一般方程

With replicator equation we established the general model of industrial labor force structure.

本文还利用复制方程建立了产业劳动力结构的一般模型，对模型性质进行了分析。

This paper is divided two chapters. The first chapter discusses the existence and uniqueness of solution for the Cauchy problem of the following quasilinear degenerate parabolic equationThe second chapter studies the geometric properties of a Riemannian manifold.

本文分两部分，第一部分是对如下形式的拟线性退化抛物方程Cauchy问题讨论了解的存在唯一性；第二部分是讨论了黎曼流形中的一些几何问题，主要是将欧氏空间平行射线的概念推广到一般黎曼流形，并研究其所具有的性质。

Firstly, the expressions of free vibration of moderately thick plates in polar coordinates are derived and the general solutions are obtained by the means of method of separation of variables.

首先，导出了用极坐标系描述的中厚板自由振动板的微分方程，用分离变量法求得其一般解。

According to the computational stability analysis conducted to the linear term time difference scheme in simple harmonic motion equation, one new semi-implicit integration scheme also is designed. By adopting a kind of revised time-explicitdifference scheme to these linear terms still included in spectral model governing equations, this defect of spectral model only partly used in semi-implicit integrating scheme, can be overcome to some degree.

以简谐振动方程中线性项时间差分格式对其计算稳定性影响为理论依据，本文设计了一种新谱模式半隐式时间积分方案，此方案通过对一般谱模式求解框架中那些隐含的线性项采用了一种显式修正的差分格式，可有效克服其国际谱模式半隐式时间求积方案实质上只是部分应用了半隐式差分格式的问题。

From proposing the problem to solving them, this thesis follows the researching method of from generality to specialty, also puts the mathematic knowledge of boundary value problem and the singular integral equation into the use of elastic mechanics and fracture mechanics, which shows the thought of combining the theory with the practical use. Throughout the thesis, the tendency that different branch of science is in fusion and penetration can also be found.

本文从提出问题到解决问题遵循由一般到特殊的研究方法，把边值问题和奇异积分方程等数学知识应用到断裂力学，弹性力学中，体现了理论联系实际及边缘学科间相互渗透的思想。

Numerical calculations were accomplished by the directly numerical method of the singular integral equations and a large amount of statistical results were obtained. So the issue of influence was systematically solved.

最后利用奇异积分方程的数值解法进行了数值计算，得到了大量的数值结果，从而系统地解决了一般倾斜裂纹对界面的影响分析。

Secondly, for a more general matrix equation in composition, we obtain another equivalent condition for the solvability of this equation and give an equivalent characterization to the solution set of the equation.

第二， 对于一般情况下的型矩阵方程，本文给出其可解的另一个等价条件，同时对其解集作了一个等价性描述。

The problem of the Hawking evaporation of Dirac particles in general spherically symmetric and charged evaporating black hole background is thus solved.

本文对一般球对称带电蒸发黑洞中Dirac粒子的Hawking辐射进行研究。利用零标架和旋系数方法，讨论了该时空背景下Dirac方程的退耦与分离变量。

This thesis first proposes the idea of EM in view of the drawbacks existing in traditional modeling methods. The main approaches and the general procedure of EM are described and the recent work of GP is surveyed using a taxonomy. Secondly, in terms of model types, the EM problem of complex functions, the EM problem of system of ordinary differential equations and the EM problem of higher-order ordinary differential equations are studied in detail. Finally, some advantages and disadvantages of the EM method are summarized at the end of this thesis.

本文首先针对传统建模方法的不足，提出了演化建模的思想，阐述了演化建模采用的主要方法和一般步骤，并分类概括了遗传程序设计目前的研究内容；然后，按照所建模型的类型不同，分三章详细研究了复杂函数的演化建模问题、常微分方程组的演化建模问题以及高阶常微分方程的演化建模问题；最后，本文对演化建模的主要特点和目前存在的主要问题作了概括和总结。

Present fluidized bed designs do not consider the effect of biofilm, but the fluidization of bioparticles is different to that of smooth carriers, thus terminal free-fall velocity u in Richardson-Zaki equation and drag coefficient C should be modified.

目前流化床设计一般没有考虑生物膜的影响，但生物颗粒的流化行为有别於光滑载体，因此需要对曳力系数C和膨胀特性方程中的u进行必要的修正。

However, as the name（read－only memory）implies, CD disks cannot be written onorchanged in any way.

然而，正如其名字所指出的那样，CD盘不能写，也不能用任何方式改变其内容。

Galvanizes steel pallet is mainly export which suits standard packing of European Union, the North America. galvanizes steel pallet is suitable to heavy rack. Pallet surface can design plate type, corrugated and the gap form, satisfies the different requirements.

镀锌钢托盘多用于出口，替代木托盘，免薰蒸，符合欧盟、北美各国对出口货物包装材料的法令要求；喷涂钢托盘适用于重载上货架之用，托盘表面根据需要制作成平板状、波纹状及间隔形式，满足不同的使用要求。