微分

In this paper, we give the method of solving the partial differential equations with the combine use of symbolic and numerical method, which is a new way of solving the extremely complicated partial differential equations.

本文作出了将符号计算方法和数值计算方法结合起来求解偏微分方程的研究工作，这是求解比较复杂的偏微分方程的新途径。

The finite difference method is applied to reduce the system of partial differential equations to ordinary differential equations.

采用有限差分方法，将由偏微分方程组描述的空间连续系统约化为由常微分方程组描述的空间离散高维动力系统。

It is proved that equilibrium solutions of this differential system are solutions to the complementarity problem and a numerical algorithm is given based on the numerical integration of the system of ordinary differential equations.

在一定条件下，证明了微分方程系统的平衡点是非线性互补问题的解并且基于一般微分方程系统的数值积分建立了一个数值算法。

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。

One combines the initial value computing method of system of ordinary differential equations (Runge-Kutta Method) with optimization method, another co...

1是将常微分方程组初值的龙格-库塔法与最优化计算方法相结合；2是将常微分方程组边值差分解法与最优化计算方法及 3点插值法相结合。

To overcome the difficulties and drawbacks in modeling the dynamic systems by using traditional methods, a hybrid evolutionary modeling algorithm is proposed to model the dynamic system with a system of ordinary differential equations whose main idea is to embed genetic algorithm in genetic programming where GP is employed to optimize the structure of a model, and GA is employed to optimize the parameters of a model.

针对采用传统方法解决动态系统的微分方程建模问题所遇到的困难和存在的不足，文中设计了将遗传程序设计与遗传算法相嵌套的混合演化建模算法，以遗传程序设计优化模型结构，以遗传算法优化模型参数，成功地实现了动态系统的常微分方程组建模过程自动化。

To overcome the difficulties and the draw backs in modeling dynamic systems by traditional methods, a hybrid evolutionary modeling algorithm was proposed to model the Dynamic system with a system of ordinary differential equations whose main idea was to embed string coded idea and evolution algorithm optimize system.

针对传统方法解决动态系统微分方程建模问题所遇到的困难和存在的不足，设计将方程进行串结构编码并用进化方法进行演化建模的算法，以串形结构表示结构，用进化算法优化结构和参数，成功地实现了动态系统的常微分方程组建模过程的自动化。

The Fourier transfermation about the azimuthal angle and Hankeltransfermation about the radial dirction have been used to turn the basic dis-placement equatioons and constitutive equations under cylindrical coordinatesystem into a system of second order ordinary differential equations in thewavenumber domain,by use of the initial prarameter method to solve differ-ential equations.

利用关于方位角的Fourier变换及关于径向的Hankel变换，将柱坐标系下位移基本方程和本构方程转化为波数域内二阶常微分方程组，利用求解微分方程的初参数法，建立了介质层的传递矩阵，导出了层状弹性半空间在地表作用任意静荷载情形下的解析解。

Then, it studies the supply chain management system as a complex system to confirm the state existing during operating of the system. After that, it conducts a probability analysis on the state which the system located by applying supplement variable method, and establishes the model of distributed parameter system in a form of partial differential equations. Combining C0 ? semigroup theory in the functional analysis, it conducts a dynamic analysis on the established mathematical model. Using this method, it obtains the mathematical expression of the dynamic solution and the steady state solution, and proves the uniqueness, non-negativity and the asymptotic stability of the system solution. This dissertation applies the Matlab tool and uses two-step, three-step Simpson integral equation to imitate the condition of system solution. Then, it adds possible mode of failure and the optimization adjustment state to the system, based on which it has established the distributed parameter system model which is described by partial differential system of equations. Combining the functional analysis C0 ? semigroup theory, it studies the established mathematical model, and obtains the mathematical expression of the dynamic solution system and the steady state solution. It has proven the existing of uniqueness of the system solution, the asymptotic stability of system solution and the system solution. In addition, it has lying the theory rationale for further analysis and the research on the optimization of system.

本文首先简要综述了供应链理论、可靠性研究、鲁棒性研究以及供应链鲁棒性研究的现状；然后，将供应链系统作为一个复杂系统来分析，确定了系统运行过程中所经历的状态，通过引入补充变量的方法，建立了用偏微分方程组描述的分布参数系统模型，用泛函分析中的C_0 -半群理论得到了系统动态解和稳态解的数学表达式，证明了系统解存在的唯一性、非负性和指数阶渐近稳定性；并借助Matlab工具，利用二阶、三阶辛普森积分方程模拟系统解的性态，并给出系统动态解的仿真图；本文又对上述系统增加了系统可能失效状态和优化调整状态，并在此基础上建立了用偏微分方程组描述的分布参数系统模型，同样用泛函分析中的C_0 -半群理论对所建立的数学模型进行了研究，得到系统动态解和稳态解的数学表达式，证明了系统动态解存在的唯一性、非负性及渐近稳定性，为进一步分析和研究供应链优化奠定了理论基础。

The discretisation of the velocity space in the kinetic theory of gases allowsus to replace an integro-partial-differential equation,the Boltzmann equation,by a system of hyperbolic semi-linear partial differential equations.

在气体运动论中将速度空间离散化处理，使得我们可以用一个双曲型的半线性偏微分方程组来取代Boltzmann方程这个积分微分方程。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。