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: In this paper, an approach to construct multi-soliton asymptotic solutions for non-integrable equations is described, and the general idea is realized in the case of three waves and for the KdV-type equation with nonlinearity $u^4$.
Abstract: We describe an approach to construct multi-soliton asymptotic solutions for non-integrable equations. The general idea is realized in the case of three waves and for the KdV-type equation with nonlinearity $u^4$. A brief review of asymptotic methods as well as results of numerical simulation are included.
5 citations
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TL;DR: In this article, the consistency of the Maximum Likelihood Estimator (MLE) of the unknown system parameter of a stochastic differential equation system with constant coefficients is proved.
Abstract: In this paper the consistency of the Maximum-Likelihood-Estimator of the unknown system parameter of a inhomogeneous stochastic differential equation system with constant coefficients is proved. Sufficient conditions are given for the asymptotic normality and asymptotic efficiency of the MLE in the stable case.
5 citations
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TL;DR: In this paper, the authors considered the behavior of solutions of parabolic inequalities and related problems in a bounded domain in E and studied the behavior as t −> 00 in R of those solutions u which satisfy the additional condition t ≥ 0.
Abstract: and A is a second order elliptic operator. The asymptotic behavior of solutions of parabolic inequalities and related problems have been considered by Agmon and Nirenberg [ l ] , Cohen and Lees [2], Lax [3], and the author [4]. Let D be a bounded domain in E and suppose w(#i, • • • , # » , £ ) = u(x, t) is a solution of (1.1) in the cylindrical region R = DXI where / is the half-infinite interval 0 ^ / < 00. We shall study the behavior as t—> 00 in R of those solutions u which satisfy the additional condition
5 citations
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TL;DR: Genera t ing functions for the number of fanout-free and cascade networks and a set of symmetric gates are studied, finding that the average number of gates in n-input networks grows near ly with n, in contrast to the situation when a much larger set of gates is al lowed.
Abstract: Genera t ing functions for the number o f fanout-free and cascade networks buil t f rom an a rb i t ra ry set of symmetric gates are studied Recurslons and asymptot ic estimates are obtained. The average number o f gates in n-input networks .s studied It grows hnear ly with n, in contrast to the situation when a much larger set o f gates is al lowed
5 citations