解域

Leading resistant factor into the necessary condition can also enlarge the quadratic convergence region near optimal solution so that it is very efficient to use the known flash calculations at one condition to iteratively compute another optimal solution at other conditions where pressure, temperature and mole fractions of components are close to known ones respectively.

在极值必要条件式中引入阻尼因子能扩大真解附近的平方收敛域，尤其在利用已知条件下的汽液平衡结果作初值直接用极值条件方程迭代计算压力、温度和组成变化不严重的相邻点的汽液平衡极值解方面效果十分显著，适合于加快组分模型的计算速度。

By using Lee\'s matching law, the excess pore-air pressure, excess pore-water pressure and settlement in the Laplace-transformed domain are obtained for one-dimensional consolidation in unsaturated soils, under the large-area uniform instantaneous loading. A computer program using the method by Crump and Durbin is developed to obtain the semi-analytical solution of the excess pore-air pressure, excess pore-water pressure and settlement under the boundary conditions of the top surface permeable to water and air and the bottom impermeable to water and air.

8采用李氏比拟法，应用Merchant粘弹性模型，得到了Laplace变换域内粘弹性非饱和土地基一维固结时超孔隙水压力，超孔隙气压力以及土层沉降的解；采用Crump及Durbin方法实现Laplace逆变换，获得大面积均布瞬时加荷，在顶面排气排水，底面不排气不排水情况下粘弹性非饱和土地基一维固结时的半解析解。

Since the multiple scattering should be considered, the scattering problem of many-cylinders is more complicated than single cylinder. By using scattering matrix method to solve the scattering problem of many-cylinders, first we have to express the incident fieldand scattered field by special function（for example, Bessel function and Hankel function）under cylindrical coordinate, then use the addition theorem of special function to get a linear system of equations to relate the incident field coefficients and scattered field coefficients. The incident and scattered field coefficients for every cylinder can be solved from the linear equations by matching electromagnetic boundary condition pointwisely.

单颗圆柱散射体的散射场解析解很早就被解出，而多个圆柱阵列的散射场问题因为涉及到入射光在圆柱与圆柱间的多重散射，故散射行为较单颗圆柱的散射复杂，因此圆柱阵列的多重散射问题需要利用加法定理来处理；散射矩阵法的主要精神即是先用圆柱座标下的特殊函数对平面波和圆柱散射体的内外域电磁场做无穷级数展开，再藉由特殊函数的加法定理将所有圆柱散射体的展开中心移到同一个展开中心，最后可以得到一组连结整个散射系统的入射电磁场系数及散射电磁场系数的线性方程组，将该组线性方程配合电磁场在散射体边界的连续条件，便可分别求出圆柱阵列中各个圆柱体的内部电磁场与外部散射场，再利用线性叠加原理即可求得整个圆柱系统的全域电磁场分布。

In the paper , we gives a condition and an expression of general solution of a matrix equation AXB=C by using some matrix techniques and elementary operations on matrices.

文章应用矩阵的初等变换等技巧，给出了任意域上矩阵方程AXB =C的有解条件、实用解法及通解。

Under the assumption that the feasible region of the problem is n dimension, if the algorithm is terminated after finite step, the point obtained must be a global optimal solution of the problem, else each accumulation point of sequence {vk} which the algorithm produces must be a global optimization solution of the problem.

在问题的可行域是n维的条件下，如果这个算法有限步后终止，得到的点必是问题的整体最优解；否则，该算法产生的点的序列{vk}的每一个聚点也必是问题的整体最优解。

Using the method of linear response theory in lattice dynamics on the basis of Tyson's model, the response displacements of atoms on cleavage plane at the incipience of brittle fracture was derived and an expression for evaluating brittle fracture surface energy of metals was found.

本文在Tyson模型的基础上，应用点阵动力学线性响应的理论方法，导出了脆断发生时解理面上原子的响应位移，并进而给出金属脆断表面能的计算公式。这种处理方式既保持了解理断裂面是结晶的表现，避免了局域"熔化"和"沸腾"模拟脆断的简单模型中出现的非晶化问题，也对解理面上原子临界位移做了合理估计，避免了人为规定临界位移的随意性，同时，从理论上得出的脆断时产生的声发射信号与实际探测到的量级相近。

The result for an aluminum sphere with gaussian pulse incident wave was compared to the theor y value obtained by inverse Fourier transform from the product of Rayleigh serie s with incident wave in the frequency domain, which shows a good agreement.

计算了高斯形脉冲入射下弹性铝球的无量纲反向散射声压，并和由频域的Rayleigh 简正级数解与入射波的频谱的乘积作反变换得到的精确解做了比较，两者趋势基本一致。

For different polynomials g, if the characteristic polynomial of a n matrix A is irreducible, then we get some theorems to determine matrix equations g =A solvable; if it is reducible, then, to see n-dimension space vectors M over a field F as F-module, we use module theory to determine these equations solvable such that it is simpler and clearer to investigate these questions.

对于不同多项式g，当n阶矩阵A的特征多项式为不可约的，我们给出了矩阵方程g=A有解的判定定理；当A的特征多项式为可约的，把域F上的n维线性空间M作为由A导出的F -模，我们利用模论知识来决定矩阵方程g=A有解性，从而使这一问题变了简单，研究思路更加清晰。

In this paper,we present a new class of second order linear differential equation s with meromorphic coefficients and investigate the problems on the fixed points and hyper order of solutions and their 1st,2nd derivatives.

该文提出了一类新型的亚纯函数系数的二阶线性微分方程，研究了其亚纯解及其一阶和二阶导数的不动点及超级问题，得到了有关复域微分方程亚纯解及其一阶和二阶导数的不动点性质。

In this paper,we present a new class of second order linear differential equations with meromorphic coefficients and investigate the problems on the fixed points and hyper order of solutions and their 1st,2nd derivatives.

该文提出了一类新型的亚纯函数系数的二阶线性微分方程，研究了其亚纯解及其一阶和二阶导数的不动点及超级问题，得到了有关复域微分方程亚纯解及其一阶和二阶导数的不动点性质。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失