查询词典 weak approximation theorem

The use of the Chinese remainder theorem transforms the operation of producing the multiplicative inverses into two corresponding operations with shorter numbers and a faster combination step so that, compared with methods not using the Chinese remainder theorem, an acceleration by factor 4 can be achieved.

采用中国余数定理，形成将倍数逆数的运算转换为两个具有较短数字和一个较快结合的运算的步骤，使得相较于没有中国余数定理的方法可获得因子4的加速。

Recently , the classical Riesz representation theorem on Hilbert spaces has been generalized onto complete random inner product modules ,in this paper the classical Friedrichs theorem on Hilbert spaces is generalized onto complete random inner product modules.

最近，经典的Riesz 表示定理已经被推广到完备随机内积模上，在此基础上本文将Hilbert 空间上经典的Friedrichs 定理推广到完备随机内积模上。首先，证明完备随机内积模上任一正Her2 mite 型惟一地对应一个正自共轭算子。

Finally, it investigate QF-ring with right gpm-injective, and obtain the following theorem:Theorem The following statements are equivalent:(1) R is quasi-Frobeniusean ring:(2) R is right noetherian, left pm-injective ring, right pm-injective ring;(3) R is right noetherian, left pm-injective ring, right GP-injective ring;(4) R is right noetherian, left gpm-injective ring, right gpm-injective ring;(5) R is right noetherian, right gpm-injective ring and each right minimal ideal is right annihilator.

最后用右gpm-内射对QF环进行研究，得到了如下定理：定理下列条件等价：(1) R是quasi-Frobeniusean环；(2) R是右Noether，左pm-内射环，右pm-内射环：(3) R是右Noether，左pm-内射环，右GP-内射环；(4) R是右Noether，左gpm-内射环，右gpm-内射环；(5) R是右Noether，右gpm-内射环且每个极小右理想是右零化子。

By using cross-iteration technique and the Schauder fixed point theorem, the existence theorem of travelling wave solutions of this system is established.

针对反应项的不同单调性，引进交互迭代格式，利用Schauder不动点定理建立了行波解的存在性定理，并将所得结论应用到时滞竞争系统。

In chapter II,the preliminary knowledgefor accomplishing this research is presented,and the well-posed problem ofthe thin-plate flow of non-Newtonian viscous fluids is testified.By using themonotone operator theory and Schauder's fixed point theorem,the generalizedsolution's existence and uniqueness theorem for the thin-plate flow problem ofnon-Newtonian viscous fluids is obtained under reasonable conditions.

第二章给出了进行本项研究所需的一些预备知识，对非牛顿粘性流体薄板流问题广义解的适定性进行了研究，应用单调算子理论和不动点定理，在合理的条件下，证明了非牛顿粘性流体薄板流问题广义解的存在性，唯一性定理。

In Chapter 3 Firstly, the exponential stability in mean square and almost sure exponential stability for neutral stochstic neural networks with time-varying delay can be discussed by using the linear matrix inequality and the semimartingale convergence theorem; And our sufficient conditions are less conserative; Secondly, by utilizing the fixed point theorem, some sufficient and necessary conditions ensuring the asymp- totic stability in mean square for neutral stochastic neural networks with time-varying delays can be given.

第三章首先，利用线性矩阵不等式方法和半鞅收敛定理，考虑了一类具变时滞中立型随机神经网络的二阶矩指数稳定性和几乎必然指数稳定性，所得到的条件保守性要好；其次，采用不动点方法，给出了具变时滞中立型随机神经网络的二阶矩渐近稳定性的充要条件。

Then relative interior is introduced and an alternative theorem of generalized convex set-valued maps is established by using the separation theorem.

引进了相对内部，应用凸集分离定理建立了一个广义凸集值映射的择一性定理。

In chapter 1, similarity and perturbations of nest subalgebras of factor von Neumann algebras are studied. A similarity theorem is given (see Theorem 1. 2. 3), and it is shown that similar nests in a factor von Neumann algebra are close.

第一章研究因子von Neumann代数中套的相似性和套子代数的摄动，获到一个相似定理（定理1.2.3），其几何意义是：因子von Neumann代数中相似的套聚拢在一起并可向外扩展。

Using two new methods, this paper prores one pertubation theorem on the finite Hilbert space of 2×2 operator matrices, and gereralizes this theorem to the infinite Hilbert space of selfadjoint operators.

给出了有限维Hilbert空间中2×2算子矩阵的数值域扰动定理的两种证明方法，并且将该定理推广到无限维Hilbert空间上的自伴算子。

First, a switching function is designed to guarantee that the movement of the system is asymptotically stable in the switching manifold. And the equation of the switching surface is given based on pole assignment theorem; Then a discrete robust adaptive quasi-sliding-mode tracking controller is presented by constructing the two adaptive gains, and the globally asymptotically stability of the system is proved based on the Lyapunov-Razumikhin stability theorem.

首先，利用广义系统的概念给出了系数矩阵为能控标准型的滑模面方程，并利用极点配置定理给出了能使系统稳定的滑模面；其次，构造了含有自适应律的离散趋近律，设计了能够使系统达到同步的变结构控制器，并利用Lyapunov稳定性定理，证明了系统的趋近运动的稳定性。

Bob Eckert has been chairman and chief executive of Mattel for eight years.

美泰董事长兼首席执行官鲍勃·埃克尔特在任已8年。

The outlook for honors and disgraces carries on and surpasses the traditional outlook for honors and disgraces theoretically, and carries on and develops the theory of construction of socialist mora...

社会主义荣辱观的提出在理论上是对传统荣辱观的一次继承和超越，是对社会主义道德建设理论的继承和发展，在实践上有利于形成良好的社会风尚。