Showing papers on "Asymptotology published in 1988"
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TL;DR: In this article, a new asymptotic method of attack on the connection problem around the point at infinity for Painleve transcendents of the first and second kind is developed.
68 citations
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16 citations
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01 Jan 1988TL;DR: In this article, the authors pointed out that an estimator, though asymptotically much less efficient than another, may still have much greater probability concentration than the latter.
Abstract: Partly of an expository nature this note brings out the fact that an estimator, though asymptotically much less efficient (in the classical sense) than another, may yet have much greater probability concentration (as defined in this article) than the latter.
8 citations
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5 citations
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4 citations
17 May 1988
TL;DR: In this paper, an asymptotic theory for a class of initial-boundary value problems for weakly nonlinear wave equations is presented, which implies the well-posedness of the problem in the classical sense and the validity of formal approximations on long time-scales.
Abstract: This chapter aims to contribute to the foundation of the asymptotic methods for initialboundary value problems and initial value problems for weakly nonlinear hyperbolic partial differential equations of order two. In this chapter an asymptotic theory for a class of initial-boundary value problems for weakly nonlinear wave equations is presented. The theory implies the well-posedness of the problem in the classical sense and the validity of formal approximations on long time-scales. As an application of the theory an initial-boundary value problem for a Rayleigh wave equation is studied in detail using a two-timescales perturbation method. From an aeroelastic analysis it is shown that this initial-boundary value problem may be regarded as a model describing the growth of wind-induced oscillations of overhead transmission lines.
3 citations
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01 Jan 1988TL;DR: In this article, a brief outline of strongly elliptic boundary integral equations is given for the standard boundary element methods as point collocation, Ritz-Galerkin and least squares, and the corresponding asymptotic error estimates.
Abstract: Here we give a brief outline of the concept of strongly elliptic boundary integral equations. For the standard boundary element methods as point collocation, Ritz-Galerkin and least squares, we collect the corresponding asymptotic error estimates. The class of integral equations contains the Fredholm equations of the second kind, some of the first kind, Cauchy singular integral equations and hypersingular equations.
2 citations
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1 citations
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1 citations
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01 Mar 1988-Compel-the International Journal for Computation and Mathematics in Electrical and Electronic Engineering
TL;DR: In this article, the asymptotic stability of zero-solution systems with and without impulses is investigated. And the results obtained are formulated in four theorems, including the theorem of Marachkov on the stability of systems without impulses.
Abstract: In this paper the asymptotic and globally asymptotic stability of the zero solution of systems with impulses is investigated. For this purpose piecewise continuous auxiliary functions are used which are an analogue to Lyapunov's functions. The theorem of Marachkov on the asymptotic stability of systems without impulses is generalized. The results obtained are formulated in four theorems.
01 Aug 1988
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01 Jan 1988
TL;DR: The final author version and the galley proof are versions of the publication after peer review that features the final layout of the paper including the volume, issue and page numbers.
Abstract: • A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers.
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TL;DR: Asymptotic solutions of the Orr-Sommerfeld equation describing the transition from laminar to turbulent flow of a viscous liquid are constructed in this paper, where the case when the equation has a point of rotation of arbitrarily high order is considered.
Abstract: Asymptotic solutions of the Orr-Sommerfeld equation describing the transition from laminar to turbulent flow of a viscous liquid are constructed. The case when the equation has a point of rotation of arbitrarily high order is considered. The terms of the asymptotic expansion in the region of the point of rotation are expressed in terms of Mellin-Barnes integrals.