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Books in Mathematics

The Mathematics collection presents a range of foundational and advanced research content across applied and discrete mathematics, including fields such as Computational Mathematics; Differential Equations; Linear Algebra; Modelling & Simulation; Numerical Analysis; Probability & Statistics.

BooksJournals

    • Extreme Value Theory in Engineering

      • 1st Edition
      • August 28, 1988
      • Enrique Castillo
      • English
      • Paperback
        9 7 8 0 1 2 3 9 5 9 4 4 7
      • Hardback
        9 7 8 0 1 2 1 6 3 4 7 5 9
      • eBook
        9 7 8 0 0 8 0 9 1 7 2 5 2
      This book is a comprehensive guide to extreme value theory in engineering. Written for the end user with intermediate and advanced statistical knowledge, it covers classical methods as well as recent advances. A collection of 150 examples illustrates the theoretical results and takes the reader from simple applications through complex cases of dependence.

    • Infinite-Dimensional Topology

      • 1st Edition
      • Volume 43
      • December 1, 1988
      • J. van Mill
      • English
      • Paperback
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      • Hardback
        9 7 8 0 4 4 4 8 7 1 3 3 6
      • eBook
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      The first part of this book is a text for graduate courses in topology. In chapters 1 - 5, part of the basic material of plane topology, combinatorial topology, dimension theory and ANR theory is presented. For a student who will go on in geometric or algebraic topology this material is a prerequisite for later work. Chapter 6 is an introduction to infinite-dimensional topology; it uses for the most part geometric methods, and gets to spectacular results fairly quickly. The second part of this book, chapters 7 & 8, is part of geometric topology and is meant for the more advanced mathematician interested in manifolds. The text is self-contained for readers with a modest knowledge of general topology and linear algebra; the necessary background material is collected in chapter 1, or developed as needed.One can look upon this book as a complete and self-contained proof of Toruńczyk's Hilbert cube manifold characterization theorem: a compact ANR X is a manifold modeled on the Hilbert cube if and only if X satisfies the disjoint-cells property. In the process of proving this result several interesting and useful detours are made.

    • Unimodality, Convexity, and Applications

      • 1st Edition
      • July 28, 1988
      • English
      • Hardback
        9 7 8 0 1 2 2 1 4 6 9 0 9
      • eBook
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      In this book, the basic notions and tools of unimodality as they relate to probability and statistics are presented. In addition, many applications are covered; these include the use of unimodality to obtain monotonicity properties of power functions of multivariate tests, minimum volume confidence regions, and recurrence of symmetric random walks. The diversity of the applications will convince the reader that unimodality and convexity form an important tool in the hands of a researcher in probability and statistics.

    • Ring Theory V1

      • 1st Edition
      • Volume 127I
      • June 1, 1988
      • English
      • eBook
        9 7 8 0 0 8 0 8 7 4 4 6 3

    • Topology and Geometry for Physicists

      • 1st Edition
      • January 4, 1988
      • Charles Nash + 1 more
      • English
      • Paperback
        9 7 8 0 1 2 5 1 4 0 8 1 2
      • eBook
        9 7 8 0 0 8 0 5 7 0 8 5 3
      Applications from condensed matter physics, statistical mechanics and elementary particle theory appear in the book. An obvious omission here is general relativity--we apologize for this. We originally intended to discuss general relativity. However, both the need to keep the size of the book within the reasonable limits and the fact that accounts of the topology and geometry of relativity are already available, for example, in The Large Scale Structure of Space-Time by S. Hawking and G. Ellis, made us reluctantly decide to omit this topic.

    • Graph Theory and Applications

      • 1st Edition
      • Volume 38
      • January 1, 1988
      • J. Akiyama + 2 more
      • English
      • Paperback
        9 7 8 0 4 4 4 5 5 7 1 4 8
      • Hardback
        9 7 8 0 4 4 4 7 0 5 3 8 9
      • eBook
        9 7 8 0 0 8 0 8 6 7 7 8 6

    • Ring Theory V2

      • 1st Edition
      • Volume 127II
      • July 1, 1988
      • English
      • eBook
        9 7 8 0 0 8 0 8 7 4 4 7 0

    • Theory of Difference Equations Numerical Methods and Applications by V Lakshmikantham and D Trigiante

      • 1st Edition
      • Volume 181
      • April 28, 1988
      • Lakshmikantham + 1 more
      • English
      • Hardback
        9 7 8 0 1 2 4 3 4 1 0 0 5
      • eBook
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      In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; andmethods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.As a result, the book represents a blend of new methods in general computational analysis,and specific, but also generic, techniques for study of systems theory ant its particularbranches, such as optimal filtering and information compression.

    • Introduction to Operator Theory and Invariant Subspaces

      • 1st Edition
      • Volume 42
      • October 1, 1988
      • B. Beauzamy
      • English
      • Paperback
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      • eBook
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      This monograph only requires of the reader a basic knowledge of classical analysis: measure theory, analytic functions, Hilbert spaces, functional analysis. The book is self-contained, except for a few technical tools, for which precise references are given.Part I starts with finite-dimensional spaces and general spectral theory. But very soon (Chapter III), new material is presented, leading to new directions for research. Open questions are mentioned here. Part II concerns compactness and its applications, not only spectral theory for compact operators (Invariant Subspaces and Lomonossov's Theorem) but also duality between the space of nuclear operators and the space of all operators on a Hilbert space, a result which is seldom presented. Part III contains Algebra Techniques: Gelfand's Theory, and application to Normal Operators. Here again, directions for research are indicated. Part IV deals with analytic functions, and contains a few new developments. A simplified, operator-oriented, version is presented. Part V presents dilations and extensions: Nagy-Foias dilation theory, and the author's work about C1-contractions. Part VI deals with the Invariant Subspace Problem, with positive results and counter-examples.In general, much new material is presented. On the Invariant Subspace Problem, the level of research is reached, both in the positive and negative directions.

    • Recent Results in the Theory of Graph Spectra

      • 1st Edition
      • Volume 36
      • January 1, 1988
      • D.M. Cvetkovic + 3 more
      • English
      • Paperback
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      • eBook
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      The purpose of this volume is to review the results in spectral graph theory which have appeared since 1978.The problem of characterizing graphs with least eigenvalue -2 was one of the original problems of spectral graph theory. The techniques used in the investigation of this problem have continued to be useful in other contexts including forbidden subgraph techniques as well as geometric methods involving root systems. In the meantime, the particular problem giving rise to these methods has been solved almost completely. This is indicated in Chapter 1.The study of various combinatorial objects (including distance regular and distance transitive graphs, association schemes, and block designs) have made use of eigenvalue techniques, usually as a method to show the nonexistence of objects with certain parameters. The basic method is to construct a graph which contains the structure of the combinatorial object and then to use the properties of the eigenvalues of the graph. Methods of this type are given in Chapter 2.Several topics have been included in Chapter 3, including the relationships between the spectrum and automorphism group of a graph, the graph isomorphism and the graph reconstruction problem, spectra of random graphs, and the Shannon capacity problem. Some graph polynomials related to the characteristic polynomial are described in Chapter 4. These include the matching, distance, and permanental polynomials. Applications of the theory of graph spectra to Chemistry and other branches of science are described from a mathematical viewpoint in Chapter 5. The last chapter is devoted to the extension of the theory of graph spectra to infinite graphs.

Related subjects

Mathematics and applied mathematics

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