结构方程

The coefficients in trial function can be gained by the point collocation method, then the solution of the boundary value problems is obtained. Non - uniform beams and irregular plates on Winkler foundation and plates on elastic half space foundation can be numerical calculated by the introduced method.

为对土与结构物的相互作用进行研究，在采用适当的土体模型的基础上，必需求解地基与基础的共同作用方程，而该共同作用方程一般是偏微分方程或微分积分方程，除一些简单的模型外，其解析解较难获得，因此只能采用数值方法求其结果，加权残仇法是一种L作鼠少、简便易行的数仇方法{2，但其解的精度'。

The grids can be densified locally where the flow is complicated for the sharp change of water depth.(5) 2-D hydrodynamic equations in the generalized curvilinear coordinates have been derived with the contravariant velocities as main variables. The new equations keep the original styles and physical meanings. Based on the water depth correction method, the 2-D flow numerical model has been established and validated by the measured data.

推导了广义曲线坐标系下以逆变流速张量作为主变量的二维水动力方程，新方程保持原有结构形式及物理含义，采用水位校正法建立了二维水流数学模型，经实测资料验证后的模型，模拟并分析了分流角度、宽深比等因素变化对分汊流平面二维水流结构的影响。

Wahlquist and Estabrook proposed a theory of prolongation structures of the nonlinear evolution equations in terms of Cartans exterior differential form method and successfully applied it to kdv equation.

Wahlquist和Estabrook最早利用Caftan的外微分形式方法提出了非线性演化方程的延拓结构理论，并且成功地讨论了kdv方程的延拓结构。

Combined with the new process and new products, we have developed their characteristic equations and models, especially for hollow; heteromorphism and composite fibers.

结合新工艺和新产品的开发，本文推导了高速纺丝、热管纺丝、热辊纺丝等工艺的特征单元方程及中空、异形、复合纺丝等新品种的特征单元方程，着重推导了圆形纤维、中空纤维、三叶异形纤维、皮芯复合纺丝的分层结构模型及分块模型，并对高速纺丝及中空纤维的不对称冷却结构进行了系统的数学模拟。

In accordance with the situation that the damping was the non-classical damping,the structure was asymmetric,and random wind spectrum was irrational fraction wind spectrum,the equations obtained were decoupled with the complex mode theory.

建立运动方程，用第一振型将主体结构展开，针对非经典阻尼和非对称结构以及脉动风谱为非有理分式风谱的情况，运用复模态理论将所得方程进行解耦，获得了以第一振型表示的结构随机风振响应的解析解。

Content: By learning this course, students should grasp the elementary solution of first order differential equation, the structure theory of linear differential equation or system of linear differential equations and the solution of constant coefficient differential equation or system of constant coefficient differential equations.

主要内容：通过对本课程学习，使学生掌握一阶微分方程的初等解法、线性微分方程的结构理论和常系数方程的解法，对微分方程初值问题的一些基础理论有一定的了解，对

Around the finite solution problem of fuzzy differential equation, the fuzzy structure element method is put forward about the calculation of fuzzy analysis, and this method is applied to systematically study many problems such as formulation of fuzzy-valued function, difference of fuzzy-valued function, integration of fuzzy-valued function under the Riemann meaning, and the solution structure of fuzzy differential equation etc..

围绕模糊微分方程定解问题，提出了模糊分析计算的模糊结构元方法，并利用模糊结构元的方法对模糊值函数的表述问题、模糊值函数的微分、黎曼意义下的模糊值函数积分以及模糊微分方程的解的结构等问题，进行了深入系统的研究。

Secondly, based on the different structure characteristics and additional conditions, we study several kinds of inverse problems of pseudoparabolic equations. One is a kind of pseudoparabolic inverse problem of identifying a constant coefficient solved by combining the formal solution of the problem and the additional condition properly. The second is the pseudoparabolic inverse problems of identifying an unknown boundary function and an unknown source term solved by using the Riemann function method to get the formal solution of the problem and then using the additional condition to transform the problem into a Volterra integral equation of the second kind. The third is a kind of backward heat flow problem of nonlinear pseudoparabolic equation solved by combining the Riemann function method and the fixed point theory properly.

其次，根据不同模型的结构特点和附加条件，研究了几类伪抛物型方程的反问题：一是利用问题的形式解并结合附加条件，解决了一类伪抛物型方程常数系数的反问题；二是利用Riemann函数方法获得问题的形式解，利用附加条件将问题转化成求解第二类Volterra积分方程问题，解决了一类伪抛物型方程未知边界值的反问题和未知源项的反问题；三是将Riemann函数方法和不动点定理相结合，解决了一类非线性伪抛物型方程的后向热流问题。

A general matrix perturbation method for complex modes using singular value decomposition;2. The modal character,the error of the substituting by real modes and the best way to extract real modes from complex modes are discussed.

建立运动方程，用第一振型将主体结构展开，针对非经典阻尼和非对称结构以及脉动风谱为非有理分式风谱的情况，运用复模态理论将所得方程进行解耦，获得了以第一振型表示的结构随机风振响应的解析解。

Chapter 5 and 6 are concentrated on the fundamental problem how to con-struct finite-dimensional and infinite-dimensional Liouville integrable Hamiltonsystem.Starting from two isospectral problems,Tu's scheme is applied to gen-erate the corresponding CKdV hierarohy and coupled Burgers hievachy,andthey are shown to be Liouville integrable Hamilton systems.Two spectral prob-lems,which contain three and four potentials respectively,are also studied byTu's scheme.Two new Liouville integrable Hamilton hierarchy are estab-lished.A new general approach using Lenard's gradient sequence is presentedto obtain Lax integrable hierarchy and their zero curvature representation,andsome examples are given.The nonlinearization procedure is applied to theeigenvalue problem of coupled Burgerrs hierarchy.It is shown that underBargmann constraint,the spatial part of the Lax pairs is nonlimearized to be afinite-dimensional Liouville completeiy integrable Hamilton system.

第五、六章研究如何从一个谱问题出发构造可积发展方程族及其零曲率表示、Hamilton结构和判断Liouville可积性：通过对二类具有2个位势的等谱问题直接研究，利用屠格式生成了耦合KdV族和耦合Burgers族，并证明它们均为Liouville可积的广义Hamilton方程族；而通过分别具有3个和4个位势的等谱问题，遵循屠格式构造了二族新的Liouville可积的广义Hamilton方程族；给出了利用Lenard梯度递推序列产生发展方程族及其零曲率表示的一种方法，作为应用，讨论了CKdV族，BPT族及耦合Burgers族的产生及其零曲率表示；应用非线性化技巧，证明了在Bargmann约束下，耦合Burgers族的Lax组可被线性化为Liou-ville完全可积的Hamilton系统。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。