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However, methods and references for difference equation are relatively less. The new method proposed in this paper transfer the complex boundary value problem into the existence and uniqueness of the solution of the linear equations. For linear case , we obtained the necessary and sufficient conditions for the existence and uniqueness of the solution for the BVP; For the nonlinear case ,we got a series of new sufficient conditions by using contraction mapping theory and cone theory .

而差分方程边值问题的研究方法和文献还很少，文中新的研究差分方程边值问题的方法是将复杂的边值问题求解转化为代数理论中的线性方程组解的存在和存在唯一问题；对线性情形，较容易地获得了边值问题的解存在以及唯一的充分必要条件，而对非线性情形，则通过压缩原理和锥理论等各种不动点定理，获得了一系列新的充分条件。

The exact solution and approximate analytical solution of the mathematical model for constant rate production are obtained by using Laplace transform.

引入异常扩散指数θ，运用该参数来刻画裂缝网络的连通状况，并能反映渗流发生在裂缝网络时的异常情况。

Keywords constrained matrix equation problem;sub matrix constraint problem; matrix norm; optimal approximation solution;least-squares solution

约束矩阵方程问题；子矩阵约束问题；矩阵范数；最佳逼近解；最小二乘解

Using the method of dividing variables , the solution of elastic dynamics can be changed into the eigen value problem of Hamilton's space differential operator matrix , and the total solution of dual variables (modal strain and modal strain rate ) can be obtained by expanding the eigen solutions .

尽管方程的个数增加了1倍(未知量个数增加了1倍)，但方程对时间微分的次数下降到1阶。通过分离变量后，可以将其转变为Hamilton空间算子矩阵的本征值问题，从而使复杂力学问题的解析解成为可能。

Using the method of dividing variables , the solution of elastic dynamics can be changed into the eigen value problem of Hamilton s space differential operator matrix , and the total solution of dual variable s (modal strain and modal strain rate ) can be obtained by .

采用分离变量方法，将弹性动力学解转变为Hamilton空间算子矩阵的本征值问题，对偶变量的全解通过本征解来展开而获得。

In addition, in the solution set of corresponding equation, the expression of the optimalapproximation solution to given matrix is derived.

另外，导出了在线性流形上矩阵方程的解集合中与给定矩阵的最佳逼近解的表达式。

In addition, in the solution set of corresponding equation, the expression of the optimal approximation solution to given matrix is derived.

另外，导出了在矩阵方程的解集合中与给定矩阵的最佳逼近解的表达式。

First, a new explicit parametric solution of the matrix equation is proposed. Second, an existing solution of this matrix equation is extended.

首先给出了该矩阵方程的一种新的显式参数通解，其次对该矩阵方程已有的一类显式参数解进行了推广。

The amount of solution elevation, the vapor amount and the maximum height of the elevated solution are related to different heat loads.

得出了浓溶液的提升量、蒸汽发生量、浓溶液最大提升高度对应于不同的加热负荷的关系曲线，实验发现这种蒸发管是一种有效的强化传热管。

The significant solution with the maximum approximative degree is the optimal solution to the multi-objective problem.

因此，采用普通优化方法求解很困难，而模糊数学对研究多目标优化问题恰好是有效的。

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷