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101.
Wei-Liem Loh 《Annals of the Institute of Statistical Mathematics》1994,46(1):147-164
This paper contains two results. The first establishes, under mild assumptions, the validity of an Edgeworth expansion with remaindero(N
–1/2) for aU-statistic with a kernel of degree two using observations from anm-dependent shift. The second result gives a necessary and sufficient condition for the distribution of a sum ofm-dependent random variables to possess an Edgeworth expansion. This generalizes a result of Bickel and Robinson from the i.i.d. case to them-dependent case.This research was supported in part by National Science Foundation, Grant DMS 89-23071. 相似文献
102.
Raimundas Vidunas Nico M. Temme 《Journal of Mathematical Analysis and Applications》2002,269(1):317-331
Computer algebra algorithms are developed for evaluating the coefficients in Airy-type asymptotic expansions that are obtained from integrals with a large parameter. The coefficients are defined from recursive schemes obtained from integration by parts. An application is given for the Weber parabolic cylinder function. 相似文献
103.
本文基于生成函数的Taylor展开式及逐步简化步骤,提出了计算偏微分方程组的Lie群与高阶对称群的Taylor多项式算法,把标准算法中的求解超定偏微分方程组的问题转化为求解代数方程组的问题,降低了求解的难度,提高了计算效率,并且易用计算机代数系统在计算机上全过程实现,并得到重要的对称群 相似文献
104.
In this paper, on basis of [O.A. Oleinik, A.S. Shamaev, G.A. Yosifian, Mathematical Problems in Elasticity and Homogenization, North-Holland, Amsterdam, 1992], we present a local error estimate of the method of multi-scale asymptotic expansions for second order elliptic problems with rapidly oscillatory coefficients. 相似文献
105.
广义Taylor映射与Hénon映射具有混沌条件的改进 总被引:3,自引:0,他引:3
本文进一步讨论了近年来动力系统中关于对具有混沌现象的Taylor映射,Henon映射等函数所做的研究,并着重分析了所讨论函数的参数. 相似文献
106.
Multi-input multi-output (MIMO) sampling scheme which is motivated by applications in multi-channel deconvolution and multi-source separation has been investigated in many aspects. Common for most of results on MIMO systems is that the input signals are supposed to be band-limited. In this paper, we study vector sampling expansions on general finitely generated shift-invariant subspaces. Necessary and sufficient conditions for a vector sampling theorem to hold are given. We also give several examples to illustrate the main result. 相似文献
107.
Martin P. Gelfand Rajiv R. P. Singh David A. Huse 《Journal of statistical physics》1990,59(5-6):1093-1142
A systematic method for developing high-order, zero-temperature perturbation expansions for quantum many-body systems is presented. The models discussed explicitly are spin models with a variety of interactions, in one and two dimensions. The wide applicability of the method is illustrated by expansions around Hamiltonians with ordered and disordered ground states, namely Ising and dimerized models. Computer implementation of this method is discussed in great detail. Some previously unpublished series are tabulated. 相似文献
108.
We describe high-precision computations of the Pearcey integral Pe(x,y) for real x and y by means of Hadamard expansions. Numerical results for (x,y) situated in different regions of the x,y-plane are given to illustrate the levels of precision that can be achieved. Particular emphasis is given to computation in the neighbourhood of the two cusped curves associated with Pe(x,y) across which there is either a coalescence of saddles or a Stokes phenomenon. 相似文献
109.
A novel finite point method is developed to simulate flow problems. The mashes in the traditional numerical methods are supplanted by the distribution of points in the calculation domain. A local interpolation based on the properties of Taylor series expansion is used to construct an approximation for unknown functions and their derivatives. An upwind‐dominated scheme is proposed to efficiently handle the non‐linear convection. Comparison with the finite difference solutions for the two‐dimensional driven cavity flow and the experimental results for flow around a cylinder shows that the present method is capable of satisfactorily predicting the flow separation characteristic. The present algorithm is simple and flexible for complex geometric boundary. The influence of the point distribution on computation time and accuracy of results is included. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
110.
A study is made of the dynamics of oscillating systems with a slowly varying parameter. A slowly varying forcing periodically crosses a critical value corresponding to a pitchfork bifurcation. The instantaneous phase portrait exhibits a centre when the forcing does not exceed the critical value, and a saddle and two centres with an associated double homoclinic loop separatrix beyond this value. The aim of this study is to construct a Poincaré map in order to describe the dynamics of the system as it repeatedly crosses the bifurcation point. For that purpose averaging methods and asymptotic matching techniques connecting local solutions are applied. Given the initial state and the values of the parameters the properties of the Poincaré map can be studied. Both sensitive dependence on initial conditions and (quasi) periodicity are observed. Moreover, Lyapunov exponents are computed. The asymptotic expressions for the Poincaré map are compared with numerical solutions of the full system that includes small damping. 相似文献