查询词典 maximum ergodic theorem

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。

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。

Defined circulation, introduced Stokes theorem, and gave an arm waving proof for Stokes theorem.

定义环流，介绍Stokes定理，并用动作来演示。

We divide the existence of generalized solutions into three theorems becauseof the existence of a generalized supersolution we need in the proof.To ob-tain this fact,we discuss three different cases separately.WhenΩhas strictconvexity,it can be proved that the generalized supersolution of (1)(2)is theconvex-monotone hull of 〓in 〓,this is theorem 2.WhenΩdoesn't hasthe strict convexity,in theorem 3 we have to suppose there exists a generalizedsupersolution.

我们的广义解的存在性结果之所以分成三个定理陈述，主要是因为在我们的存在性证明中，一个重要的事实就是广义上解的存在性，而为了得到这个事实，我们分别讨论了三种不同的情况：在定理2中的假设〓具有严格凸性时，我们证明了问题（1）（2）的广义上解就是初边值〓的凸单调包，而在〓没有严格凸性时，我们在定理3中假定了一个广义上解的存在性。

Using the method of analysis to study strong limit theorem proposed by professor Liu Wen, and a plying Legbesuge theoremon differentiability of monotone function, a new proof of the theorem of strong law of large numbers for the sequence of random variables of the product distribution of Poisson is forwarded.

利用文献[1]刘文教授提出的研究强极限的纯分析方法，通过构造适当的辅助函数，然后利用单调函数异数存在定理，给出具有乘积泊松分布的随机变量序列的一个强大数定理的新证明。

First, a few methods of fatigue experiment, the structure theorem of thefatigue experiment machine and some basal conception and theorem are assaiedideally.

首先，从理论上分析了几种疲劳试验方法，以及疲劳试验机的结构原理和计算机控制的一些基本概念和理论。

In this part, the author draws out an alternative theorem—the organic-centralization of urban spatial structure. According to this theorem, the paradoxical tendencies of concentration and decentralization could be compatible and complementary.

针对上述问题，该章重点从产业结构的调整与聚居模式的选择，交通可达性提高及生态保护等空间机制方面对南京城市空间结构中集中与分散现状按有机集中的结构模式进行调整。

We would like to point out that our proof of the singularity层次structure theorem (Theorem 7.1.1) is different from that of Perelman in two aspects:(1) we avoid using his crucial estimate in Claim 2 in Section 12.1 of [103];(2) we give a new approach to extend the limit backward in time to an ancient solution.

这个特解大致上走的正是小佩避免使用定理7.4的那条路，不过曹朱强调：在这个"完整证明"中所用的定理7.1.1证明与小佩所采用的方式有两点不同

You'll be in trouble it you don't watch out .

如果你不注意，你会有麻烦的。

Shaped like a biconvex lens.Of, relating to, or having the form of a hyperbola.

双曲线的属于双曲线的，与之有关的，或有双曲线形状的