等价函数

In the implementation, each complementary condition is reduced to an equation by means of so-called NCP function to solve, the discrete structural optimization problems with standard optimization software.

离散优化到基于NCP函数的连续优化变换在理论上是等价的，可以利用普通的数学规划方法实施求解。

To realize reduced equivalent representation for functional dependency set, sameroot row, same-class row and same-class row family are presented, merging rules of same-root row in a schema matrix are defined, merging algorithm of same-root row and solving algorithm of same-class row family in a schema matrix are discussed.

为了实现函数依赖集的最简等价表示，提出了同根行、同类行、同类行族的概念，定义了模式矩阵M中同根行的合并运算规则，讨论了模式矩阵M中同根行合并算法，同类行族求解算法。

This article investigates the two-point boundary value problem to a coupled system of nonlinear fractional differential equations. By applying growth conditions on the nonlinear terms, we obtain an existence result of solutions. Our analysis relies on the Schauder fixed-point theorem and the reduction of the considered problem to the equivalent coupled system of integral equations.

本文讨论非线性分数阶微分方程耦合系统的两点边值问题，应用Green函数，将其转化为等价的积分方程耦合系统，并设非线性项在无穷远处有增长条件，应用Schauder不动点定理证明解而非限于正解的存在性。

In some literatures, another equivalence between the WKB method and the path integral approach has been discussed, a set of rules of constructing semiclassical green functions with respect to the position and energy which is the fourier transformation of the semiclassical path integral propagator with respect to position and time was established.

一些文献讨论了WKB方法和路径积分方法的等价性，得到了求解作为坐标和时间域的传播子的傅立叶变换的坐标和能量空间的格林函数的一套规则。

Firstly, we give out a reduction way for quasilinear generalized system A〓=G , and the concept of the index κ geometrically nonsingularity, where A is singular and of smooth kernal space. By using the canonical projection mappings onto the space of ker A , a class singular pointimpasse point only owned by nonlinear generalized system is also studied and we also prove that the regular index κ quasilinear generaized system A〓=G defined on the region W is equivalent with an ODEs 〓 defined on a submanifold W〓 of the W, so we reduce the problem of quasilinear generalized system to the problem of an ODEs.

首先利用投影函数，给出了拟线性广义系统A〓=G的一种归约方法，提出了指数κ几何非奇异的概念，同时对广义系统特有的一类奇点-寂点进行了研究，证明了正则指数κ的拟线性问题A〓=G等价于在其定义域W中某一个子流形W〓上的正常微分方程〓，从而将拟线性广义系统的问题归结为常微分方程问题。

This paper has investigated the expression on rotational motion of earth's surface and Earth's deformation fields with complex vector surface spherical harmonic function, theoretical definition of the crust-fixed reference frames and the terrestrial reference system, and theoretical substantiating to the consistency between them.

徐州师范大学国土信息与测绘工程系，徐州 221116；2。中国科学院测量与地球物理研究所，武汉 430077摘要：本文研究了内核地球模型下的地球表面的旋转运动和地球形变场的复数矢量球函数表示，以及外壳固定参考架、地球参考系的理论定义和它们之间等价性的理论证明。

We prove the equivalence of coloured petri net and extented coloured petri net in teachability space.

针对有色Petri网在建模能力方面的限制进行若干扩展，提出了一种扩展有色Pertri网，增加了容量限制及阈值弧函数，这将丰富CPN模型的语义，增强CPN对系统的描述能力，有助于大型复杂系统的建模，在此基础上证明了ECPN与CPN从可达空间的角度来说两者之间的等价性。

By introducing a smooth merit function for linear inequalities system problem, the problem was equivalently reformulated as an unconstraint optimization problem.

通过引入线性不等式组问题的一类光滑价值函数，将其求解问题等价地转化为无约束优化问题的求解。

Thirdly, as a special case of Carleson type measure, logarithmic Carleson measures on the unit ball are discussed.

利用Bloch函数给出了有界和消没p对数s-Carleson测度（参数s∈（1，∞））的等价条件。

The problem of solving linear equations changed equivalently into the problem of searching the minimum of unconstrained optimizations of function by variation principle in the paper.

首先通过变分原理将求解线性方程组的问题转化为等价的求解无约束函数最优化问题的极小值。

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷