等价方程

In Chapter 4, we introduce the definition of implicit complementarity problems and struct an equivalent projection differential equation system. And then we prove the equilibrium point of system is exact the solution of the implicit complementarity problem.

本文的第4章介绍了有关隐式互补问题的相关知识，并且利用投影算子建立了与之等价的微分方程系统，这个微分方程系统的平衡点就是隐互补问题的解。

This paper proposes an equivalent second order elastic wave equation to solve the problem of being unable to completely separate the coupled P and S wave by full elastic wave equation.

给出了一种等价的二阶弹性波动方程，以解决弹性波场中完全弹性波动方程不能完全分离耦合的纵、横波波场问题。

Due to equivalent transformation during the simplification procedure of equations, the solution set of equations can neither expand and nor contract, and also the transformed equations for four displacement functions are compact in the form and easy to find their solutions.

由于方程化简过程是等价变形，从而可以保证方程的解集既不会扩大也不会缩小，而位移势函数便给出了一维六方准晶中弹性解的一个通解公式。

In this paper, we construct the differential equation to solve the unconstrained optimization problem. Such methods solving the ill-conditioned problems are very effective. It indicates that the asymptotically stable region of explicit the Euler method to solve the differential equation equals to the descent region of the gradient method to solve the original unconstrained optimization problem.

我们发现，在用Euler方法求解二次优化问题的等价动力系统的方程时，由方法的步长确定的稳定区域对应于这些方法所得到的迭代公式的步长满足单调下降算法的条件确定的单调下降区域，因此我们可以利用这个性质构造解无约束优化问题的数值方法而不采用标准的常微分方程的数值求解公式。

Exterior problem ; boundary integral equations; equivalent boundary integral equations

外边值问题；边界积分方程；等价边界积分方程

Finite element discretization was carried out on the mathematical model to get a fully coupled finite element equation with the parameters of element nodal displacement and element nodal pore pressure as unknown variables. Finally, the transient nonlinear finite element equation in incremental form for reservoir fluid-solid coupling is obtained by means of time discretization in implicit difference scheme.

基于与微分方程等价的加权余量公式，在空间域采用有限元离散，对时间域进行隐式差分格式离散，导出了以单元节点位移和单元节点孔隙压力为未知量的储层流固耦合的非线性有限元增量方程。

Further more, the equivalent boundary integral expressions of the set of potential functions satisfying the inhomogeneous field equation are rigoro...

获得 Poisson问题的间接变量等价边界积分方程；通过一些例子，详细讨论了传统的外问题和边界积分方程的形式，表明它们不具有普遍适用性

Moreover we extend this method to the unbounded Stokes problem, the boundary of which is an open straight or an open arc segment.

另外，本文推导了开区域(特别是边界是直线段或开弧段情况下无限域)上的Stokes 方程的Dirichlet 外问题的边界积分表达式以及等价的变分方程。

The viscosity solutions for partial differential equations of parabolic type havethree different basic definitions.The three definitions are equivalent when the equa-tions are continuous.But for the discontinuous equations,the equivalence of themare still unknown.

因为抛物型方程粘性解有三种基本定义法，它们在方程为连续时相互等价，对于不连续情况，它们间关系尚不明确，因而在本章里，我们特别证明了其中二个定义：定义1，定义2之间的关系。

The result shows: at different temperatures the outcomings obtained in determining dissociation constants with such two theories can be seen effective, but the doubly reciprocal curves of quenching equation are not conformed to quenching curves based on dynamic and static quenching mechanism as those of fluorescence enhancement.

通过荧光和紫外方法研究盐酸左氧氟沙星、氟罗沙星、加替沙星和沃氟沙星四种喹诺酮类药物与人血清白蛋白的作用，在不同温度下对荧光加强和猝灭理论公式的等价性和精细差异进行了比较，结果表明：在不同温度下两种理论公式尽管在求取解离常数上所得结果都可视为有效，但猝灭方程的双倒数图反而不及荧光加强方程的双倒数图与体现动态、静态猝灭机理的猝灭曲线一致。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失