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排序方式: 共有380条查询结果,搜索用时 15 毫秒
1.
I. J. Lozada J. C. Osorio D. V. Griffiths M. Cerrolaza 《Numerical Methods for Partial Differential Equations》2006,22(2):296-316
The semi‐analytical integration of an 8‐node plane strain finite element stiffness matrix is presented in this work. The element is assumed to be super‐parametric, having straight sides. Before carrying out the integration, the integral expressions are classified into several groups, thus avoiding duplication of calculations. Symbolic manipulation and integration is used to obtain the basic formulae to evaluate the stiffness matrix. Then, the resulting expressions are postprocessed, optimized, and simplified in order to reduce the computation time. Maple symbolic‐manipulation software was used to generate the closed expressions and to develop the corresponding Fortran code. Comparisons between semi‐analytical integration and numerical integration were made. It was demonstrated that semi‐analytical integration required less CPU time than conventional numerical integration (using Gaussian‐Legendre quadrature) to obtain the stiffness matrix. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006 相似文献
2.
François Ledrappier Mark Pollicott 《Bulletin of the Brazilian Mathematical Society》2005,36(2):143-176
In this paper we study the ergodic properties of the linear action of lattices Γ of SL(2,ℚp) on ℚp × ℚp and distribution results for orbits of Γ. Following Serre, one can define a “geodesic flow” for an associated tree (actually
associated to GL(2,ℚp)). The approach we use is based on an extension of this approach to “frame flows” which are a natural compact group extension
of the geodesic flow. 相似文献
3.
XIE Fu-Ding Xiao-Shan LIU Feng 《理论物理通讯》2004,42(11)
Based on the rank analysis method, algorithmization idea, and symbolic computation, in this paper we have presented a method to construct the conservation laws for nonlinear evolution equations. The polynomial conservation laws for K (n 2, n) equations and mnK(m, n) equations are found by using of this approach and some new results have been obtained. 相似文献
4.
Examples of exact expressions for the moments (mainly of the mean) of functions of sample moments are given. These provide checks on alternative developments such as asymptotic series for n, and simulation processes. Exact expressions are given for the mean of the square of the sample coefficient of variation, particularly in uniform sampling; Frullani integrals studied by G. H. Hardy arise. It should be kept in mind that exact results for (joint) moment generating functions (mgfs) are of interest as they produce a means of obtaining exact results for (cross) moments—including moments with negative indices. Thus an exact expression for the joint mgf of the 1st two noncentral moments can be used to obtain the mean of the (c.v.)2 (but not for the mean of the c..). A general expression is given for the moment generating function of the sample variance. The limitations of Fisher's symbolic formula for the characteristic function of sample moments (or more general statistics) are noted.This research was sponsored by the Applied Mathematical Sciences Research program, Office of Energy Research, U. S. Department of Energy under contract DE-AC0584OR21400 with the Martin Marietta Energy Systems. Inc. 相似文献
5.
The numerical simulation of turbulence is one of the most challenging tasks in the field of the modern computational science. At present, the most advanced approach is the large eddy simulation (LES) technique wherein a formal separation between resolved (large) and unresolved (small) scales of the motion is in effect by means of a filtering operation applied onto the governing equations. However, LES requires very sophisticated numerical discretizations in terms of both accuracy and efficiency. Often, the modelling of the unresolved subgrid scale terms adds further computational complexities. This paper illustrates the suitability in using software packages for symbolic computation (in the present case, Maple© for helping in the production of subroutines for a new multidimensional, high‐order accurate finite volume‐based LES code. Specifically, it will be detailed how producing, rapidly and efficiently, the routines for computing convective, diffusive as well as subgrid scale modelling fluxes. It is particularly detailed how exploiting the package for differential calculus and linear algebra for the analytical integration of the flux polynomials over the finite volume faces. The structure of the LES code is illustrated, and an accuracy analysis of the local truncation errors is performed comparing the third‐order accurate multidimensional upwind and the classical second‐order centred reconstruction in the wavenumbers space. Then, some numerical results for the turbulent plane channel and some brief points concerning the parallelization issue are addressed. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
6.
符号函数sgnx是数学分析中一个特殊的分段函数,在积分运算中,经常被误认为是常值函数,被提到积分符号的前面,从而导致结果错误.本文将通过具体的例子来分析常见的错误. 相似文献
7.
An Implementation for the Algorithm of Janet bases of Linear Differential Ideals in the Maple System
Shan-qingZhang Zhi-binLi 《应用数学学报(英文版)》2004,20(4):605-616
In this paper, an algorithm for computing the Janet bases of linear differential equations is described, which is the differential analogue of the algorithm JanetBasis improved by Gerdt. An implementation of the algorithm in Maple is given. The implemented algorithm includes some subalgorithms: Janet division,Pommaret division, the judgement of involutive divisor and reducible, the judgement of conventional divisor and reducible, involutive normal form and conventional normal form, involutive autoreduction and conventional autoreduction, PJ-autoreduction and so on. As an application, the Janet Bases of the determining system of classical Lie symmetries of some partial differential equations are obtained using our package. 相似文献
8.
9.
On the Distribution of Long-Term Time Averages on Symbolic Space 总被引:2,自引:0,他引:2
The pressure was studied in a rather abstract theory as an important notion of the thermodynamic formalism. The present paper gives a more concrete account in the case of symbolic spaces, including subshifts of finite type. We relate the pressure of an interaction function to its long-term time averages through the Hausdorff and packing dimensions of the subsets on which has prescribed long-term time-average values. Functions with values in
d
are considered. For those depending only on finitely many symbols, we get complete results, unifying and completing many partial results. 相似文献
10.
ZHANG Ya-Xing ZHANG Hai-Qiang LI Juan XU Tao ZHANG Chun-Yi TIAN Bo 《理论物理通讯》2008,49(4):833-838
In this paper, we put our focus on a variable-coe~cient fifth-order Korteweg-de Vries (fKdV) equation, which possesses a great number of excellent properties and is of current importance in physical and engineering fields. Certain constraints are worked out, which make sure the integrability of such an equation. Under those constraints, some integrable properties are derived, such as the Lax pair and Darboux transformation. Via the Darboux transformation, which is an exercisable way to generate solutions in a recursive manner, the one- and two-solitonic solutions are presented and the relevant physical applications of these solitonic structures in some fields are also pointed out. 相似文献