广义变系数KdV,mKdV方程的精确类孤子解

利用截断展开法和延拓齐次平衡法同时求出了广义变系数KdV方程和广义变系数mKdV方程的精确钟状类孤子解 .其基本思想是 :设方程的解形式为u(x ,t) =∑nm=0υm(t)Fm,　F =eα( ξ+ξ0 )1+eα( ξ+ξ0 )代入给定方程确定出n ,并令F的各次幂项的系数为零 ,得到超定可积分方程组 ,由此求出给定方程的精确类孤子解 .     

有挠引力量子化初探

研究了有挠时空的引力量子化问题，获得了一次型有挠引力的Ｗｈｅｅｌｅｒ－Ｄｅｗｉｔｔ方程，超空间的号差是洛仑兹的。在小超空间近似下，如果宇宙波函数是正规的，或者取无边界边界条件，都得出均匀各向同性量子宇宙以无挠方式演化的结论。     

非均匀内热源组合球壁稳态导热微分方程组的解

用热流分流和叠加，直接得出非均匀内热源组合球壁稳态导热微分方程组，分别在第一类、第二类和第三类边界条件下的解。     

New Boundary Treatment Methods for Lattice Boltamann Method

In practical fluid dynamic simulations, the boundary condition should be treated carefully because it always has crucial influence on the numerical accuracy, stability and efficiency. Two types of boundary treatment methods for lattice Boltzmann method (LBM) are proposed. One is for the treatment of boundaries situated at lattice nodes, and the other is for the approximation of boundaries that are not located at the regular lattice nodes. The first type of boundary treatment method can deal with various dynamic boundaries on complex geometries by using a general set of formulas, which can maintain secon-order accuracy. Based on the fact that the fluid flows simulated by LBM are not far from equilibrium, the unknown distributions at a boundary node are expressed as the analogous froms of their corresponding equilibrium distributions. analogous forms of their corresponding equilibrium distributions. Therefore, the number of unknowns can be reduced and an always-closed set of equations can be obtained for the solutions to pressure, velocity and special boundary conditions on various geometries. The second type of boundary treatment is a complete interpolation scheme to treat curved boundaries. It comes from careful analysis of the relations between distribution functions at boundary nodes and their neighboring lattice nodes. It is stable for all situations and of second-order accuracy. Basic ideas, implementation procedures and verifications with typical examples for the both treatments are presented. Numerical simulations and analyses show that they are accurate, stable,general and efficient for pracitical simulations.     

消去常数项法解非齐次线性方程组

消去AX=B常数项,使方程的个数减少一个,得到一个齐次线性方程TX=O,通过解齐次线性方程组TX=O,从而得到非齐次线性方程组AX=B的通解.     

关于m—正齐次算子的一些性质

本文给出了m—正齐次算子的一些基本性质,其中包括连续性、有界性、可微性以及这些性质之间的联系。文中部分结果是线性算子性质的推广。     

关于一个不定方程组的解

本文讨论不定方程组{x1^2 x2^2=x4^2 (1) x1^2 x3^2=x5^2 (2) x2^2 x3^2=x6^2 (3)的正整数解的问题，作者给出该不定方程组的一些参数解，由此说明该问题有解且有无穷多个解。     

可信软件系统中基于模糊集理论的信任推理模型研究

通过分析可信软件系统的信任变化特性，引入母体参数和基本参数，在保证转移矩阵随机性的前提下，利用模糊推理的方法模拟了可信软件系统中信誉的变化情况．实验表明：利用模糊非齐次马尔可夫系统管理软件系统的信誉方法是切实有效的．     

自由降膜在横向波纹竖壁上的流动与蒸发的分析

对竖直放置的横向波纹形壁面上的定型层流自由降落液膜的运动与蒸发传热进行了分析.对这种运动的控制微分方程及边界条件作无量纲化处理,以壁面波纹为摄动参数对方程组进行幂级数展开,得到了摄动分析模型.通过求解该模型获得了液膜流速、温度和自由表面位置的表达式,讨论了壁面波纹对液膜运动的影响.分析表明,在一定的壁面波幅和波教条件下,横向波纹对这种流动的传热有增强作用.