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71.
72.
We consider nonautonomous equations v′=A(t)v in a Banach space that exhibit stable and unstable behaviors with respect to arbitrary growth rates ecρ(t) for some function ρ(t). This corresponds to the existence of a “generalized” exponential dichotomy, which is known to be robust. When ρ(t)≠t this behavior can be described as a type of parabolic dynamics. We consider the general case of nonuniform exponential dichotomies, for which the Lyapunov stability is not uniform. We show that for any sufficiently small perturbation f of a “generalized” exponential dichotomy there is a stable invariant manifold for the perturbed equation v′=A(t)v+f(t,v). We also consider the case of exponential contractions, which allow a simpler treatment, and we show that they persist under sufficiently small nonlinear perturbations. 相似文献
73.
O. M. Davydov 《Acta Appl Math》2003,75(1-3):51-54
Complexity is a function which maps a set of 3-manifolds to a set of nonnegative integers. This function has some natural properties (finiteness, additivity, etc.) and it shows, in some sense how complex the manifold is. This function seems important for the classification of 3-manifolds. We evaluate of the complexity of 2-fold branched coverings of a 3-sphere. We present a theoretical estimate and compare it with experimental data. 相似文献
74.
Gerald Moore. 《Mathematics of Computation》2004,73(245):211-242
We present an algorithm, based on approximation by Laguerre polynomials, for computing a point on the stable manifold of a stationary solution of an autonomous system. A superconvergence phenomenon means that the accuracy of our results is much higher than the usual spectral accuracy. Both the theory and the implementation of the method are considered. Finally, as an application of the algorithm, we describe a fully spectral approximation of homo- and heteroclinic orbits.
75.
为了准确分析T 形曲梁的静力学特性,该文考虑了剪滞翘曲应力自平衡条件、剪力滞后和剪切变形等因素的影响. 同时为了更好地反映T 形曲梁翼板的位移变化,4 个广义位移函数被引入,分析中以能量变分原理为基础建立了T 形曲梁静力学特性的控制微分方程和自然边界条件. 算例中,分析了剪滞翘曲应力自平衡条件、不同载荷形式和曲梁半径R 等因素对T 形曲梁静力学特性的影响,该文解析解与有限元数值解吻合更好,说明了该文方法的有效性. 相似文献
76.
Finite element approximation of spectral problems with Neumann boundary conditions on curved domains
This paper deals with the finite element approximation of the spectral problem for the Laplace equation with Neumann boundary conditions on a curved nonconvex domain . Convergence and optimal order error estimates are proved for standard piecewise linear continuous elements on a discrete polygonal domain in the framework of the abstract spectral approximation theory.
77.
We investigate the ratio of spin precession frequency to orbital frequency for a spinning charged particle confined to circular
orbit in the equatorial plane of a compact object, with a uniform magnetic field, as described by the Wald and the Ernst potentials.
In order to see the difference in behaviours for particles with differentg values we consider the cases of electron and proton separately. 相似文献
78.
We suggest a new set of equations to employ smoothed particle hydrodynamics (SPH) in a curvilinear space, and we refer to it as curvSPH. In classical SPH, the horizontal and vertical resolution of discretization is supposed to be equal for fluid particles. However, curvSPH makes the horizontal and vertical resolutions independent from each other. This is performed by transformation of physical space into an appropriate computational space with a different scale in horizontal and vertical directions. Solving a problem using SPH in a curvilinear space also provides capability to model curved boundaries as straight lines. In classical SPH, special care is needed to reach a uniform mass distribution along curved boundaries; however, producing uniform mass distribution along a line using curvSPH is straight forward. Different simulations, including simulation of a flip bucket are performed to demonstrate the applicability of the proposed method. Good agreement of results with experimental data and classical SPH confirms the capabilities of curvSPH. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
79.
E. M. Romanova 《Russian Mathematics (Iz VUZ)》2008,52(7):33-37
We consider the quotient set of the set of nondegenerate affinor fields with respect to the action of the group of nowhere vanishing functions. This set is endowed with a structure of infinite-dimensional Lie group. On this Lie group, we construct an object of linear connection with respect to which all left-invariant vector fields are covariantly constant (the Cartan connection). 相似文献
80.
Kazutoshi Maegawa 《Proceedings of the American Mathematical Society》2008,136(8):2875-2879
For a dominant algebraically stable rational self-map of the complex projective plane of degree at least 2, we will consider three different definitions of the Fatou set and show the equivalence of them (Ascoli-Arzelà type theorem). As a corollary, it follows that all Fatou components are Stein. This is an improvement of an early result by Fornæss and Sibony.