可解方程

This paper presents the boundary value problem solved as the biharmonic equation of upper plane and strip domain with Green functional method and it deals with the numerical solution of bihormonic equation, using the Matlab program calculation to realize the visualization of numeric solution.

用Green函数法求解了区域为上半平面和带形区域的双调和泊松方程的边值问题；以及探讨了双调和方程的数值解，并用Matlab编程计算实现了双调和方程数值解的可视化。

Experimental results show the recognition rate of the method is 95%for a known expresser and 72% for a novel expresser. Aiming at the shortcomings of optical flow technique,two improved optical flow algorithms are presented.One way is to introduce forward and backword constraint eqution and Hessian matrix of optical flow equation is computed.The well- posedness of each point of local neighbourhood is examined and the weight of Lucas-Kanade's method is defined as the reciprocal of the conditioning number of its Hessian Matrix.

3针对传统光流法的缺点，分别提出了两种不同的改进方法：其一为引入前向-后向光流方程，计算其Hessian矩阵，把Hessian矩阵条件数的倒数作为Lucas-Kanade光流法的加权阵，可有效消除局部邻域中不可靠约束点，同时提高基本约束方程解的稳定性；其二为针对传统光流法只适用于刚体运动的特点，在扩展约束光流方程的基础上引入了div-curl样条函数作为扩展光流约束方程的附加约束条件，给出了一阶和二阶div-curl样条约束下光流的数值解。

First, we introduce the concept of polarizable Carnot group and give some new properties of its homogeneous norm. Then we construct a class of non-divergence equations as well as their nontrivial solutions. The failure of corresponding A-B-P type estimate and uniqueness to the Dirichlet problems in space~ follow.

首先引入可极化Carnot群的概念，给出了可极化Carnot群上齐次模的若干性质，然后构造了一类非散度型次椭圆方程及其非平凡解，由此证明此类方程Dirichlet问题的解在函数空间L~中不唯一，进而证明相应的Alexandrov-Bakelman-Pucci型估计不成立。

The direct displacement problem can be changed into solving a polynomial equation called the equivalent polynomial equation.

研究表明其正解问题最后可转化为一个高次多项式方程求解问题，称此方程为正解的等价多项式方程。

This paper makes use of a Lyapunov function and a nonlinear integral inequality of Gronwall-Bellman-Bihari type to study the asymptotic hehaviors of solutions of a second-order nonlinear functional differential equation.

本文利用李雅普诺夫函数及一个Gronwall—Bellman—Bihari型的非线性积分不等式，研究一类二阶非线性泛函微分方程解的渐近性态，在第一部份，给出一组方程的全体解可延展到t=+∞的充分条件及三组方程的全体解有界的充分条件。

This paper makes use of a Lyapunov function and a nonlinear integral inequality of Gronwall-Bellman-Bihari type to study the asymptotic hehaviors of solutions of a second-order nonlinear functional differential equation. In part I, a group of sufficient conditions is given on continuation of solutions and three groups of sufficient conditions are given on boundedness of solutuicns of equation.

本文利用李雅普诺夫函数及一个Gronwall—Bellman—Bihari型的非线性积分不等式，研究一类二阶非线性泛函微分方程解的渐近性态，在第一部份，给出一组方程的全体解可延展到t=+∞的充分条件及三组方程的全体解有界的充分条件。

For the compressible materials, in order to satisfy the higher-order compatibility equation of the rate of deformation in the centered fan sector, which is a quite difficult problem unresolved in the previous studies, a particular term must be added to the expansions of the stress components in the regular logarithmic power series adopted by many researchers before. A higher-order near tip field with tangential velocity jump ahead of the crack tip is derived first, of which the dominant terms are the solution widely accepted.

对可压缩材料，本文首先采用非规则的对数幂级数渐近展开方法，克服了过去研究中存在的中心扇形区变形率协调方程的高次渐近式不能被满足的困难，并得到了一个切向速度在裂尖前方存在间断的高阶渐近解，该解的主项就是目前被广泛接受的关于可压缩材料的尖端场解。

The detailed comparisons between the higher—order near tip solution and the well—known modified Prandtl field are also given in this paper.For the compressible materials, in order to satisfy the higher-order compatibility equation of the rate of deformation in the centered fan sector, which is a quite difficult problem unresolved in the previous studies, a particular term must be added to the expansions of the stress components in the regular logarithmic power series adopted by many researchers before. A higher-order near tip field with tangential velocity jump ahead of the crack tip is derived first, of which the dominant terms are the solution widely accepted.

对可压缩材料，本文首先采用非规则的对数幂级数渐近展开方法，克服了过去研究中存在的中心扇形区变形率协调方程的高次渐近式不能被满足的困难，并得到了一个切向速度在裂尖前方存在间断的高阶渐近解，该解的主项就是目前被广泛接受的关于可压缩材料的尖端场解。

Our analysis framework relies on the reflected Backward Stochastic Differential equation approach.We characterize the value functions of the noncallable bonds in terms of the reflected Backward Stochastic Differential equation,Then the relationship between the value function of convertible bonds and reflected backward stochastic differential equations with single reflect is built at the same time,and provide the optimal conversion strategy for bondholders.2:We get the value of non-callable convertible bonds by numerical methods.

探讨了可转换债券的最优停时价值与带反射边界倒向随机微分方程解的关系，在市场完备，公司价值只包括股权和可转债这两种权益等各种假定下，给出不可赎回可转换债券的价值函数，证明了不可赎回可转换债券的最优停时问题的解是存在的，同时给出了其最优的转换策略。2：通过数值方法求解不可赎回可转换债券的价值。

When the matrix equation is consistent, its centrosymmetric solution can be obtained within finite iterative steps in the absence of round off errors for any initial centrosymmetric matrix X1, and its least-norm centrosymmetric solution can be derived by choosing a suitable initial iterative matrix.

当矩阵方程AXB+CXD=F有中心对称解时，在有限的误差范围内，对任意初始中心对称矩阵X1，运用迭代算法，经过有限步可得到矩阵方程的中心对称解；选取合适的初始迭代矩阵，还可以迭代出极小范数中心对称解。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。