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Initial boundary value problem of two dimensional unsteady diffusion equations is solved in this paper. By using time-dependent fundamental solution of two dimensional diffusion equations and the extension of double layer potential, we establish virtual boundary integral expression of diffusion equations. Then virtual boundary element method is used to implement the numerical computation.

本文在求解二维非定常扩散方程的初边值问题时，利用二维扩散方程与时间有关的基本解，基于双层位势的延拓，建立二维扩散方程的虚边界积分表达式，然后利用虚边界元法进行数值计算。

According to the simulation results, the three-dimensional condition for three dimensional trapping of low refractive double layer sphere is analyzed.

通过数值模拟的结果，分析了俘获低折射率双层球的三维条件。

PartⅡ,Applying the developed and extended direct algebraic methods that presented in recent years and based on the 2+1 dimensional variable separation solutions,abundant Jacobi elliptic function doubly periodic waves and periodic propagating wave patterns for many 2+1 dimensional nonlinear wave models are obtained,and in long wave limit solitary waves are derived as well.

第二部分，本文拓展和推广(来源：a2AB7aC论文网www.abclunwen.com)了新近发展的几种典型的直接代数方法和基于分离变量解的间接方法，获得多个2+1维非线性波动模型丰富的雅克比椭圆函数双周期波解和周期传播波模式，并得到长波极限情形下存在的非线性孤立波。

The computer separately connects and controls the I/O end and A/D converter; the I/O end connects and controls the X, Y axis driving circuit and the semiconductor laser; the X, Y axis step-by-step driving circuit connects and controls the X, Y step-by-step electrical machines to control the dimensional platform; the beam of the semiconductor laser passes through the focusing drawtube with 0.1mm diameter to form the facula with the diameter less than 0.1mm; the facula irradiates on the detector surface of the XY dimensional displacement platform to produce the corresponding electric signals; the detector surface connects the A/D converter through the amplifier; the electrical signal is amplified and is converted into the data signal by the A/D converter and is sent to the computer for processing.

由计算机分别连接并控制I/O端口和A/D转换器，I/O端口分别连接并控制X、Y轴步进电机驱动电路和半导体激光器，X、Y轴步进电机驱动电路分别连接并控制X、Y轴步进电机，从而控制二维位移平台，半导体激光器的光束经过设有直径0.1mm小孔的聚焦镜筒形成＜0.1mm直径的光斑，光斑照射于设在XY二维位移平台上的探测器表面使其产生响应的电信号，探测器表面经放大器连接A/D转换器，电信号经放大器放大后，由A/D转换器转换为数据信号送计算机处理。

It is confirmed from both the experimental investigation and numerical analysis that the constitutive correlation of the drift velocity in which the effect of the gravitational force and the acceleration of fluid flow on the drift velocity of the vapor phase is taken into account has reasonable accuracy and it can be used to determine the drift velocity of the vapor phase of two-dimensional and three-dimensional two-phase flow.

本文结合实验测量和数值计算两方面，验证了同时考虑重力和流体本身加速作用对汽相漂移速度的影响是合理的，这种漂移速度结构关系式可以用来计算二维和三维汽相漂移速度。

In the numericalstudy, three-dimensional elastodynamics equations and Morison equation are applied tosimulate the time histories of dynamic response of submarine pipelines suspended over flatbeds sucessfully. The three-dimensional interaction of pipeline and internal flow isnumerically simulated by applying the iterative computation to the fluid-structure interfacesand using the elastodynamic equation and the incompressible fluid N-S equation andcontinuity equation.

在数值研究方面，本文利用三维弹性动力学方程，结合莫里森方程，较好地模拟了规则波浪作用下近壁悬跨弹性海底管线动力响应过程，结合不可压缩流体N-S方程和连续方程，进行管线及其内部流体的三维流固耦合数值计算，基于数值计算结果探讨内流管线系统的动力特性和管内流体特征。

In Chapter 2, the two dimensional electron gas in heterostructures and the state density of the low dimensional electron gas are presented.

第二章给出了在异质结中二维电子气的形成过程，以及低维电子气的态密度。

In Chapter 2, the of two dimensional electron gas in heterostructures and the state density of the low dimensional electron gas are presented.

第二章给出了在异质结中二维电子气的形成过程，以及低维电子气的态密度。

Second,around each of m-dimensional tori of elliptic or mixed type there arehigher-dimensional invariant tori.

第二，环绕在m维椭圆型和混合型环面的周围存在维数更高的不变环面。

This software take full advantage of the multimedia technique , especially the three-dimensional animation, to open out the abundant meanings and scientific theories in structural chemistry by using lush graphical interfaces, lifelike animation, lifesome sound effects, alluring exhibitive technique, translate bald contents and nonobjective theories into visual, direct-viewing, lively demonstration, change static and plane teaching method into dynamic and three-dimensional teaching process with attraction and infection, realize visual and enlightened teaching.

本软件充分应用计算机多媒体特别是三维动画制作技术以丰富的图形界面、逼真的视频动画、生动的音响效果、引人入胜的表现手法揭示了结构化学中包括的丰富内涵和科学原理，将原来枯燥的内容和抽象的理论转变为形象、直观、生动的演示，使以前静态的，平面式的教学变为动态的、三维立体的教学过程，具有吸引力和感染力，实现了形象化、启发式教学。

I'm going tor her!

我这就去救她！

As rise are design to help keep a several toney , a brain chemical at continues lever.

SSRI被设计来帮助保持血液中的复合胺即在大脑中一个连续水平的化学物质。