极小条件

Recently, some characterizations of solutions of VVI and its weak sharp minima under strong monotonicity have been proved.

近年来，得到了广泛的研究，其解的性质得到了刻画，其解的弱尖极小已经在强单调条件下得到了证明。

A polynomial algorithm about minimal marking of structural live Petri nets was presented. In an empty marking net, it was verified that the reproducibility can be held under operations. These results can be used in process mining.

本文还利用结构理论解决了结构活网到活系统的极小标识求解算法，并对Petri网的一类特殊性质：空标识可再生性进行了求证，解决了空标识可再生网在运算中的保持条件。

In practical engineering, it is difficult to find out the minimal surface meeting the architecture demands and the boundary restrictions, hence, the difference in the stress distribution should be controlled in a special range.

在实际工程中，由于膜结构建筑要求和边界条件的限制，找到具有极小曲面性质的初始平衡形状较难。因此，一般把应力的差值控制在一定的范围内。

A complete novel assumption is presented. Then, we prove the existence of two nontrivial solutions for a class of second order superlinear difference systems with the help of Minimax principle and Linking theorem in critical point theory,.6. Two applications in physics are given. Firstly, a coupled differential system coming from second harmonic waves is discussed.

利用Ricceri建立的三临界点定理，证明了一类含参数二阶差分方程在某些新的条件下至少存在三个解；随后，利用临界点理论中的极小极大原理和环绕定理，讨论了一类二阶超线性差分方程组多重解的存在性。

A minimax theorem generally involves three assumption conditions: space structures on sets X and Y, the continuity of the functions and the concavity and convexity of functions.

一个极大极小定理一般涉及三个假设条件：集合X和Y的空间结构，函数的连续性和函数的凹凸性。

The method is based on the first-order optimalitycinditions for a local minimizer of the augmented Lagrangian,with different form,being transformed into another nonliner system.

该方法是以增广Lagrangian函数局部极小点的一阶最优性条件为基础，通过不同的形式，将其转化为另外一个非线性系统。

The problem control points of free-form surface are modified automatically can be reduced to the solution of energy functionals minimum under the condition of constraint.

将自由形状曲面的控制点自动修改问题归结为一个在约束条件下求解能量函数的极小值问题。

Under some conditions we obtain the existence of nontrivial solution by analyzing the best Sobolev embedding constant and by use of the minimax theorems without conditions.

通过使用没有条件的极小极大定理，以及对最佳Sobolev嵌入常数的详细分析，得到了一些具临界Sobolev指数的半线性椭圆系统的真正非平凡解的存在性，并讨论了解的一些性质。

And the expression of its subdifferential is developed in the case that the effective domain of the optimal value function is a non-empty convex set.

最后利用方向导数和次微分导出了广义半无限极大极小规划的一个一阶最优性条件及其等价形式。

And the absolute localization length reaches a minimum under the resonance Mie-scattering condition.

在共振米散射条件下，绝对局域化长度取极小值。

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