向量方程

Based on the element-free Galerkin method, the basic equations for steady thermal conductivity problem are deduced; and then the shaping of the coefficient matrices and load vectors in the discretization form of them are presented.

基于无单元伽辽金法基本理论，推导了稳态热传导问题的基本积分方程，并介绍了其离散形式中，包含刚度矩阵在内的各个系数矩阵和荷载向量的主要形成过程。

Based on the analogy of structural mechanics and optimal contro1, and a1so based on carrying the minimum potential energy variational principle in elastici- ty to the generalized one, the theory of Hami1tonian system can be introduced into theory of e1asticity and e11iptic PDE. The transverse eigensolutions of the Hamiltonian operator matrix and its expansion solution method can be deduced.

利用结构力学与最优控制相模拟的理论，将弹性力学势能变分原理导向部分一般变分原理，并将哈密尔顿体系的理论引入到弹性力学与椭圆型偏微分方程之中，导出一套横向哈密尔顿算子矩阵的本征函数向量展开解法。

For the ill conditioned load flow caused by the error produced in the transformation from electricity quantities to average power, direct current load flow and sensitivity vector are presented to find out the ill node, then by adjusting the load curve and generation curve in a certain principle, which is shown in detail with several flow charts, a new operation mode is reestablished to ensure the convergence of the calculation. Optimal multiplier method is proposed to work out the least square solution according to ill conditioned structural power network. The electricity quantities flow method enhances the reliability and accuracy of the calculation of the power transmission losses.

该方法可根据当前输电网中各个变电站24小时的电量记录，利用电量潮流计算对输电网总线损和各条线路损耗进行计算，使计算的精度满足降损措施分析和指标考核的要求；并且对于由负荷出力曲线转化成平均功率计算潮流时引入的误差，进而导致潮流计算不收敛的情况，采用直流潮流法，依据相角对有功功率的灵敏度向量判断出"网络异常点"，并且给出了解决此种情况的方法流程图；针对结构病态的电力系统潮流计算不收敛的情况，运用非线性约束优化方法中的最优乘子法求解潮流方程的最小二乘解，从而解决了电量潮流法计算理论线损时的收敛性问题，增强了该方法的适用性。

Moreover, it is shown that each equation in the resulting hierarchy is Liouville integrable.

它们是著名的薛定鄂方程族的向量形式，并且是Liouville可积的。

In order to improve calibration precision,projection matrixes of camera were obtained by optimization based on Householder orthogonalization transformation which has character of not changing the length of transformed vector.

根据豪斯赫尔德正交变换具有不改变被变换向量长度的特性，采用优化的方法来求得法方程的解析解，得到摄像机的投影矩阵，以提高标定精度。

By the theory of difference equation and the construction of proper vector Liapunov function, we for the first time get the sufficient conditions for the permanence, extinction and balancing survival for this ndimensional system, which are all independent on the delays, hence under peroper conditions the time delays of this system are both harmless and profitless.

通过运用差分方程理论以及构造适当向量Liapunov泛函的方法，首次得到了此类系统多维自治的情形下系统持续生存、灭绝和残存的充分条件，这些充分条件均不依赖于时滞，因而在一定条件下，此系统中的滞后因素既是无害时滞也是无益时滞。

In the second chapter, we deal with the global of systemBy virtue of the abundant results of Lienard equation, integrated with the theory of rotated vector field, we discussed of the number and distribution of limit cycles of the system and obtain its global structure.

第二章讨论了系统的全局结构。利用定性理论中关于Liénard型方程已有的丰富结果及旋转向量场理论讨论了极限环的个数及其相对位置，得到了系统的全局结构。第三章讨论了系统的局部分支。

In order to calculation Lyapunov exponent spectrum of unknown system,firstly,reconstruct phase space of observed one-dimensional time series,secondly,use Least-Squared Support Vector Machine approximate dynamical equation of reconstruction system and calculation Lyapunov exponent spectrum by Jacobian matrix.

为了计算未知系统的Lyapunov指数谱，首先，对一维观测数据序列进行相空间重构，然后，利用最小二乘支持向量机逼近重构系统的动力学方程，再通过雅克比矩阵计算Lyapunov指数谱。

Methods Get the norm of solution vector to the equivalent integral equation using numerical calculation in every sampling point at imaging region,and represent the norm with gray to reconstruct the scattering shape.

方法通过数值计算，求解等效积分方程，获取解向量在成像区域内每一采样点的范数，利用灰度表示其范数，重构散射体形状。

The stochastic expansions given here depend only on the independent normal random variables and curvature arrays, therefore they are easy to understand and to deal with.

f'(0)一f(二'，0)。二'为已知的自变量，相应的因变量和随机误差为y'和。'，0为p维未知参数，其参数空间为R中的子集习。在约束方程(2)中，甲(0)为k维向量k

We have no common name for a mime of Sophron or Xenarchus and a Socratic Conversation; and we should still be without one even if the imitation in the two instances were in trimeters or elegiacs or some other kind of verse--though it is the way with people to tack on 'poet' to the name of a metre, and talk of elegiac-poets and epic-poets, thinking that they call them poets not by reason of the imitative nature of their work, but indiscriminately by reason of the metre they write in.

索夫农 、森那库斯和苏格拉底式的对话采用的模仿没有一个公共的名称；三音步诗、挽歌体或其他类型的诗的模仿也没有——人们把&诗人&这一名词和格律名称结合到一起，称之为挽歌体诗人或者史诗诗人，他们被称为诗人，似乎只是因为遵守格律写作，而非他们作品的模仿本质。

The relationship between communicative competence and grammar teaching should be that of the ends and the means.

交际能力和语法的关系应该是目标与途径的关系。