查询词典 theorems

By restricting the covariance structure, some theorems of the complete convergence and strong law of large numbers for PA random variables sequences are obtained by applying the properties and inequalities of PA random variables.

在这里通过对协方差结构的限制，应用关于PA随机变量序列的性质、不等式，建立了PA随机变量序列的完全收敛定理和强大数定律。

In this paper,we mainly make a deep and systematic study of sample path prop-erties for high and infinite dimensional Gaussian processes,especially for high andinfinite dimensional Wiener process in stronger norm-Holder norm than ever(everbefore,there used to be uniform norm and the process was limited to one dimen-sion).We not only deal with all kinds of functional moduli of continuity,but alsoconcern with different forms of functional limit theorems of C-R increments.

本文主要对高维的以至无穷维的Gauss过程、特别是Wiener过程的样本轨道性质在较以往更强的范数—〓范数下作了系统深入的研究（以往通常采用一致范数，过程限于一维），研究的内容不仅包括各种形式的泛函连续模，而且还包括各种形式的C-R增量的泛函极限定理。

Prof. Hsio-Fu Tuan,a member of Academia Sinica and eminent mathematician in China, has made outstanding contributions in the theory of modular representations of finite groups, algebraic Lie algebras and the study of p-groups,especially their "Anzanl" theorems.

从30年代末开始，他在有限P群、有限群模表示论和代数李代数方面做出了一系列重要贡献，得到了被冠以布饶尔－段－斯坦顿原则，布饶尔－段指标块分离原则，布饶尔－段定理等名称的突出成就，在中国开辟了代数群论等研究领域并形成了富有特色的研究群体。

In Chapter 2, we recapitulate some fundamental definitions and propositions of topological degrees and some fundamental results about the computation of topological degrees;in Chapter 3, applying relative definitions and propositions of topological degrees, we establish product formulae of topological degrees in product space, in particular, the product formula of fixed point index on product cone, moreover, combining with the fundamental propositions and the computation of fixed point index, we obtain some fixed point theorems on product cone.

为此，在第二章中，我们给出了拓扑度的基本概念和性质以及拓扑度计算方面的基本结果；在第三章中，运用拓扑度的有关知识，我们建立了乘积空间中各类映射的拓扑度的乘积公式，特别是乘积锥上的紧连续映射的不动点指数的乘积公式，进一步，结合不动点指数的基本性质和不动点指数计算方面的基本结果，得到了乘积锥上的若干不动点定理。

In this thesis, we mainly study several problems on geometry and topology of Rieman-nian submanifolds, which contains the geometric rigidity, topological sphere theorems and eigenvalue problems of Laplace-Beltrami operator on Riemannian submanifolds.

本文着重研究黎曼子流形上几何与拓扑的若干问题，主要内容包括子流形的几何刚性、拓扑球面定理和Laplace-Beltrami算子的特征值问题。

The frequency range and distortion model affected by Faraday rotation were analyzed. A kind of calibration algorithm was introduced, in which trihedral corner reflectors were used to calibrate POLSAR image subject to channel imbalance, Faraday rotation and RCS distortion. [2]Three kinds of target decomposition theorems used to extract polarimetric features of SAR image were studied in detail. A kind of POLSAR MLC image data decomposition method based on classical coherent decomposition theorem of POLSAR SLC image was introduced, which was used to extract polarimetric features of POLSAR MLC image.

当工作频率小于1GHz时，法拉第旋转是影响低频星载极化SAR图像定标的一个重要因素，论文分析了受法拉第旋转影响的波段范围和误差模型，提出了一种校正通道不平衡度、法拉第旋转和绝对幅度增益的极化定标算法，仅使用一种点目标——三角反射器作为定标体，应用于受法拉第旋转影响的极化SAR图像定标； [2]深入研究了三类用于SAR图像极化特征提取的目标分解理论。

We introduce some concepts, such as yon Neumann algebras, factor von Neumann algebras, nest algebras and so on, and give some well-known theorems that we will use in this paper. In Chapter 2, we put our attention on linear maps that preserving zero Jordan triple product on nest subalgebrasof factor yon Neumann algebras.

第二章首先对因子von Neumann代数中套子代数上保Jordan三重零积的线性映射进行了研究，证明了从因子von Neumann代数中套子代数到任一有单位元的Banach代数的保Jordan三重零积的单位线性双射是Jordan同构。

Definition: A demonstration that a mathematical proposition is true based on axioms, definitions, and proven theorems

定义：一个用公理，定义，已证明的定理来证实数学上的命题是真实的一个演绎过程。

This thesis concerns convergence theorems and truncation error bounds for all kinds of continued fractions with applications to matrix function computation.

这扁论文讨论了各类连分式的收敛性与误差估计以及它在矩阵函数计算方面的一些应用。

He theorems of Turing tell us that certain problems cannot be solved

uring 的定理告诉我们某些问题是不能解决的。

The network space is the typical form of abstract space when it comes to the digital stage.

网络空间是抽象空间数字化阶段的典型形式。

The Notarial System,as the system of judicial certification in our country,is both the constructor and the defender of social credit system,It has its special value and function in the social honesty.

公证制度作为我国司法证明制度，既是社会信用体系的建设者，同时也是社会信用的捍卫者，在诚信中有其特殊的价值和功能。