查询词典 necessary and sufficient conditions

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。

Meantime, the Namioka-Bauer's and Wong's positive extension theorem are generalized to ordered locally convex spaces (see Theorem 5.1) and hence some new necessary and sufficient conditions of positive extension in ordered locally convex spaces are obtained

同时Namioka-Bauer 定理和 Wong定理也被推广到半序局部凸空间中(定理5.1)，从而得到了一些新的关于半序局部凸空间中正延拓的充分必要条件

Both the infimum Vm of the Volume Vof M and the necessary and sufficient conditions of "V=Vm" are obtained under 2 cases of minimal M and pseudoumbilical M.

研究了复射影空间CP4中共形平坦的正曲率全实子流形M，分别在M极小与M 伪脐2种情况下，得到M的体积V的下确界Vm和达到下确界的充要条件。

With the matrix direct product and straightening operator, the necessary and sufficient conditions of the linear matrix equations have solutions and have unique one solution are given.

本文介绍了矩阵直积的有关概念和性质，利用矩阵直积和拉直算子给出了线性矩阵方程有解的充分必要条件以及有惟1解的充分必要条件。

Necessary and sufficient conditions for the existence and the expressions of selfconjugate solution, perselfconjugate solution, centrosymmetric solution, bisymmetric solution, skewselfconjugate solution, skewperselfconjugate solution, skewcentrosymmetric solution, and skewbisymmetric solution to 4 kinds of systems of linear matrix equations over a regular ring with an involutorial antiautomorphism are given.

利用矩阵技巧和所建立的矩阵理论，给出了正则环上五类矩阵方程组有解的若干充要条件和一般解的表达公式。这些矩阵方程组除了它们在理论上有重要的意义外，还有重要的应用价值。在具有对合反自同构的正则环上，给出了四类矩阵方程组有双对称解，中心对称解，斜中心对称解，广自共轭解，斜广自共轭解，自共轭解以及斜自共轭解的充要条件及其这些解的具体表达式。

And the sufficient and necessary conditions of the monotone set function which is continuous of the empty set and the full set are given.

李军[6]引入了强序连续性概念，证明了单调测度空间上实值函数的Lebesgue定理成立的充要条件是单调集函数具有强序连续性。

The first section studies general inverse of morphism with generalfactorization, and gives some necessary and sufficient conditions for their existence and expression.

第一部分我们研究了具有广义分解的态射的广义逆，得到了他们存在的充分和必要条件以及他们的表达式。

The fourth section studies general inverse of morphism sum. and obtains some necessary and sufficient conditions for their existence and expression.

第四部分我们研究了态射和的广义逆，得到了他们存在的充分和必要条件以及他们的表达式。

The second section studies general Moore-Penrose inverse of morphism with general factorization, and gives some necessary and sufficient conditions for their existence and expression.

第二部分我们研究了具有广义分解的态射的广义Moore-Penrose逆，得到了他们存在的充分和必要条件以及他们的表达式。

The sufficient and necessary conditions of the nondegeneracy and struc- tural asymptotical stability for complex systems (parallel systems, series sys- tems and closed systems) are proved.

在这基础上，给出了系统在串联、并联及反馈时构成的复杂系统的非变阶条件和结构渐近稳定的充分必要条件。

Objective:To explore the feasibility of laparoscopy in diagnosing and treating of abdominal diseases.

目的：探讨腹腔镜用以诊断腹部外科疾病及选择治疗方案的可行性。

The lifetime of nylon 1010 and nylon 1010/POSS composites decreased with increasing temperature.

热重-红外联用分析表明尼龙1010在氮气气氛下的降解产物主要为小分子的低聚物，POSS并不改变尼龙1010降解产物的组成。