查询词典 spaces

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。

It is a main task of General Topology to compare different spaces.Mappings which connect different spaces are important tools to complete it.

一般拓扑学的一个主要任务是不同拓扑空间类的比较，映射直接建立了不同拓扑空间类的联系，是实现该任务的重要工具。

This theorem which is a constructive bridge between the deterministic and indeterministicphenomena shows that the periodic behavior of chaotic dynamical systems in probability spaces is the origin of their periodicityin Hausdorff metric spaces.

该定理成功地跨越了确定性现象和随机现象间的鸿沟，揭示了Hausdorff周期律和概率周期律间的依存关系，它表明混沌动力系统的Hausdorff周期律是其概率周期律的一种表象。

Chapter 2 converts the solutions of saddle point problems in Hilbert spaces intothe equilibrium points of some dynamic system by means of the projection method,and gives some conditions of global asymptotic stability by extending the LaSalleinvariance principle to Hilbert spaces.

第三章把约束鞍点问题转化为等价的无约束问题，然后利用投影法构造了一个神经网络模型进行求解，并利用第二章结论证明了在适当条件下，模型大范围收敛于问题的精确解。

Generalized Morrey spaces;Maximal operator;Homogeneous spaces

广义Morrey空间；极大算子；齐型空间

Functional Analysis is primarily concerned with the structure of infinite dimensional vector spaces and the transformations, which are frequently called operators, between such spaces.

功能分析主要关注的是无穷维向量空间的转换，它们通常被称为运营商之间的空间结构。

For the analysis properties of infinite matrix,first,it establishes the automatic conti-nuity theorems on the sequence spaces with 0-GHP or WGHP,and the automaticboundedness theorem on the sequence spaces with 0-GHP.

在无穷矩阵的分析性质方面，建立了具有0-GHP或具有WGHP的矢值序列空间上无穷矩阵算子的自连续性定理，以及具有0-GHP矢值序列空间上无穷矩阵算子的自有界性定理。

The growth of functions in these spaces depends on a weighted function ρ. We investigate the relation between growth and boundary values of the functions, and prove that a function or its radial derivative is in one of the spaces if and only if the p'integral average of the difference of its boundary value function is integrable or bounded.

研究这些函数空间中函数的增长性与边界值的关系，得到了函数或其径向导数属于相应空间的充分必要条件是其边界值差分的p次积分平均应具备一定的可积性或有界性。

The main contents include: Some preliminary theory (introduction to Sobolev spaces and variational formulations for differential equations); finite element methods for one-dimensional elliptic problems; the construction methods for general finite elements; error estimates for interpolation operators and inverse inequalities for finite element spaces; a priori and a posteriori error estimates for the finite element method for high-dimensional elliptic problems; some typical spectral methods for partial differential equations; error analysis for the spectral approximation for some linear and nonlinear partial differential equations.

主要内容有：准备知识（Sobolev空间的基本概念和主要结果，微分方程的变分描述）；一维椭圆型方程有限元方法；一般有限元的构造；插值算子误差估计和逆不等式；高维椭圆型方程的先验、后验误差估计；求解偏微分方程的几类谱方法；线性与非线性问题谱逼近的误差分析等。

The main topics are: set theory foundation, Lebesgue measure and Lebesgue integral, basic theories on linear normed spaces and Hilbert spaces and introduction to linear bounded operators.

本课程基本内容包括集合论基础、Lebesgue测度与Lebesgue积分、线性赋范空间与Albert空间的基本理论和有界线性算子简介。

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。