Topic
Asymptotology
About: Asymptotology is a research topic. Over the lifetime, 1319 publications have been published within this topic receiving 35831 citations.
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TL;DR: An overview of the very recent asymptotic results in the problem of testing homogeneity against a two-component mixture is provided and illustrations of new and known results are presented.
29 citations
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TL;DR: In this article, an asymptotic expansion for smooth solutions of the Navier-Stokes equations in weighted spaces was derived, which removes previous restrictions on the number of terms of the coefficients, as well as on the range of the polynomial weights.
29 citations
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TL;DR: Asymptotic formulae for solutions to the Stokes problem in domains which, outside a ball, coincide with the three-dimensional layer are derived in this paper, where the procedure of dimension reduction is employed together with estimates for miscellaneous weighted norms of the solutions.
Abstract: Asymptotic formulae are derived for solutions to the Stokes problem in domains which, outside a ball, coincide with the three-dimensional layer \( {\Bbb R}^2 \times (0,1) \). The properties of detached asymptotic terms differ in the transversal and longitudinal directions. In order to justify the asymptotic expansions the procedure of dimension reduction is employed together with estimates for miscellaneous weighted norms of the solutions.
29 citations
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TL;DR: In this paper, the complete asymptotic expansion for the Kantorovich polynomials Kn as n→∞ is presented in a form convenient for applications, where all coefficients of n−k (k=1,2,...) are calculated explicitly in terms of Stirling numbers of the first and second kind.
Abstract: We present the complete asymptotic expansion for the Kantorovich polynomials Kn as n→∞. The result is in a form convenient for applications. All coefficients of n−k (k=1,2,...) are calculated explicitly in terms of Stirling numbers of the first and second kind.
28 citations
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TL;DR: In this article, the authors studied the asymptotic behavior of solutions of a mixed inhomogeneous boundary value problem and a spectral Neumann problem in a thin perforated domain with rapidly varying thickness.
Abstract: For a second-order symmetric uniformly elliptic differential operator with rapidly oscillating coefficients, we study the asymptotic behavior of solutions of a mixed inhomogeneous boundary-value problem and a spectral Neumann problem in a thin perforated domain with rapidly varying thickness. We obtain asymptotic estimates for the differences between solutions of the original problems and the corresponding homogenized problems. These results were announced in Dopovidi Akademii Nauk Ukrainy, No. 10, 15‐19 (1991). The new results obtained in the present paper are related to the construction of an asymptotic expansion of a solution of a mixed homogeneous boundary-value problem under additional assumptions of symmetry for the coefficients of the operator and for the thin perforated domain.
28 citations