求解

Secondly, by applying inverse Fourier integral transform to the displacement, and uniting the constitutive and geometrical equations, the analytical expression of stress in Laplace domain were derived. Thirdly, by defining dislocation density functions, the Cauchy singular integral equations were obtained according to the boundary condition and interface connection conditions, and the problem was reduced to algebraic equations by Chebyshev orthogonal polynomial. Based the these, the unknown coefficient of the algebraic equations can be solved by Schmidt method. Finally, the time response of dynamic stress intensity factor and energy release rate are obtained by inverse Laplace transform.

首先，利用积分变换方法，推导出粘弹性层的控制方程组；其次，引入位错密度函数，并结合边界条件和界面连接条件，导出反映裂纹尖端奇异性的Cauchy型奇异积分方程组，然后，应用Chebyshev正交多项式化奇异积分方程组为代数方程组，并采用Schmidt方法对其数值求解，最后，经过Laplace逆变换，求得动态应力强度因子和能量释放率的时间响应。

A nonlinear dimension chain has both length dimension variable and the angular dimension variable. So the nonlinear dimension chain can't be calculated by simple algebraic sum.

对于非线性尺寸链，既有长度尺寸变量，又有角度尺寸变量，不能运用简单的代数和求解。

An algorithm for computing the geodesic line between the two points of an algebraic surface was presented.

给出了求解代数曲面上两点之间测地线的一种算法。

The system of differential equations for a geodesic line on an algebraic surface was discredited into a nonlinear system. Then it was solved numerically based on iterative methods.

在算法中，把决定代数曲面测地线的微分方程组离散为一个非线性方程组，然后采用迭代数值方法求解。

If the surface isrepresented by an implicit algebraic equation,the mapping can be constructed bythe theory of parametrization of algebraic surfaces;If the surface is represented byan parametric equation,the parameter values on the parameter plane can be solvedby numerical method or Grobner Basis method.

若曲面由代数隐式方程给出，可通过代数曲面参数化理论构造映射；若曲面由参数方程给出，可通过数值方法或Grobner基方法求解参数型值点。

In this paper, we present a method to solve system of algebraic equations or system of parametric algebraic equations by computing the normal zero decomposition of polynomial systems.

本文提出一种利用多项式系统的正规零点分解的算法来求解代数方程组以及带有参数的代数方程组的方法。

In conclusion, all our results further enrich, develop and perfect the theoretical system of the algebraic multigrid method.

代数多重网格方法是根据一般多重网格方法的原理建立起来的一种自动求解线性代数方程组的快速算法，它采用分层思想通过一种纯代数的多水平方法处理矩阵方程，特别是二维或三维大规模无结构方程组。

To overcome the shortcomings of existing algorithms, the distributed parallel reactive power optimization algorithm based on sub-area division of the power systems is proposed according to the distributed and decentralized charac

针对目前无功电压优化算法存在的不足，根据电力系统分布、分散的特点，提出了基于电网分区的分布式并行无功优化算法，并对其进行了多目标、软约束的模糊化处理和离散控制变量的罚函数处理，利用直接非线性原—对偶内点法寻优求解。

The proposed algorithm use the related deduction of division with reminder of polynomials and the key equation is solved by column transformation of matrix. Then the formula of quotient and reminder can be got quickly which can reduce the times of iterative operation.

该算法利用多项式带余除法的相关推论，通过矩阵的列变换来求解关键方程，这样可以快速地得到商式和余式，从而可以减少迭代运算的次数。

To overcome the shortcomings of existing algorithms, the distributed parallel reactive power optimization algorithm based on sub-area division of the power systems is proposed according to the distributed and decentralized characteristics of the power system. Here, multi-objective function and soft constraints are modeled using fuzzy sets, and the multi-objective reactive power optimization problem is solved by the direct nonlinear primal-dual interior point algorithm.

针对目前无功电压优化算法存在的不足，根据电力系统分布、分散的特点，提出了基于电网分区的分布式并行无功优化算法，并对其进行了多目标、软约束的模糊化处理和离散控制变量的罚函数处理，利用直接非线性原—对偶内点法寻优求解。

Plunder melds and run with this jewel!

掠夺melds和运行与此宝石！

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻，也许正是在通往天国的路上，我体验着这白色的晕旋。