条件方程

According to the plane cross section assumption, configuration of a rod is expressed as a history of the cross section with arc coordinate. A special solution which stands for equilibrium in straight line state is obtained from differential equilibrium equation. Linear perturbation equation is derived and its general solution is obtained in which the integral constants are determined by constrained conditions at two ends of the rod. The condition of existence of non zero solution of the integral constants gives to the Greenhill formula of exact elastic rod model, which shows that the boundary of stable area is a closed curve and of symmetry, and inference of shearable and extensible to stability of the rod is depend on three factors: difference between flexibility of shear and extension of a section of the rod, bending stiffness and the length of the rod.

基于平面截面假定，弹性杆的位形表达为截面的弧坐标历程，根据平衡微分方程得到了两端受力螺旋作用时的直线平衡特解，导出了线性化扰动方程及其通解，积分常数根据两端铰支时的边界条件确定，并根据其存在非零解的条件得到弹性直杆精确模型的Greenhill公式，表明稳定域为一对称的封闭区域，拉/压和剪切对稳定性的影响取决于：拉/压柔度与剪切柔度之差，抗弯刚度和杆长这三个因素

According to the model's actual background,discussing the random variable coefficient equation and using direct method,we obtain sufficient condition for the uniform stability and the globally asymptotic stability of difference equation,and also give examples to show they can not substitute each other.

本文根据种群模型的实际背景，讨论了任意变系数方程利用直接方法获得了所讨论方程的零解的一致稳定和全局渐近稳定的充分条件，并举例说明了这两个充分条件不能相互代替。

Then the weak formulation of the control equations considering the contact constraint conditions has been developed. Combined the Lagrange multiplier and penalty function methods, the augmented Lagrangian method is used to treat the contact constraint and solved the non-linear and non-smooth problems of the mechanical response perfectly. A finite element model has been applied for the test project of the reinforced slope and to study the mechanism of the interaction of the soil and reinforced material.

本文在Lagrangian网格的控制方程中引入接触界面条件，并采用了经典的Coulomb摩擦模型作为界面切向面力的本构模型，继而发展了考虑接触约束条件的控制方程的弱形式；在求解方法上，综合了Lagrange乘子法与罚方法的优点，采用增广的Lagrangian方法处理接触界面约束，很好地解决了接触问题中的高度非线性和响应不平滑性。

The one-dimension Terzaghi consolidation differential equation with boundary conditions,in which the top is drainable and the bottom is undrainable was solved,and the solutions obtained from several different references were analyzed.

解答了顶面不排水、底面排水边界条件下的太沙基一维固结微分方程，并比较分析了不同坐标系统下、不同边界条件下的单面排水太沙基一维固结微分方程的解答。

The force equilibrious equation and the approximate plastic conditions are set up,solved using the boundary condition and the strenth static coefficient σ/σs of fixed cycles short core when the tube is drawn so calculating the drawing force at every pass.

建立近似的力平衡方程，近似的塑性条件。应用边界条件联解上述方程，求出固定圆柱形短芯头拔管时的应力状态系数σ_拉/σ_S，以计算各道次的拔制力。

To investigate the characteristics of thermo-hydrodynamic lubrication with micropolar fluids, the energy equation for micropolar fluids is derived, based on the theory of micropolar fluids and the laws of conservation and conversion of energy.

为考察微极流体的热流体动力润滑特性，根据微极流体的基本理论和能量守恒与转换定律，推导了微极流体的能量方程；依据其润滑条件假设，得出了润滑条件下微极流体的能量方程的简化形式。

Seventhly, we sets up the reaction-diffusion equations about population-resource relationships; Further more, we analyzes these typical conceptual models making use of differential equation theory. The conclusion shows that human with natural environment co-exist conditions when human-environment is conflicting, mutual, predacious, harmonious. The relation both human and environment has to harmonious each other for the population-resource benefit maximum.

在连续时间条件的假设下给出了关于人口与农业生态资源的具有代表性的几种反应扩散方程形式；根据微分方程定性理论，对所建立的几种模型进行分析研究，得出当人类与生态环境处于冲突、互助、掠夺与和谐状态时，双方能长久共存的稳定条件，并得出只有在人口与资源和谐共处的情况下，才能使环境承载力及人类总数达到最大化的结论。

Based on the upper and lower solutions method,under suitable conditions,existence of solution of a three-point boundary value problem forthird-order ordinary differential equation with nonlinear mixed boundary conditions is obtained.

基于上下解方法，在一定条件下，得到了一类带有非线性混合边界条件的三阶常微分方程的非线性三点边值问题解的存在性，作为上述存在性结果的应用，在推论中给出了一类三阶非线性微分方程三点边值问题解的存在性。

Then the relationship between the vibration frequency of the plate in water and that in vacuo and the effect of nondimensionalized added virtual mass incremental are obtained by utilizing Rayleigh method.

引 言机械结构在水中振动要涉及到具有挑战性的流-固耦合问题[1，2 ] ，通常求解的方法是对结构用有限元方法写出振动方程，对流体用边界元方法写出控制方程，再利用边界条件及辐射条件将两者联系起来求解。

The basic thoughts of applying genetic algorithms in pipe network design is: concerning the objectives of pipe diameter, defining the costs of pipe network as objective function, and considering hydraulic situation(continuous equation and cycle equation of the crossover of pipe network), velocity of flow of pipes as restraining elements, this thesis carries out the optimal calculation on the design of pipe network.

运用遗传算法进行管网优化设计的基本思路是：将管网管径作为求解对象，以管网造价为目标函数，以水力条件（管网节点连续方程和环方程）、管段流速作为约束条件进行优化计算。

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。