向量解析

The optimal control law obtained is composed of feedforward and feedback optimal terms without time-delay in analytic forms and a compensation term with time-delay in a sequence limit form of adjoint vectors.

得到的最优控制律由解析的无时滞前馈－反馈控制部分和伴随向量序列极限形式的时滞补偿控制部分组成。

The obtained optimal control law consists of analytical linear feedforward and feedback terms and a nonlinear compensation term which is the limit of the adjoint vector sequence.

得到的最优控制律由解析的线性前馈－反馈项和伴随向量序列极限形式的非线性补偿项组成。

The optimal control law obtained consists of linear analytic functions and a compensation term which is a series sum of the adjoint vectors. The analytic functions can be found by solving a Riccati matrix difference equation and a matrix difference equation. The compensation term can be obtained by a recursion formula that solves adjoint vector equations.

得到的最优输出跟踪控制律由状态向量的线性解析函数和伴随向量级数形式的补偿项组成，其解析函数由一次性求解Riccati矩阵差分方程和矩阵差分方程得到，补偿项由求解伴随向量差分方程的递推公式得到。

Solutions of the network are represented by the eigenvalues and eigenvectors of the symmetric matrix, and the asymptotic behavior of the solutions is analyzed.

这一表达式是由对称矩阵的特征值与特征向量表达的，因而非常清晰。利用解的解析表达式分析了网络的解的全局渐近行为。

Special solutions for the ring circular domain with crack surfaces acted on uniform compressive force, linear compressive force and linear shearing force are deduced in polar coordinate employed the eigenfunction expansion technique in the Hamiltonian system of elastic mechanics. Combined with the general solution for the above problems, the analytical solutions for crack tip fields with surfaces acted on the above three kinds of loads are obtained. These solutions offer theoretical basis to construct analytical elements for plastic analysis of crack.

从弹性力学哈密顿体系理论出发，利用平面弹性力学极坐标系下的本征向量展开求解，推导了环形圆形域裂纹边作用有均布压力、线性压力和均布剪切力情况下的特解，从而得到了裂纹表面作用有以上三种荷载情况下的裂纹尖端场的解析解，为进一步构造进行弹塑性裂纹分析的奇异解析元奠定了理论基础。

Extended the semi-analytical finite element method into the Dugdale model of elastic-plastic fracture mechanics, the analytical elements based on the Dugdale model of mode Ⅰ and mode Ⅱ crack are constructed. The formulas for the stiffness matrices and load vectors of analytical elements are deduced.

将上面的半解析有限元法应用于弹塑性断裂力学中的Dugdale模型，分别构造了基于Ⅰ型和Ⅱ型Dugdale模型的裂纹解析元，并建立了解析单元的出口刚度阵和荷载向量的列式。

Utilizing plane sectorial domain Hamilton system function via variable substitutes and eigenfunction expansion method, an analytical element is proposed in this paper for the crack analysis of reinforced concrete structures combining the bridging model and Dugdale model. Combined with finite element, nolinear crack problems of reinforced concrete structure can be analyzed.

利用平面扇形域哈密顿体系方程，通过分离变量法及共轭辛本征函数向量展开法，结合Dugdale模型和桥联力模型，推导了钢筋混凝土结构裂纹尖端的解析元列式，将此解析元与普通有限元结合，可用于分析钢筋混凝土的非线性断裂问题。

Based on the Hamiltonian governing equations of plane elasticity for sectorial domain, the variable separation and eigenfunction expansion techniques are employed to develop a novel analytical finite element for the fictitious crack propagation linear force model in fracture mechanics of concrete in this paper.

利用平面扇形域哈密顿体系的方程，通过分离变量法及共轭辛本征函数向量展开法，以解析的方法推导出基于混凝土虚拟裂缝扩展线性粘聚力模型的平面裂缝解析元列式。

Improve the accuracy of the initial rotor position estimator by using the Fourier series expansion.

在永磁同步的马达启动方面，则透过送出不同向量空间角度的定子电压向量脉冲所量测到的d轴定子电流的大小来估测转子的初始位置，并利用d轴定子电流在空间向量角度以2π为周期的特性，应用傅立叶级数分析做曲线拟合的方式提高转子位置估测解析度，以提高转矩/电流比节省不必要的功率浪费。

In this paper,the Riemann boundary value problem for bianalytic vector function s is investigated using the theory of boundary value problem for analytic functions,we have not only found the solution method for bianalytic vector function s,but also established an explicit form of the general solution and the conditions for the solvability of the above problem.

利用解析向量函数边值问题理论，提出了双解析向量函数的R iem ann边值问题，并研究了问题的解法和解的一般表达式及可解性条件，得到了相应的可解性定理，同样方法可解决多解析向量函数的边值问题

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。