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It is almost impossible to access the analytical solutions of relaxation equations, so the computer program for numerical solutions is developed. By means of the program and the Bloch equations, the steady state solutions of two...

在此基础上，编制了弛豫方程组数值解的计算程序，分别用此程序和Bloch方程计算了双自旋体系在不同情况下的稳态解，并对计算结果进行了简要的分析和讨论。

The first is how to determine boundary curve of surface in triangular domain and after deducing, simultaneous equations is proposed in the dissertation. The second is how to determine the coupling parameter. The third is present simultaneous equations in order to obtain G1 continuous considering the continuity between two triangular patches and the fitness rules.

具体的工作体现在三个方面：一是对拟合条件下的三角域曲面边界线的确定，本文经过推演给出了求解方程组；二是对耦合参数的确定；三是在考虑相邻两片三角域曲面连续性的同时将拟合的规则纳入，给出了求解方程组以达到G 1连续。

The contact curved surface equations and the contact plane surface equations have been worked out. The boundary curve eqations of the contact surface have been founded.

运用数学分析方法，首次对板式楔横轧工艺的轧件稳定旋转条件、轧件不产生缩颈拉裂条件进行了理论研究。

Applied Green's function, the differential equations will be transformed into the equivalent of integral equations, sufficient conditions for existence and uniqueness of positive solutions for fourth-order nonlinear singular continuous boundary value problems with p-Lapacian operator are obtained.

文中，利用格林函数，将微分方程转化成等价解的积分方程，给出了该奇异非线性四阶p-Lapacian微分方程边值问题的正解的存在及惟一性的一个充要条件。

The boundary value problem of ordinary differential equations is an important domain in differential equations.

常微分方程的边值问题是微分方程的一个重要研究领域。

Major research work and conclusions are summarized as follows:1 The development of molecular distillation are reviewed in respect of the principle, model research and application; The technical and structure parameters are analyzed with respect to the evaporation rate and separation factor.2 Based on analysis of heat transfer and mass transfer process in WFMD, the discretization forms of bow wave ordinary differential equations and film partial differential equations are obtained with Runge-Kutta method and finite difference method respectively.

主要工作与研究结果如下： 1 综述分子蒸馏技术的应用及其发展现状，从分子蒸馏技术的原理、模型研究及其应用的发展等进行了系统评述；并结合蒸发速率和分离效率这两个评价分子蒸馏效果的重要指标，对刮膜分子蒸馏器工艺参数与结构参数进行了分析与讨论。

It showed that the inverse circular function equation had the best fitting to the process of yellow soil releasing cadmium at conditions with different acid rain. Besides, polynomial equations and two-constant equations can also describe this process properly.

结果表明，反三角函数方程对多种酸雨条件下黄壤吸附态镉释放过程的拟合度最佳，此外多项式方程、双常数方程也能较好地描述这一过程。

Based on the projection theorem in the finite-dimensional inner product space, by making use of the generalized singular value decomposition and the canonical correlation decomposition of matrix pair simultaneously, we transform the least-squares problems of the abovementioned inconsistent matrix equations into the problems of solving the consistent matrix equations over given matrix set, and obtain the general expressions of the corresponding least-squares solutions.

S使得‖-X~*‖=‖-X~*‖，其中‖·‖为Frobenius范数，S分别表示矩阵方程 AXB=D，AXA~T+BYB~T=D，AXB+CYD=E和矩阵方程组=，=在一般矩阵集合或对称矩阵集合上不相容时的最小二乘解集合。

By discussing the position hypothesis of fractional-dimension derivative about general function and the formula form the hypothesis of fractional-dimension derivative about power function, the concrete equation formulas of fractional-dimension derivative, differential and integral are described distinctly further, and the difference between the fractional-dimension derivative and the fractional-order derivative are given too. Subsequently, the concrete forms of measure calculation equations of self-similar fractal obtaining by based on the definition of form in fractional-dimension calculus about general fractal measure are discussed again, and the differences with Hausdorff measure method or the covering method at present are given. By applying the measure calculation equations, the measure of self-similar fractals which include middle-third Cantor set, Koch curve, Sierpinski gasket and orthogonal cross star are calculated and analyzed.

通过讨论一般函数的分维导数的位置假设及幂函数的分维导数的形式假设，进一步明晰了幂函数的分维导数、分维微分及分维积分的具体方程形式，给出分维导数与分数阶导数的区别，随后讨论了基于一般分形测度的分维微积分形式定义导出的自相似分形的测度计算方程具体形式，给出了其与目前 Hausdorff 测度方法的区别，并对包括三分 Cantor 集合、 Koch 曲线、 Sierpinski 垫片及正交十字星形等自相似分形在内的测度进行了计算分析。

For the Riemann boundary value problems for the first order elliptic systems , we translates them to equivalent singular integral equations and proves the existence of the solution to the discussed problems under some assumptions by means of generalized analytic function theory , singular integral equation theory , contract principle or generaliezed contract principle ; For the Riemann-Hilbert boundary value problems for the first order elliptic systems , we proves the problems solvable under some assumptions by means of generalized analytic function theory , Cauchy integral formula , function theoretic approaches and fixed point theorem ; the boundary element method for the Riemann-Hilbert boundary value problems for the generalized analytic function , we obtains the boundary integral equations by means of the generalized Cauchy integral formula of the generalized analytic function , introducing Cauchy principal value integration , dispersing the boundary of the area , and we obtains the solution to the problems using the boundary conditions .

对于一阶椭圆型方程组的Riemann边值问题，是通过把它们转化为与原问题等价的奇异积分方程，利用广义解析函数理论、奇异积分方程理论、压缩原理或广义压缩原理，证明在某些假设条件下所讨论问题的解的存在性；对于一阶椭圆型方程组的Riemann-Hilbert边值问题，利用广义解析函数理论、Cauchy积分公式、函数论方法和不动点原理，证明在某些假设条件下所讨论问题的可解性；广义解析函数的Riemann-Hilbert边值问题的边界元方法是利用广义解析函数的广义Cauchy积分公式，引入Cauchy主值积分，通过对区域边界的离散化，得到边界积分方程，再利用边界条件得到问题的解。

Yet, Edith says, there was always money in the bank.

但是Edith说，她的银行户口里面总是有钱。

We have created a series of files that resolve this problem--one for each day of the 40 days of purpose.

我们制作一系列的档案去解决这问题---一个为标竿40天中的每一天。