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Yury Podlipenko

  1. Estimation of parameters of boundary value problems for linear ordinary differential equations with uncertain data.

    Ср, 12/16/2009 - 16:01 — SomNambul
    Authors: Yury Shestopalov, Yury Podlipenko, Olexandr Nakonechnyi
    Subjects: Classical Analysis and ODEs
    Abstract

    In this paper we construct optimal, in certain sense, estimates of values of
    linear functionals on solutions to two-point boundary value problems (BVPs) for
    systems of linear first-order ordinary differential equations from observations
    which are linear transformations of the same solutions perturbed by additive
    random noises. It is assumed here that right-hand sides of equations and
    boundary data as well as statistical characteristics of random noises in
    observations are not known and belong to certain given sets in corresponding
    functional spaces.

  2. Estimation under uncertainties of acoustic and electromagnetic fields from noisy observations.

    Ср, 10/14/2009 - 11:03 — SomNambul
    Authors: Yury Shestopalov, Yury Podlipenko, Vladimir Prishlyak
    Subjects: Analysis of PDEs
    Abstract

    The creation and justification of the methods for minimax estimation of
    parameters of the external boundary value problems for the Helmholtz equation
    in unbounded domains are considered. When observations are distributed in
    subdomains, the determination of minimax estimates is reduced to the solution
    of integro-differential equations in bounded domains. When observations are
    distributed on a system of surfaces the problem is reduced to solving integral
    equations on an unclosed bounded surface which is a union of the boundary of
    the domain and this system of surfaces.

  3. Estimation under uncertainties of acoustic and electromagnetic fields from noisy observations.

    Ср, 10/14/2009 - 11:03 — SomNambul
    Authors: Yury Shestopalov, Yury Podlipenko, Vladimir Prishlyak
    Subjects: Analysis of PDEs
    Abstract

    The creation and justification of the methods for minimax estimation of
    parameters of the external boundary value problems for the Helmholtz equation
    in unbounded domains are considered. When observations are distributed in
    subdomains, the determination of minimax estimates is reduced to the solution
    of integro-differential equations in bounded domains. When observations are
    distributed on a system of surfaces the problem is reduced to solving integral
    equations on an unclosed bounded surface which is a union of the boundary of
    the domain and this system of surfaces.

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