条件方程

In chapter 4, in the frame of partially ordered F-type topological space, we research the existence of the solution of a nonlinear operator equation Lx = Nx, and the convergence of the iterative sequence {u_n} which satisfies Lu_(n+1)= Nu_n for a solution of the equation. Then, we give the conditions for multiplicity of the solutions of this operator equation.

第四章，在半序F-型拓扑空间框架下研究一类非线性算子方程Lx=Nx解的存在性，以及满足Lu_(n+1)=Nu_n的迭代序列{u_n}对于方程解的收敛性，并给出这类算子方程具有多解性的条件。

Since the governing equations for atmosphere movement can be reduced to a convective equation, so, to verify the validity of SFEBS, the propagation of one dimensional wave packet and shock governed by convective equation are simulated and compared with the boundary scheme that is based on the idea of Taylor series expansion.

因为大气运动的控制方程简化后可以归结为一个对流方程，所以作为边界格式之间的比较和检验，在一维情况下用对流方程和数值模拟中具有代表性的波包和激波作为算例，将其与传统的基于Taylor展开思想构造的边界条件进行了比较。

Thirdly,we study certain Riemann boundary value problems and Singularintegral equations with values in a universal Clifford algebra 〓,by com-bining the classical methods of solving Riemann boundary value problems andsingular integral equations with the Taylor's expansion of regular function in Clif-ford analysis,proving a lemma which is similar to the Painleve theorem in theclassical complex analysis,and the Plemelj formula in Clifford analysis,we obtainthe better results under weaker condition than before.

第三，本文第一次借助于用来解决经典的Riemann边值问题与奇异积分方程的方法来研究Clifford分析中的某些Riemann边值问题与奇异积分方程，获得了在比以前文献中条件更弱的情况下，结论更广的结果，并且，它为更进一步地解决在Clifford分析中一般的Riemann边值问题与奇异积分方程提供了基本的解决思想，为这一新的研究领域奠定了基础。

In this thesis,we mainly study the following three type of equations under certain non-Lipschitz conditions: stochastic Volterra type integral equation,backward stochastic Volterra type integral equation(including two cases:with jump and in infinite dimensional space),multivalued stochastic evolution equation.

本文将在某些给定的非Lipschitz条件下，依次讨论随机Volterra型积分方程，倒向随机Volterra型积分方程(包括带跳情况和无穷维情况)，多值随机发展方程。

The problem has been studied from two sides, firstly, from the viewpoint of applicability, based on the development strategic objectives of the oil company, with the aim to unify the exploration and extraction decisions of the resources in an integrated framework, and integrate the macro economic and technical objectives with micro economic and technical models of an oil well, an integrated non-linear dynamic optimal control model has been constructed, the objective is the benefit maximum of the exploration and extraction of the resources, and the optimalstrategies are obtained by changing the problem into a non-linear mathematical programming problem, on the other hand, from the more macro level, based on the analysis of the characteristics of the exploration and extraction activities of oil and gas resources, a conclusion is easily deduced that the procedure is full of randomicity, then discovering procedure of oil deposit is proved to be a Poisson process, and the reserves process is a supermartingale process, so the model of exploration discovery rate and the reserves model could be constructed.

其次从相对更宏观的层次上，通过对油气资源勘探与开发的特点分析，认为具有很强的随机性，证明了勘探活动发现油气藏的过程为一泊松过程，所发现的油气藏储量为一上鞅过程，在此基础上，建立了油气藏勘探发现率模型及储量模型，在油气价格服从几何布朗运动条件下，以油气开采收益最大化为目标，建立了一个油气资源勘探与开发的随机最优控制模型，采用动态规划方法得到了值函数的HJB方程，并针对方程的特点，以及方程及其变量所对应的经济学意义，对最优策略的求解进行了一些讨论。

According to the neural cable model, this dissertation deduced a stable solution. Based on the lead model, the vibratory equation of electriferous lead in a static magnetic field is set up under the condition of coupling magneto-acoustic field. It is verified that the vibration in bio-tissue is proportional to with the product of the magnitude of the magnetic field, the current amplitude and the sinusoid of angle between them.

根据神经的电缆模型，论文导出直流稳态解；基于导线模型，根据洛仑兹方程和细弦上的波动方程，论文建立了磁声耦合条件下带电导线在磁场中的振动方程，导出生物组织中的振动与磁场的大小、电流的大小和磁场与电流角度的正弦值乘积成正比。

Specially,at lower power density of laser,quasi static model is used to simulate the radial heat dissipation from irradiated region to nonirradiated regions.

在数值计算中，应用部分线性法处理非线性非齐次热传导方程，得到相应的隐格式差分方程，再用追赶法求解隐格式差分方程，得出绝热边界条件下的温度的时间和空间分布，从而得出激光退火的再结晶厚度。

Second, based on the spherical vector wave function in uniaxial anisotropic medium, and the first, second, third and fourth spherical Bessel functions satisfy the same differential equation and recursive formula. The scattering fields in terms of spherical vector wave function from a uniaxial anisotropic spherical shell and an anisotropic uniaxial-coated conducting sphere by a plane wave are derived. The electromagnetic fields in uniaxial anisotropic medium and free space can be expressed in terms of spherical vector wave functions in uniaxial anisotropic media and isotropic medium.

二、在建立均匀各向异性单轴介质球矢量波函数理论的基础上，利用二阶线性偏微分方程的性质和第一、第二、第三和第四类球Bessel函数满足相同的微分方程和递推关系，我们分别研究了单轴介质球壳和单轴介质涂覆导体球对平面波的电磁散射特性，首先给出了各个区域的电磁场用球矢量波函数来表示的解析表达式，进而利用电磁场在边界上满足电磁场切向连续的边界条件和球谐函数的正交性，得出了各向异性单轴介质球结构中电磁场用球矢量波函数表示的系数所满足的矩阵方程。

Firstly several vehicle dynamics models and tire models are analysed. Combining with the present condition and studying require, 3 dynamic differential functions about bodyworks velocity, roll and vertical displacement are gained. Furthermore based on the following rear wheel rev function and front-and-rear wheels vertical moving function, a 6-DOF, two wheels, lognitudinal dynamics model of the bus is set up.

本文首先对几种车辆动力学模型和轮胎模型进行了分析，结合现有条件和研究需要，得到关于汽车车身的速度、俯仰角和垂向位移的3个动力学微分方程，结合利用Simulink得到的前后轮垂向运动方程和将在后续研究中给出的后轮转速方程，建立了客车两轮6自由度纵向动力学模型。

A high-speed camera is used to visualize the flow structures,and Laser Doppler Velocity is employed for velocity measurement.The osculations are conducted on the two-dimensional hydrofoil section,based on a single-fluid model of the cavitation:the liquid/vapor mixture is considered as a homogeneous fluid whose eompsition is regulated by mass tranfer equation.The RNG k-ε turbulence model with modified eddy viscosity coefficient is used for computing,and the coefficient is related to the vapor and liquid densities in cavitated regions for simulating the cavitating flow.

实验采用高速录像技术观察了云状空化随时间的结构变化，应用 LDV 测量了云状空化条件下翼型周围的速度分布；采用 N-S 方程和基于空泡动力学方程的空化模型计算了绕水翼云状空化流场，湍流模型采用了 RNG k-ε方程，为了改善空化流动的计算精度，引入了一种与空化区域水汽相密度相关的系数，对湍流涡黏性系数进行了修正。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。