查询词典 locally convex space

In anti-fuzzy number space, the conjugate mapping of convex fuzzy mapping is concerned, and convexities of conjugate set and conjugate mapping of convex fuzzy mapping are proved.

在研究模糊向量空间、模糊凸集和模糊凸映射的基础上，我们研究了模糊规划的Lagrange对偶和凸模糊规划的KKT条件，并将有关结果应用到模糊线性规划和模糊二次规划的研究中。

In the last section ,according to the basis theory of rough set ,we propose the definition of an approximation space which is basing on the convex cone that contain the origin ,and define the upper and the lower approximation of convex cone ,then discuss some operation properties.

文章的最后是基于粗糙集的基本理论，提出了可利用含原点的凸锥构造一个近似空间，定义了此空间的上、下近似，总结了一些运算性质。

It is proved that strictly efficient point set of the objective space is connected when objective function is cone convex－like,and that if objective function is cone convex set－valued mapping,then strictly efficient solution set is also connected.

证明了当目标函数为锥类凸的集值映射时，其目标空间里的严有效点集是连通的；若目标函数为锥凸的集值映射时，其严有效解集也是连通的。

In virtue of this,some properties of convex polyhedroid are studied and the definite values and extreme values of convex polygon in Euclidean plane are extended to the case in n-dimensional space.

提出n维欧氏空间中广义重心坐标的概念，建立了广义重心坐标下两点间的距离公式，并利用于研究凸多胞形的若干性质，将欧氏平面上凸多边形的一些定值与极值性质推广到n维空间。

Different from the former study,the value region of projective operator in the neural network which they study was a general closed convex subset of n demensional Euclidean space and it wasn't a compact convex set in general,that is,the value region of projective operator was probably unbounded.

与以前研究投影算子的值域一般是n维欧氏空间中的紧凸子集不同，而是n维欧氏空间中未必有界的闭凸子集，同时目标函数也是一般的连续可微函数，未必为凸函数。

Different from the former study, the value region of projective operator in the neural network which they study was a general dosed convex subset of n demensional Euclidean space and it wasn＇ t a compact convex set in general, that is, the value region of projective operator was probably unbounded.

与以前研究投影算子的值域一般是n维欧氏空间中的紧凸子集不同，而是n维欧氏空间中未必有界的闭凸子集，同时目标函数也是一般的连续可微函数，未必为凸函数。

Xu and Noor had proved the theorem on convergence of three-step iterations for asymptotically nonexpansive mapping on nonempty closed, bounded, and convex subset of uniformly convex Banach space.

王娴 ，何震Xu和Norr已经证明了建立在一致凸Banach空间的一个非空有界闭凸子集上的渐进非扩张映射的三步迭代的收敛定理问题。

Based on the flaw of the probability reliability model in the case of small amount of information,non-probability and mixed probability/non-probability reliability models are presented. When the uncertainty of the basic random variable is described by convex, analytical and numerical methods are constructed to calculate the convex of response variable. The infinite norm index, which is the minimal infinite norm distance from original coordinate point to the surface of the limit state in the standard interval space, is presented to measure the safety of the structure.

针对概率可靠性模型在小子样信息下的缺陷，建立了非概率可靠性模型及概率—非概率混合可靠性模型；给出了用集合来描述变量不确定性时，极限状态变量变化集合的解析解和数值迭代解法；提出了物理概念明确且十分易于工程应用的度量结构、机构安全程度的无穷范数指标，它是标准区间空间中坐标原点到极限状态表面的最小无穷范数距离。

In the product space of unanimity convex Hilbert, we obtained the theory of existence and uniqueness of best approximation element on weakly closed t convex set .

讨论了凸集及凸包的形态学运算的几个几何特性，并使某些文献中的几个错误结论得到修正和完善。

Its applications are so broad that these theories and applications are in their rapid developing stages. Undoubtedly, more and more new and exciting results will be found in the near future. In this paper, the KKM principle and its variation are studied in the G -convex spaces and the product space of the G -convex spaces.

由于其广泛的应用前景，这些理论和应用的研究正处于迅速发展阶段，毫无疑问，越来越多的令人兴奋的新结果在以后将被发现。

Summary In copyright infringement cases,if the alleged infringer uses or even plagiarizes the copyrighted works or parts thereof,which causes no substantially adverse effect on the normal exploitation of the work,nor does it inflict any substantial damages to the right owner,the de minis doctrine should be applied to exempt the liabilities of the defendant and seek the balance of interests between the right owner and the general public embodied by the copyright law.

在侵犯著作权案件中，如果被控侵权行为人虽未经著作权人的同意，使用甚至抄袭了受著作权保护的作品或作品的片段，但若情节轻微，未对该作品的正常使用产生任何实质不利的影响，亦未对权利人的权利造成实质性的损害，则应适用&不计琐细原则&，免除行为人的责任，以寻求在权利人利益与著作权法所体现的社会公共利益之间的平衡。

This new product will become our best seller.

这个新产品会成为我们最畅销的产品。