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Showing papers on "Asymptotology published in 1990"




01 Jan 1990
TL;DR: In this paper, a symmetric positive definite matrix (B$ ) is used as a Liapunov function to investigate the asymptotic behaviors of solutions of (1.2) and (3) problems.
Abstract: where $A$ is a constant $n¥times n$ matrix, $C(t, s)$ is an $n¥times n$ matrix continuous for $ 0¥leqq s¥leqq t<¥infty$ and $D(t)$ is an $n¥times n$ matrix continuous for $t$ $¥geqq 0$ . In case $A$ is a stable matrix, there exists a symmetric positive definite matrix $B$ such that (1.4) $A^{T}B+BA=-I$ , and we can use the function $V=x^{T}Bx$ as a Liapunov function to investigate asymptotic behaviors of solutions of (1.2) $(¥mathrm{c}.¥mathrm{f}. [6, 12])$. For the equation (1.3) there is another method, that is, we can use a nice resolvent $Z(t)$ for (1.3)

25 citations


Journal ArticleDOI
TL;DR: In this paper, a method of derivation of global asymptotic solutions of the hydromagnetic dynamo problem at large magnetic Reynolds number was proposed, based on the assumption that properties of global solutions of kinematic dynamo are determined by the distribution of the generation strength near its leading extrema and by the number and distribution of extremas.
Abstract: We propose a method of derivation of global asymptotic solutions of the hydromagnetic dynamo problem at large magnetic Reynolds number. The procedure reduces to matching the local asymptotic forms for the magnetic field generated near individual extrema of generation strength. The basis of the proposed method, named here the Maximally-Efficient-Generation Approach (MEGA), is the assertion that properties of global asymptotic solutions of the kinematic dynamo are determined by the distribution of the generation strength near its leading extrema and by the number and distribution of the extrema. The general method is illustrated by the global asymptotic solution of the α2-dynamo problem in a slab. The nature of oscillatory solutions revealed earlier in numerical simulations and the reasons for the dominance of even magnetic modes in slab geometry are clarified. Applicability of the asymptotic solutions at moderate values of the asymptotic parameter is also discussed. We confirm this applicability u...

18 citations





Proceedings ArticleDOI
23 May 1990
TL;DR: In this article, it was shown that the asymptotic inverse kinematic problem can be reduced to the problem of observing the state variables of a certain nonlinear dynamic system.
Abstract: It is shown that the asymptotic inverse kinematic problem can be reduced to the problem of observing the state variables of a certain nonlinear dynamic system. A simple asymptotic observer is used in the state estimation and the singular perturbation theory is used in the convergence proof of the algorithm. It is also shown that the classical methods of Newton and of the gradient can be obtained as particular asymptotic observers.

9 citations





01 Jan 1990
TL;DR: The theorem is called Hajek-Le Cam because it was proved by Hâjek (1972) for the asymptotically normal (more precisely LAN) case and how the theorem can be applied to problems recently studied by Donoho and Liu (1990), by M. Low (1989) and by Golubev and Nussbaum (1990).
Abstract: One of the simplest results in asymptotic theory of estimation is the Hajek-Le Cam asymptotic minimax theorem. Besides being simple, it has many applications. We review the theorem and give brief indications on some applications. The theorem is called Hajek-Le Cam because it was proved by Hâjek (1972) for the asymptotically normal (more precisely LAN) case. There was a previous theorem by Le Cam (1953). Hajek's result was substantially extended in Le Cam (1979). Section 2 below gives a summary of definitions and notation. Section 3 reviews the asymptotic minimax theorem. Section 4 indicates how the theorem can be applied to problems recently studied by Donoho and Liu (1990), by M. Low (1989) and by Golubev and Nussbaum (1990). For further applications of the asymptotic minimax theorem, see Millar (1983).






Journal ArticleDOI
TL;DR: In this paper, a zeroth-order boundary-layer asymptotic expansion is constructed and proved for solving a mixed boundary-value problem for a parabolic equation in the critical case.
Abstract: A zeroth-order boundary-layer asymptotic expansion is constructed and proved for solving a mixed boundary-value problem for a parabolic equation in the critical case. A smoothing procedure is applied to the nonsmooth terms of the asymptotic expansion when constructing the solution.

Journal ArticleDOI
TL;DR: In this article, the asymptotic form of the energy radiated by a random harmonic oscillatory source in an infinite sphere is calculated, and the energy can be expressed as a function of the number of oscillators in the system.
Abstract: The asymptotic form of the energy radiated by a random harmonic oscillatory source in an infinite sphere is calculated.