条件方程

The formal solution of partial differential equations is given on characteristic line, the existence of the optimal control is proven by using Ekeland\'s variational principle, Gronwall Lemma and adjoint system, then the necessary condition of optimality is obtained by means of the conception of normal cone.

用特征线法表示出偏微分方程的形式解，利用Ekeland变分原理，Gronwall引理和共轭系统证明了最优控制的存在性，并借助于法锥概念得到了最优控制的必要性条件。

Some nonexistence results for p-degenerate sub-elliptic first order evolution inequalities associated with the generalized Baouendi-Grushin vector fields are given. The method is an improvement of the admissible function method in Euclidean space. The proof hardly depends on the properties of the generalized Baouendi-Grushin vector fields.

通过改进欧氏的容许函数法，应用广义Baouendi-Grushin向量场的一些性质，选取特殊的容许函数，利用Hlder不等式和Young不等式，证明了由广义Baouendi-Grushin向量场构成的p-退化次椭圆一阶发展不等方程，在适当条件下非平凡弱解的不存在性。

But in fact, the system of half-tracked air-cushion vehicle is over complicated. When the vehicle drives in an unknown soil, the parameters and structures of controlled member will change with load or disturbances. This system is nonlinear and time-variant, and it is very difficult to analyze its transfer function and state function quantitatively.

然而在实际工作中，由于本课题中的系统过于复杂，当行驶在未知土壤条件下时，被控对象往往随着载荷或干扰因素影响，其特性参数或结构发生改变，属于非线性和时变性的不确定系统，它的传递函数或状态方程难于用传统的定量分析方法加以实现。

With Airy stress function, a plane elasticity problem can be simplified to solve a biharmonic function equation.

通过引入Airy应力函数，平面问题可以归结为在给定的边界条件下求解一个双调和方程。

And the methods how to combine them with the discretized algebraic eigenvalue equation for generalized Rayleigh and Love waves are also given.

推导了这三种边界条件的公式，并且给出了它们进入离散化后的Rayleigh波与Love波的代数特征方程方法。

Based on a modified algebraic Riccati equation, this paper provides the conditions for the existence of the previous performance robust controllers.

基于一个修正的代数Riccati方程，给出了上述性能鲁棒控制器的存在条件及解析表达式，并举出相应的数值例子，以说明本文设计方法的简单性与直接性。

The relationship between stress and strain of concrete in prestressed concrete bridge s is written as algebraic form within load duration and the equilibrium equations of internal force and compatibility conditions are introduced.

首先将预应力混凝土桥梁中考虑收缩、徐变影响的任意时刻混凝土应力、应变关系在持荷时段内写成代数形式，引入内力平衡方程及变形协调条件后，提出了计入截面上钢筋位置、配筋率、预应力钢筋松弛、混凝土弹性模量随时间变化等影响的徐变效应分析的全量形式自动递进法，并建立了计算式，适用于任何形式的收缩、徐变特性表达式；基于建立的全量形式公式，可方便地求解任意时刻混凝土、钢筋的应力与应变和梁体竖向变形。

Furthermore,3-D FEM algorithm based on the division of tetrahedral grids is deduced by the equations of point electrical source field.

同时，从点电源场满足的方程出发，本文推导了三维复杂地形条件下有限元数值模拟算法，并编制了计算程序。

The alternating group iterative method for the dispersive equation with periodic boundary condition is presented.

给出了求解具有周期边界条件色散方程近似解的交替分组迭代法。

From energy balance equation, using micro-piece analytical method, heat balance equation for high power fast axial flow CO〓 laser tube is established with the boundary conditions of actual fast axial CO〓 laser, the analyzed solution of the temperature distribution in the laser tube is obtained.

并应用热传导的物理边界条件，求出了热能平衡方程的解析解，得到了实际器件放电管横截面内的气体温度分布公式及温度分布曲线，并求得了激光功率变化对热致负透镜焦距的影响关系式。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新