模方程

In the second part, we study the solution of some matrix equations in field theory and module theory,i.e., it is determined whether matrix equations have solutions in a field.

第二部分我们是通过代数的域论和模论来研究矩阵方程的解的问题，即判断一个矩阵方程在在域上是否有解。

In the airfoil design for potential flow using conformal mapping technique, the metric coefficient was written as the analytical form.

在应用保角转绘技术的位流翼型设计中，研究了保角转绘网格中度规系数的解析表达；推导了将保角转绘模还原为翼型坐标的计算公式，而且将AF3算法用于位流方程的伴随方程的求解中，并在位流翼型的设计中得到了验证。

The equations of dynamics for the balance are established by Kane's method, from which derives the characteristic equation of natural frequency by means of linearization of dynamic equations, and the six natural frequencies being developed according to the theory of vibration. The law of the six natural frequencies varying with mass of the upper platform and the stiffness of the elastic element are presented,and the Finite Element Method is employed to testify the validity of theoretical results.

基于 Kane 方法研究天平的动力学及模态，通过线性化动力学方程建立天平的固有频率方程，依据振动理论推导出并联天平的六阶固有频率及其对应的振型，同时研究了天平的六阶固有频率随敏感单元刚度系数及上平台质量的变化规律，并用有限元法验证理论计算结果的正确性。

For intramolecular electron transfer reactions in solution,the fluctuations of the intramolecular vibrational modes are much faster than that of solvent mode.Thus,the reaction-diffusion equation is commonly used to describe the motion of solvent,with a sink function to treat the vibrational high-frequency mode.Based on this theory-so -called the Sumi-Marcus theory,we proposed an imaginary-time split operator approach to solve the reaction-diffusion equation.The approach is applied to evaluate the intermolecular ET rate between oxazine 1 and N,N-dimethlaniline.By measuring the two average survival times of the donor state probability and the rate constant in long time limit,the full kinetics of the ET is revealed with a variety of sink functions.

对于扩散控制的溶液中的电子转移反应，分子内振动模的运动比溶剂运动快很多，Sumi-Marcus理论提出用反应扩散方程(reaction-diffusion equation)处理溶剂的扩散运动，而分子内的振动用sink函数来表示，我们基于此理论发展了用虚时间分裂算符的方法(imaginary-time Split operator approach)解反应扩散方程，并将其应用于嗪1(oxazine 1，OX1)和N，N-二甲基苯胺分子之间的电子转移反应，Sink函数采用几种不同的微扰表达式，通过计算得到给体几率衰减的两种平均速率和长时间极限下的速率常数，揭示了该体系电子转移过程中的一些动力学性质。

In the second section, some analyses for large time behavior of the solutions of the models of scalar equation for reactors with periodic flow reversal are given by the maximum norm estimation of parabolic equations.

利用抛物型方程的最大模估计证明了单方程模型当关于单调递减时其对应的循环定态解的存在性，并且当时，模型解会趋于其对应的循环定态解。

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。

The difficuty of the dissertation is the nonlinear of the equations or the boundary conditions . When proving the existence of the solution to the singular integral equation , we must estimate the norm of the operators , the process of the estimation is a complicated process .

本文的难点是方程的非线性或边界条件的非线性，在证明奇异积分方程的解的存在性时，要进行模的估计，此估计过程是一个复杂的计算过程。

A large mode area core erbium doped K9-glass single-mode photonic crystal fiber is designed by getting the pump and signal intensity profiles from plane wave expansion methodand solving propagation-rate equations.Its diameter is 20μm,limit ellipticity error is 94.7%,and limit offset of inner ventage is 0.1μm.Then we analyze its amplifier characteristics.

根据平面波展开法给出泵浦光和信号光本征模场分布，结合速率方程和功率传输方程设计一种大单模尺寸的实芯掺铒K9玻璃大模式面积单模光子晶体光纤，芯径为20μm；分析其椭圆度容差为94.7%，最内层小孔最大允许偏移量为0.1μm；分析了掺铒K9玻璃光子晶体光纤放大器的放大特性。

So in this paper a new damage variable was defined, then, Based on damage theory and Weibull distribution damage evolution rule, a simplified ameristic damage constitutive equation was established for concrete under uniaxial compression.

为了用简单的方程将上升段和下降段连接起来，本文以峰值割线模量为基准，定义了一种新的损伤变量；并以经典损伤理论模型为基础，根据混凝土损伤演化规律的概率密度服从Weibull分布，提出了一个统一的方程来描述混凝土单轴压缩时应力应变关系的全过程。

Based on the wave equation in the acoustic fluid space and the theory of thin-wall structure, the uncoupling error in low frequency range about the nonsymmetrical coupled structure-acoustic analysis equation is studied.

该对称模型特征值的非负性及特征问题的可降阶性也在本文中进行了深入研究，同时指出了在复模态分析中应当注意的问题；（2）由声空间波动方程和薄板理论出发，对非对称声振耦合方程的低频解耦误差问题进行了研究。

He and Nina moved to California and lived at 2005 Ivar Street, Apt.

他和Nina搬到加州，并在2005年伊瓦尔街，公寓生活。

Droperidol （ potently inhibits transfected HERGchannels and this is the probable mechanism for QT prolongation.

氟哌利多有效地抑制了转染的 HERG 钾通道，可能是 QT 间期延长的机制。