查询词典 recurrence theorem

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 the paper the separate theorem of convex set with weak topology σ(L ∞,L 1) is proved, and the topological characterization about No Free Lunch with Vanishing Risk Condition is given, from it, the equivalency between exist of equivalent martingale measures and NFLVR is proved, this is the first fundamental theorem of asset pricing.

资产定价的第一基本定理是数量金融学中核心的定理之一，本文证明了在 L∞的弱*拓扑σ(L∞，L1)中的凸集分离定理，并在此定理的基础上给出了没有无风险免费午餐的拓扑描述，证明了市场公平性与没有无风险免费午餐条件的等价性，从而重新证明了资产定价的第一基本定理。

The existence theorem of generalized weak efficient solutions with respect to variable, cone for a linear G〓teaux differentiable mapping is proved with set valued mapping fixed-point theorem and the relation between a vector optimization and a variational inequality problem. The existence of weak efficient solutions for multi-objective convex vector optimization is characterized.

建立映射在线性G〓teaux可微条件下关于可变锥的广义弱有效解的存在性及多目标凸向量优化问题在G〓teaux可微条件下弱有效解的特征，利用集值映射不动点定理及向量优化与变分不等式的关系证明线性G〓teaux可微锥凸映射关于可变锥的广义弱有效解的存在性定理。

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。

Since Bloch's Theorem applies only to periodic potentials, and since unceasing random movements of atoms in a crystal disrupt periodicity, Bloch's Theorem is only an approximation, but it has proven to be a tremendously valuable approximation, without which most solid-state physics analysis would be intractable.

由于布洛赫定理仅对周期性势场的情况严格成立，而由于实际的晶体中不可避免的有各种缺陷或者原子相对于平衡位置的位移，所以布洛赫定理对于实际晶体来说只是一个近似。但是布洛赫定理对于固体物理的研究不可或缺。

A historical region of southwest France between the Pyrenees and the Garonne River. The duchy of Aquitaine was joined with France after the marriage of Eleanor of Aquitaine to King Louis VII in1137, but its possession was disputed after her subsequent marriage to Henry II of England.

阿基坦法国西南部一个历史地区，位于比利牛斯山和加隆河之间，在1137年阿基坦的埃莉诺与国王路易斯七世结婚之后阿基坦公国加入法国，但当她再嫁英国亨利二世后，其归属权便受到争议

There are moments when I look at the smiling , happy faces of my expectant staff and wonder how they will cope when confronted by an outraged housemaster along with an unrepentant and recalcitrant bleached blond teenager in 18 years ' time .

有时候，我看着那些满怀期待的员工微笑，幸福的脸，想着当他们遇到一位愤怒的宿舍管理员和一位不知悔改，叛逆，而且将头发染成白色的18岁少年时，他们会如何处理。