波动方程

In particular,the phase function of the disturbance wave system is solved by uting the characteristic theory of partial differential equation and an expan sion of Orr-sommerfeld eigenvalue problem,insteade of using the disturbance model which was given previously.

其特点是。应用偏微分方程特征理论以及O－S方程特征值的展开，求解扰动波的相函数而不是预先给定扰动波的波动形式。

First of all, the evolutionary game model of this system is built, according to a population and determinately dynamic function in evolutionary game theory, and quilibrium structure and effect factors of the evolutionary system are analyzed. Next, the evolution quilibrium characteristics of investor behaviors in China's securities market are researched as a demonstration, and the reasons why noise traders become popular in the process of investor behavior evolution are explained, based on its evolutionary mechanism. Moreover, the influences of investor behavior evolution on share market's fluctuation are researched through setting up its noise trade model. When noise traders are dominant in securities market, price discovery function and resource configuration effect are also analyzed. Finally, when noise trade become popular, the shortage of some policies, such as, enlarging institution investor and short sale is explained, and some good suggestions are provided according to former research results.

首先，应用进化博弈论中的单群体确定性模仿者动态方程建立证券投资者行为的进化博弈模型，并对进化系统的均衡结构特征及其影响因素进行分析；其次，根据我国证券市场实际，对我国证券投资者行为进化的均衡结构进行实证分析，并从投资者行为进化的角度，解释我国证券投资者行为进化为噪声交易主导市场的原因；然后，通过建立股市波动的噪声交易模型，研究投资者行为的进化对股市波动的影响，并进一步分析我国噪声交易主导市场时对市场价格发现和资源配置功能的影响；最后，根据理论及实证的研究成果，分析噪声交易主导市场时大力发展机构投资者等制度作用的有限性，并进一步提出我国证券市场相机治理的政策建议。

Using Biot's 2D elastodynamic theory solves the saturated soil equation. The Fredholm integral equation of the second kind can be built by using the fundamental solution of circular load, the compatibility condition and superposition method. The Fredholm integral equation of the second kind of pile groups can be solved by using numerical method. The numerical solutions of pile groups axial forces, pore pressures under vertical harmonic loading and shear forces, moments and pore pressures under horizontal harmonic loading can be obtained.

采用Biot提出的三维波动原理，利用圆形简谐载荷作用下的Biot固结方程的基本解和桩土之间的变形协调条件，并采用叠加原理得到饱和土中群桩的第二类Fredholm积分方程，应用数值法求解群桩的第二类Fredholm积分方程，得到在垂直简谐载荷作用下群桩的轴力、孔压随桩身变化的数值结果以及在水平简谐载荷作用下群桩的剪力、弯矩和孔压随桩身变化的数值结果。

First of all, the report introduced evolution, achievments and problems in the study of anisotropy in the inner of earth. The first-order hyperbolic system of equations is work out, which is used to describe the wave motion in 2D transversely isotropic media. Utilizing the characteristics of free-divergence, We have imposed MacCormack theme that is used to simulate multicomponent records in anisotropic media and have developed a fast high order vectorized finite-difference algorithm adapted for the vector supercomputer.

本文首先阐述了地球内部介质各向异性研究的沿革、成就和问题，接着给出了描述二维横向各向同性介质中波动的一阶双曲型方程，利用其自由发散特性，构制了各向异性介质中多波多分量地震记录数值模拟的MacCormack算式，导出了适用于并行计算的二维横向各向同性介质中波动的有限差分模拟算子，该算子具有可并行化计算、相位差小等优点。

This thesis carries on research to a class of nonlinear Schrodinger Equation with wave operator of initial value periodic problem.

本文针对一维带波动算子的Schrodinger方程周期初值问题进行数值研究，对上述方程首先构造了守恒的半离散格式，然后将p次Hermite插值方法与有限差分方法相结合构造了差分正交样条配置格式，并证明这两个格式均为稳定和收敛的格式。

Based on the elastic theory of large deflection and by taking into account the variation of the axial force and its effects on bending deformation of the drillstring in vertical section,the vibration of the drillstring induced by fluctuating weight-on-bit is described by a parametrically excited system.A Mathieu equation describing the system is established by Galerkin Method.By extending the solution into a Fourier series,the curves of dynamic bifurcation values and the dynamically unstable regions surrounded by the curves are presented.

基于弹性大变形理论，考虑到轴力沿钻柱轴线的变化及其对钻柱弯曲变形的影响等因素，将受自重作用的铅垂井段钻柱在波动钻压激励下的振动转化为一个参数激励系统，用Galerkin方法首次得到了描述此系统的Mathieu方程，并通过将方程的解展成富里叶级数的方法，得到了该振动系统的动力分岔值曲线及其所包围的动力不稳定区。

This article consists of four parts: In the first part of thesis introduced Heisenberg's early years of life and the creation of Matrix mechanics, expounded Münich、G?ttingen,Copenhagen, three places different academic atmosphere which produce to Heisenberg's institute of physics, and revealed how to set up Matrix mechanics by mathematics method; The second part introduce Schr?dinger's university life, the research results, and the establishment of Wave mechanics. The different academic atmosphere of Vienna and Zürich have the difference influence which brings to Schr?dinger's research work, how to establishment the Schr?dinger equation based on Hamilton equation of classical mechanics, and elaborated the physical controversy caused by the equivalent.; The third part analyzed two mechanics different approaches in which the way to propose the question and solve the question; The last part recommend the different philosophy interpretations, Schr?dinger's interpretation onΨfunction, the statistical interpretation of Wave mechanics, uncertainty principle, and which caused this free discussion of quantum mechanics.

文章共分为四部分：第一部分介绍了海森伯的早年生活及其创立矩阵力学的过程，阐明了慕尼黑、哥廷根、哥本哈根三地不同的学术氛围对海森伯的物理研究所产生的不同作用，并揭示了海森伯如何用数学方法建立矩阵力学方程的过程；第二部分介绍了薛定谔的大学生活、研究成果，以及波动力学的创立过程，说明了维也纳和苏黎世不同的学术气氛给薛定谔的研究工作带来的不同影响，解释了薛定谔以经典哈密顿方程为基础建立薛定谔方程的过程，并阐述了等价性所引起的物理争论；第三部分分析了两种力学的思想进路在提出问题、解决问题上的不同；最后一部分介绍了对两种力学形式不同的哲学诠释，薛定谔对Ψ函数的诠释、波函数的统计解释和测不准原理，以及由此引起的量子力学的大讨论。

The water flow movement basic equations of transient process caused by small fluctuation in the inclined roof tailrace system were deduced, and then analyzed and calculated.

推导了变顶高尾水系统小波动过渡过程水流运动的基本方程，对基本方程进行分析与求解，并以某电站为例，探讨了变顶高尾水系统小波动过渡过程的基本规律。

In the process of impact of abrasive jet on rock, resulting dynamic stress plays an important role in rock destruction. The stress wave resulted makes local rock tensile and shearing, then makes rock destructed. In the conditions of some hypotheses, the mechanical model that rock is applied by stress wave, i.e. jet wave basic equations, are set up by wave theory, and the formula of the maximum normal stress resulted by stress wave is deduced according to known boundary conditions.

描述了岩石材料在磨料射流的冲击下破坏的主要原因，分析了应力波就是岩石局部受到拉伸和剪切并最终使岩石发生破坏的根本因素，在这一假设的前提下采用波动理论建立了岩石受应力波作用的力学模型即射流波动的基本方程，在已知的边界条件下推导出了由波动引起的最大正应力的计算公式。

The scatter point plots show the volatility clustering,therefore we fit the volatility of returns series by the modelling methods in Chapter 3,while fitting the conditional mean equations of returns series with ARMA(1,1) models.

日收益率的散点图显示出波动集聚特征，因此论文分别用第三章介绍建模方法拟合收益率序列的波动，同时用ARMA（1，1）模型拟合收益率序列的条件均值方程。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。