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Elisabeth Remm

  1. A new algebraic and arithmetic framework for interval computations.

    Ср, 07/20/2011 - 15:01 — SomNambul
    Authors: Michel Goze, Nicolas Goze, Elisabeth Remm, Abdel Kenoufi
    Subjects: Numerical Analysis
    Abstract

    In this paper we propose some very promissing results in interval arithmetics
    which permit to build well-defined arithmetics including distributivity of
    multiplication and division according addition and substraction. Thus, it
    allows to build all algebraic operations and functions on intervals. This will
    avoid completely the wrapping effects and data dependance. Some simple
    applications for matrix eigenvalues calculations, inversion of symmetric
    matrices and finally optimization are exhibited in the object-oriented
    programming language python.

  2. An algebraic approach to the set of intervals (a new approach of arithmetic of intervals).

    Пт, 10/23/2009 - 14:26 — SomNambul
    Authors: Nicolas Goze, Elisabeth Remm
    Subjects: Numerical Analysis
    Abstract

    In this paper we present the set of intervals as a normed vector space. We
    define also a four-dimensional associative algebra whose product gives the
    product of intervals in any cases. This approach allows to give a notion of
    divisibility and in some cases an euclidian division. We introduce differential
    calculus and give some applications.

  3. n-Lie algebras.

    Ср, 09/09/2009 - 22:08 — SomNambul
    Authors: Michel Goze, Nicolas Goze, Elisabeth Remm
    Subjects: Rings and Algebras
    Abstract

    The notion of $n$-ary algebras, that is vector spaces with a multiplication
    concerning $n$-arguments, $n \geq 3$, became fundamental since the works of
    Nambu. Here we first present general notions concerning $n$-ary algebras and
    associative $n$-ary algebras. Then we will be interested in the notion of
    $n$-Lie algebras, initiated by Filippov, and which is attached to the Nambu
    algebras. We study the particular case of nilpotent or filiform $n$-Lie
    algebras to obtain a beginning of classification.

Math-arch

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