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Ural Bekbaev

  1. An Inversion Formula for Multivariate Power Series.

    Втр, 03/20/2012 - 15:01 — SomNambul
    Authors: Ural Bekbaev
    Subjects: Algebraic Geometry
    Abstract

    For formal multivariate power series $\varphi(x)$ an inversion formula of the
    form $$ \varphi^{-1}(x)=x +\sum_{m=1}^{\infty}\sum_{k=0}^m (-1)^k(m
    k)\varphi^{\circ k}(x) is offered$$.

  2. A radius of absolute convergence for power series in many variables.

    Ср, 01/06/2010 - 16:01 — SomNambul
    Authors: Ural Bekbaev
    Subjects: Complex Variables
    Abstract

    In this paper for power series in many (real or complex)variables a radius of
    (absolute) convergence is offered. This radius can be evaluated by a formula
    similar to Cauchy-Hadamard formula and in one variable case they are same.

  3. A matrix representation of composition of polynomial maps.

    Пнд, 08/17/2009 - 18:30 — SomNambul
    Authors: Ural Bekbaev
    Subjects: Commutative Algebra
    Abstract

    In this paper polynomial maps are represented by the use of matrices whose
    entries are numbered by pair of multiindices. A new product of such matrices is
    introduced. By the use of this and ordinary product of matrices the matrix
    representation of composition of polynomial maps is given. A norm of such
    matrices, which coincides with Bombieri's norm of a polynomial in a particular
    case, is defined and investigated as well. A generalization of Bombieri's
    inequality is offered.

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