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Sökning: WFRF:(Asekritova Irina)

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  • Asekritova, Irina, et al. (författare)
  • Diffractive Index Determination by Tikhonov Regularization on Forced String Vibration Data
  • 2009
  • Ingår i: Mathematical modelling of wave phenomena. - Melville, New York : American Institute of Physics. ; , s. 224-232, s. 224-232
  • Konferensbidrag (refereegranskat)abstract
    • Wave analysis is efficient for investigating the interior of objects. Examples are ultra sound examination of humans and radar using elastic and electromagnetic waves. A common procedure is inverse scattering where both transmitters and receivers are located outside the object or on its boundary. A variant is when both transmitters and receivers are located on the scattering object. The canonical model is a finite inhomogeneous string driven by a harmonic point force. The inverse problem for the determination of the diffractive index of the string is studied. This study is a first step to the problem for the determination of the mechanical strength of wooden logs. An inverse scattering theory is formulated incorporating two regularizing strategies. The results of simulations using this theory show that the suggested method works quite well and that the regularization methods based on the couple of spaces (L2; H1 ) could be very useful in such problems.  
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  • Asekritova, Irina, et al. (författare)
  • Distribution and Rearranement Estimates of the Maximal Functions and Interpolation
  • 1997
  • Ingår i: Studia Mathematica. - 0039-3223 .- 1730-6337. ; 124:2, s. 107-132
  • Tidskriftsartikel (refereegranskat)abstract
    • There are given necessary and sufficient conditions on a measure dμ(x)=w(x)dx under which the key estimates for the distribution and rearrangement of the maximal function due to Riesz, Wiener, Herz and Stein are valid. As a consequence, we obtain the equivalence of the Riesz and Wiener inequalities which seems to be new even for the Lebesgue measure. Our main tools are estimates of the distribution of the averaging function f** and a modified version of the Calderón-Zygmund decomposition. Analogous methods allow us to obtain K-functional formulas in terms of the maximal function for couples of weighted $L_p$-spaces.
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  • Asekritova, Irina (författare)
  • Interpolation of Approximation Spaces with Nonlinear Projectors
  • 2006
  • Ingår i: Proceedings of the Estonian Academy of Sciences. - 1406-0086 .- 2228-0685. ; 55:3, s. 146-149
  • Tidskriftsartikel (refereegranskat)abstract
    • Approximation spaces defined by multiparametric approximation families with possible nonlinear projectors are considered. It is shown that a real interpolation space for a tuple of such spaces is again an approximation space of the same type.
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