查询词典 theorems

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。

The strong and weak dual theorems are obtained in the sense of strictly efficiency in dual model which is established by scalar set-valued Lagrange mapping.

利用标量集值Lagrange映射建立了集值优化问题的对偶模型，并得到严有效性下的弱对偶和强对偶定理。

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。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。