必要条件

In this paper, the method, which is based on the theory of envelope and continuous map, is investigated.

文中用此方法分析了一些曲线的重要几何性质，即曲线段上含有尖点、重结点和拐点以及不含这些点的用控制顶点相对位置表示的充分必要条件。

I think that the necessary of contraposition is: 1, the equality of line; 2, indivisibility of integer.

然而对于我，小说对位法的必要条件是：1、个'线'的平等；2、整体的不可分割。

We get a sufficient and necessary condition of controllability about a sequence set which is an ideal.

得到了一个序列集合是一个理想的条件下可控的充分必要条件。

Leading resistant factor into the necessary condition can also enlarge the quadratic convergence region near optimal solution so that it is very efficient to use the known flash calculations at one condition to iteratively compute another optimal solution at other conditions where pressure, temperature and mole fractions of components are close to known ones respectively.

在极值必要条件式中引入阻尼因子能扩大真解附近的平方收敛域，尤其在利用已知条件下的汽液平衡结果作初值直接用极值条件方程迭代计算压力、温度和组成变化不严重的相邻点的汽液平衡极值解方面效果十分显著，适合于加快组分模型的计算速度。

Then we use Lebesguge s dominated convergence theorem to obtain some sufficient conditions for (2) and study the existence of a bounded positive solution.

接着，利用Lebesgue单调收敛定理给出了方程(2)振动的若干充分必要条件并且研究了正有界解的存在性。

For solving problem (1), this dissertation first presents a sufficient and necessary condition by dealing with inequalities using projection operator in convex analysis, and then proposes a kind of new neural network model based on the constraint domain:〓(2) Where P is a projection operator on Q.

本文利用凸分析中的投影算子处理不等式约束，首先给出二次规划问题(1)解存在的充分和必要条件，据于此提出一种新的基于约束区域神经网络模型〓(2)来进行求解，其中P为Q上的投影算子。

Chapter 5 is devoted the study of fuzzy optimization in fuzzy convex analysis structure given in chapter 4. We consider the problems of minimizing and maximizing a convex fuzzy mapping over a convex set and develop necessary and/or sufficient optimality conditions.

在第5章中，首先，在第4章所建立模糊凸分析的结构基础上，考虑了凸模糊映射的极值问题，得到了凸模糊映射取得极值的充分/必要条件。

Necessary and sufficient conditions of the robust positively invariant sets are established for the linear discrete-time system family specified by matrix convex polyhedron and additive interval disturbances.

对由矩阵凸多面体和加性区间扰动描述的线性时变离散系统族，得到了鲁棒正不变集的充分必要条件；对非线性系统族则得到有关充分条件。

Robust stability criteria, the design methods of robust stabilizing controller and guaranteeing certain robust performance controller for linear time-delay system with norm-bounded uncertainties or convex polyhedron uncertainties are studied in this paper by delay independent method and delay dependent method.

针对具有范数有界不确定参数和凸多面体不确定参数的线性不确定时滞系统，分别给出了它们时滞无关指定鲁棒H~∞性能约束可镇定的充分必要条件以及相应的控制器设计方法，结果以线性矩阵不等式的n浙江大学博士学位论文形式给出。

Tan and Xu [1] had proved the theorem on convergence of Ishikawa iteration processes of asymptotically nonexpansive mapping on a compact convex subset of a uniform convex Banach space , Then Liu Qihou [3] presents the necessary and sufficient conditions for the Ishikawa iteration of asymptotically quasi-nonexpansive mapping with an error member on a Banach space convergent to a fixed point . Xu and Noor [5] had proved the theorem on convergence of three-step iterations of asymptotically nonexpansive mapping on nonempty closed, bounded and convex subset of uniformly convex Banach space.

Tan和Xu已经证明了建立在一致凸Banach空间紧凸子集上的渐进非扩张映射的Ishikawa迭代序列的收敛原理，随之，刘齐侯又阐述了Banach空间上渐进准非扩张映射T的具误差的Ishikawa迭代序列收敛于T的不动点的充分必要条件；之后，Xu和Noor也证明了定义在一致凸Banach空间某非空有界闭凸子集上的渐进非扩张映射的三步迭代序列的收敛原理。

Recall that, in the Kolmogorov axiomatization, measurable sets are the sets which have a probability or, in other words, the sets corresponding to yes/no questions that have a probabilistic answer.

延期开工的Kolmogorov宣布要衡量所有套职能有限许多坐标限制在于衡量子寅。换句话说，如果是/否的问题回答f可看的价值观念在许多最有限坐标，然后它有一个概率的答案。

The experimental results showed that the algorithm can filter singular points and remain fixity of the target edge.

实验表明：基于模糊理论的图像智能滤波方法比常规图像滤波方法运算量小，它既能去除奇异点，又能保持图像中目标的边缘不变性，具有很好的滤波效果。