineering Communications Engineering, Networks

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Triangulations 1

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丛书名： Algorithms and Computation in Mathematics

1000年

作者： Jesús A. Loera Jörg Rambau Francisco Santos

ISBN: (数字)9783642129711

ISBN: (纸本)9783642129704;9783662502419

Triangulations appear everywhere, from volume computations and meshing to algebra and topology. This book studies the subdivisions and triangulations of polyhedral regions and point sets and presents the first comprehensive treatment of the theory of secondary polytopes and related topics. A central theme of the book is the use of the rich structure of the space of triangulations to solve computational problems (e.g., counting the number of triangulations or finding optimal triangulations with respect to various criteria), and to establish connections to applications in algebra, computer science, combinatorics, and optimization. With many examples and exercises, and with nearly five hundred illustrations, the book gently guides readers through the properties of the spaces of triangulations of "structured" (e.g., cubes, cyclic polytopes, lattice polytopes) and "pathological" (e.g., disconnected spaces of triangulations) situations using only elementary principles.

关键词： algebraic Geometry Discrete Mathematics theory of Computation Convex and Discrete Geometry Mathematics of Computing Computational Mathematics and Numerical Analysis

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Towards Mechanized Mathematical Assistants 1

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丛书名： Lecture Notes in computer Science

1000年

ISBN: (数字)9783540730866

ISBN: (纸本)9783540730835

This volume contains the collected contributions of two conferences, Calcu- ***2007wasthe14thinaseriesofconferences dedicated to the integration of computer algebra systems (CAS) and automated deduction systems (ADS). MKM 2007 was the sixth International Conference on Mathematical Knowledge Management, an emerging interdisciplinary ?eld of research in the intersection of mathematics, computer science, library s- ence, and scienti?c publishing. Both conferences aimed to provide mechanized mathematical assistants. Although the two conferences have separate communities and separate foci, there is a signi?cant overlap in the interests in building mechanized mathem- ical assistants. For this reason it was decided to collocate the two events in 2007 for the ?rst time, at RISC in Hagenberg, Austria. The number and quality of the submissions show that this was a good decision. While the proceedings are shared, the submission process was separate. The responsibility for acc- tance/rejection rests completely with the two separate Program Committees. By this collocation we made a contribution against the fragmentation of communities which work on di?erent aspects of di?erent independent branches, traditional branches (e.g., computer algebra and theorem proving), as well as newly emerging ones (on user interfaces, knowledge management, theory exp- ration, etc.). This will also facilitate the development of integrated mechanized mathematical assistants that will be routinely used by mathematicians, c- puter scientists, and engineers in their every-day business.

关键词： algebra Artificial Intelligence Data Mining and Knowledge Discovery Information Systems applications (incl. Internet) Database Management computer Communication Networks

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Numerical Fourier Analysis 2

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丛书名： Applied and Numerical Harmonic Analysis

1000年

作者： Gerlind Plonka Daniel Potts Gabriele Steidl Manfred Tasche

ISBN: (数字)9783031350054

ISBN: (纸本)9783031350047;9783031350078

New technological innovations and advances in research in areas such as spectroscopy, computer tomography, signal processing, and data analysis require a deep understanding of function approximation using Fourier methods. To address this growing need, this monograph combines mathematical theory and numerical algorithms to offer a unified and self-contained presentation of Fourier analysis.;The first four chapters of the text serve as an introduction to classical Fourier analysis in the univariate and multivariate cases, including the discrete Fourier transforms, providing the necessary background for all further chapters. Next, chapters explore the construction and analysis of corresponding fast algorithms in the one- and multidimensional cases. The well-known fast Fourier transforms (FFTs) are discussed, as well as recent results on the construction of the nonequispaced FFTs, high-dimensional FFTs on special lattices, and sparse FFTs. An additional chapter is devoted to discrete trigonometric transforms and Chebyshev expansions. The final two chapters consider various applications of numerical Fourier methods for improved function approximation, including Prony methods for the recovery of structured functions.;This new edition has been revised and updated throughout, featuring new material on a new Fourier approach to the ANOVA decomposition of high-dimensional trigonometric polynomials; new research results on the approximation errors of the nonequispaced fast Fourier transform based on special window functions; and the recently developed ESPIRA algorithm for recovery of exponential sums, among others.;will be of interest to graduate students and researchers in applied mathematics, physics, computer science, engineering, and other areas where Fourier methods play an important role in applications.

关键词： Fourier Analysis Abstract Harmonic Analysis Numerical Analysis Mathematical applications in computer Science Linear algebra

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Binary Quadratic Forms 1

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丛书名： Algorithms and Computation in Mathematics

1000年

作者： Johannes Buchmann Ulrich Vollmer

ISBN: (数字)9783540463689

ISBN: (纸本)9783540463672;9783642079719

This book deals with algorithmic problems concerning binary quadratic forms 2 2 f(X,Y)= aX +bXY +cY with integer coe?cients a, b, c, the mathem- ical theories that permit the solution of these problems, and applications to cryptography. A considerable part of the theory is developed for forms with real coe?cients and it is shown that forms with integer coe?cients appear in a natural way. Much of the progress of number theory has been stimulated by the study of concrete computational problems. Deep theories were developed from the classic time of Euler and Gauss onwards to this day that made the solutions ofmanyof *** became an object of study in their own right. Thisbookintertwinestheexpositionofoneveryclassicalstrandofnumber theory with the presentation and analysis of algorithms both classical and modern which solve its motivating problems. This algorithmic approach will lead the reader, we hope, not only to an understanding of theory and solution methods, but also to an appreciation of the e?ciency with which solutions can be reached. The computer age has led to a marked advancement of algorithmic - search. On the one hand, computers make it feasible to solve very hard pr- lems such as the solution of Pell equations with large coe?cients. On the other, the application of number theory in public-key cryptography increased the urgency for establishing the complexity of several computational pr- lems: many a computer system stays only secure as long as these problems remain intractable.

关键词： algebra number theory Mathematics of Computing Cryptology

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computers in algebra and number theory, v 4. SIAM- AMS Proceedings, New York City, NY, Mar 25- 26 1970

Am Mathematical Soc

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Am Mathematical Soc 1971年

作者： BIRKHOFF G HALL JR M

Proceedings includes 14 papers, most of which concern the applications of digital computers to algebra and number theory. However, two of the papers are concerned with the complementary role played by algebra in the science of digital computing. Following papers presented- The role of algebra in computing;G. BIRKHOFF;p 1. On performing group multiplication by switching circuits;S. WINOGRAD;p 49. applications of computers to the geometry of numbers;H. P. F. SWINNERTON- DYER;p 55. Approximation to cubic irrationals;B. J. BIRCH;p 63. On the group of an equation;H. ZASSENHAUS;p 69. Nonexistence theorems for perfect error- correcting codes;J. H. van LINT;p 89. A combinatorial packing problem;L. D. BAUMERT;p 97. Construction of finite simple groups;M. HALL Jr;p 109. Groups, lattices, and quadratic forms;J. H. CONWAY;p 135. Rank 3 groups and strongly regular groups;M. D. HESTENES, D. G. HIGMAN;p 141. Computing local structure of large finite graphs;J. J. CANNON;p 161. Subgroups and permutation characters;J. McKAY;p 177. Computing moderately large groups;J. NEUBUSERl p 191.

关键词： MATHEMATICS--computer applications

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