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IBM Journal of Research and Development

Issue 2 • March 1987

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Displaying Results 1 - 18 of 18
  • Preface

    Publication Year: 1987, Page(s): 150
    IEEE is not the copyright holder of this material | Click to expandAbstract | PDF file iconPDF (102 KB)

    The twenty-fifth anniversary of the Mathematical Sciences Department of the IBM Research Division is a good time to pause and take stock. It is time to celebrate past achievements, and to anticipate those which will be coming in the next quarter century. View full abstract»

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  • Science in industry

    Publication Year: 1987, Page(s):151 - 153
    IEEE is not the copyright holder of this material | Click to expandAbstract | PDF file iconPDF (283 KB)

    The industrial environment contains problems of practical importance. To exploit that environment, an industrial research group must accept the responsibility for forming strong and useful relationships with the rest of the company of which it is a part. Opportunities for contributing to both the industrial and academic worlds stem from the many product-related problems for which existing science ... View full abstract»

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  • Reflections on the early days of the department

    Publication Year: 1987, Page(s):154 - 157
    IEEE is not the copyright holder of this material | Click to expandAbstract | PDF file iconPDF (352 KB)

    The paper contains the reminiscences of the founding director of the Mathematical Sciences Department in IBM Research. It is interspersed with a number of anecdotes about his friend and colleague, John von Neumann. It attempts in a short space to recapitulate the history of a distinguished department of mathematics in an industrial environment in an informal and hopefully humorous manner. View full abstract»

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  • Applied mathematics, a national view

    Publication Year: 1987, Page(s):158 - 161
    IEEE is not the copyright holder of this material | Click to expandAbstract | PDF file iconPDF (448 KB)

    The development of applied mathematics in the United States during the past forty years is described, including the role of computers and computation in enlarging and changing the field. The growth of the profession is also discussed, along with needs for training and funding for the future. View full abstract»

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  • A view of Approximation Theory

    Publication Year: 1987, Page(s):162 - 168
    IEEE is not the copyright holder of this material | Click to expandAbstract | PDF file iconPDF (553 KB)

    This is a selective survey of Approximation Theory which touches on the concepts of best approximation, good approximation, approximation of classes of functions, approximation of functionals, and optimal estimation. View full abstract»

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  • Numerical analysis and the scientific method

    Publication Year: 1987, Page(s):169 - 177
    IEEE is not the copyright holder of this material | Click to expandAbstract | PDF file iconPDF (795 KB)

    The computer has given rise to a new mode of scientific practice, and today computational science stands beside theory and experiment as a fundamental methodology. The impact of the computer revolution on science can be projected from current trends. The demands to be made on computing methodologies will be reviewed. One of the demands is an ongoing need for excellence in computational methodologi... View full abstract»

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  • Some stability techniques for multistep methods

    Publication Year: 1987, Page(s):178 - 186
    IEEE is not the copyright holder of this material | Click to expandAbstract | PDF file iconPDF (656 KB)

    A partial survey is given of sundry results in the stability theory of multistep formulae when these are used to integrate time-varying or nonlinear stiff systems, with emphasis on systems arising in circuit analysis. View full abstract»

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  • Factoring logic functions

    Publication Year: 1987, Page(s):187 - 198
    Cited by:  Papers (32)  |  Patents (3)
    IEEE is not the copyright holder of this material | Click to expandAbstract | PDF file iconPDF (896 KB)

    A factored form is a representation of a logic function that is either a single literal or a sum or product of factored forms. Thus it is equivalent to a parenthesized algebraic expression. It is one of many possible representations of a logic function, but seems to be the most appropriate one for use in multilevel logic synthesis. We give a number of methods for obtaining different factored forms... View full abstract»

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  • Some aspects of the theory of statistical control schemes

    Publication Year: 1987, Page(s):199 - 205
    Cited by:  Papers (1)  |  Patents (2)
    IEEE is not the copyright holder of this material | Click to expandAbstract | PDF file iconPDF (705 KB)

    Control schemes (charts) are widely used in industrial quality control as means of monitoring the quality of manufactured products. These schemes provide a set of criteria for testing whether a given sequence of observations corresponds to an “on-target” state of the production process. In the present work, we consider some graphical, computational, and statistical aspects of control... View full abstract»

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  • The group problem and integer programming duality

    Publication Year: 1987, Page(s):206 - 212
    IEEE is not the copyright holder of this material | Click to expandAbstract | PDF file iconPDF (531 KB)

    Some duality results for integer programming based on subadditive functions are presented first for linear programs and then for the group problem. A similar result for the knapsack problem is given and then a relationship between facets for the group relaxation and facets of the knapsack problem is given. The mixed integer cyclic group problem is then considered and a dual problem given. A common... View full abstract»

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  • Fourier transforms that respect crystallographic symmetries

    Publication Year: 1987, Page(s):213 - 223
    Cited by:  Papers (1)
    IEEE is not the copyright holder of this material | Click to expandAbstract | PDF file iconPDF (710 KB)

    In crystallography one has to compute finite Fourier transforms that are often very large and often respect crystallographic symmetries. In this paper we discuss efficient finite Fourier transform algorithms on 5×5×5 points that respect a collection of crystallographic symmetries. Although the size is too small for any practical problems, the methods indicated in this paper can be ex... View full abstract»

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  • The torus and the disk

    Publication Year: 1987, Page(s):224 - 234
    Cited by:  Papers (2)
    IEEE is not the copyright holder of this material | Click to expandAbstract | PDF file iconPDF (946 KB)

    This paper is a survey of a coherent program of mathematics spanning 28 years. It begins with questions concerning classification and structure in ergodic theory and abstract dynamical systems and describes the author's involvement with toral automorphisms, topological entropy, iteration of maps on the interval, symbolic dynamics, and ultimate engineering applications. It serves as a case study of... View full abstract»

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  • The complexity of computations by networks

    Publication Year: 1987, Page(s):235 - 243
    Cited by:  Papers (10)  |  Patents (1)
    IEEE is not the copyright holder of this material | Click to expandAbstract | PDF file iconPDF (764 KB)

    We survey the current state of knowledge concerning the computation of Boolean functions by networks, with particular emphasis on the addition and multiplication of binary numbers. View full abstract»

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  • Cryptography

    Publication Year: 1987, Page(s):244 - 248
    Cited by:  Papers (1)  |  Patents (1)
    IEEE is not the copyright holder of this material | Click to expandAbstract | PDF file iconPDF (446 KB)

    This paper is concerned with two aspects of cryptography in which the author has been working. One is the Data Encryption Standard (DES), developed at IBIM and now in wide use for commercial cryptographic applications. This is a “private key” system; the communicants share a secret key, and the eavesdropper will succeed if he can guess this key among its quadrillions of possibilities... View full abstract»

    Freely Available from IEEE
  • Efficient randomized pattern-matching algorithms

    Publication Year: 1987, Page(s):249 - 260
    Cited by:  Papers (111)  |  Patents (53)
    IEEE is not the copyright holder of this material | Click to expandAbstract | PDF file iconPDF (908 KB)

    We present randomized algorithms to solve the following string-matching problem and some of its generalizations: Given a string X of length n (the pattern) and a string Y (the text), find the first occurrence of X as a consecutive block within Y. The algorithms represent strings of length n by much shorter strings called fingerprints, and achieve their efficiency by manipulating fingerprints inste... View full abstract»

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  • Recent IBM patents

    Publication Year: 1987, Page(s):261 - 264
    IEEE is not the copyright holder of this material | PDF file iconPDF (257 KB)
    Freely Available from IEEE
  • Recent papers by IBM authors

    Publication Year: 1987, Page(s):265 - 273
    IEEE is not the copyright holder of this material | Click to expandAbstract | PDF file iconPDF (925 KB)

    The information listed here is supplied by the Institute for Scientific Information. Reprints of the papers may be obtained by writing directly to the first author cited. Papers are listed alphabetically by author. View full abstract»

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  • Errata [Clarification]

    Publication Year: 1987, Page(s): 274
    IEEE is not the copyright holder of this material | PDF file iconPDF (49 KB)
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Clifford A. Pickover
IBM T. J. Watson Research Center