查询词典 radon nikodym theorem

In this paper we introduce some new definitions, they are the generalizations of those concepts in Lie theory, and we discuss initially the elementary properties of operator Lie algebras. Finally, the famous Jordan-Holder theorem and the uniqueness of decomposition theorem of operator Lie algebras are proved.

在这篇文章里，我们将李代数理论中的诸多概念加以推广，并初步地探讨了算子李代数的性质，最后还给出了算子李代数的一个分解定理，其唯一性也得到了证明。

Properties of cut sets, decomposition theorem, representation theorem of intuitionistic fuzzy sets are discussed.

在此基础上，给出了直觉模糊集的分解定理和表现定理。

In this paper a modified centroid coincidence theorem and a motion parameter decomposition theorem are introduced,which degenerate it into a pure rotation problem with only 3 degrees of freedom.

最优运动估计本质上是6自由度的非线性问题，本文提出推广的质心重合定理和运动参数分解定理，将其简化成3自由度的纯旋转问题。

The infonnation orthogonalization theorem and the information magnitude decomposition theorem are proposed and proved.

提出信息正交化定理，为解决相关信息最优融合问题找到了统一的途径。

Accordingly,they can result in the celebrated Jordan theorem and the third decomposition theorem of space directly and, moreover,they can give a new deep insight into the exquisite and subtle structure of the Jordan ...

因而，它们能够直接导致著名的Jordan定理及空间的第三分解定理，且能给出对Jordan形精致微妙结构的新的深刻洞察。后者表明，复线性变换的Jordan标准形是一种在双重任意选择下具有不变性的结构。

In chapter 5,we persue the ctiticality and complexity of thecritical sets.We describe carefully the Whitney's example in 1935.Meantime,we introduce some rsults about the critical sets and thecritical value sets,in particular,on W-sets and C-sets.And usingthe Lebesgue density theorem and the Vitali covering lemma weprove a rank zero theorem with Hausdorff measures.Finally wegive some examples to prove our results are sharp in the sense thatthe numbers k,m,n,s,〓,etc.,in the hypothesescan not be improved.

第五章研究临界点集的临界性和复杂性，并详细地描绘了Whit-ney在1935年的例子，同时也介绍了关于临界点集和临界值集的一些结果，尤其是W-集和C-集的一些结果，并利用Lebesgue密度定理和Vitali覆盖引理证明了一个与Hausdorff测度相关的秩零定理，最后举例证明我们的结果在定理的假设中的那些数字如k，m，n，s，a，r+/等不能被改进的情况下是最佳的。

For example, we cannot copy an unknown state exactly because of "the no-cloning theorem"(no-deleting theorem), which is known as one of the most significant differences between classical and quantum information. Therefore to get to know what we can and cannot do in QIS or in quantum physics becomes an important and interesting problem. Particularly, in quantum communication and quantum cryptography, many novel schemes are based on the fact that nonorthogonal states cannot be discriminated determinately.

例如，经典信息中，编码状态是可以精确复制、区分的；而在量子信息中，由于叠加性的存在，使得非正交态不可区分，量子态不可复制、删除等；故而以往既成的观念都被打破，探讨在量子信息的框架下编码信息的估计、物理可实现的操作，以及这些量子体系在外界通过物理方法进行识别过程中的差异，是量子信息学、乃至物理学中的重要也很基本的问题。

The monotone class theorem of multiple dimension functional format.This is the generalization from the one dimension monotone class theorem.

给出了多维函数形式的单调类定理，它是一维函数形式单调类定理的推广，也是处理多维可测函数、多维随机过程的有力工具。

Under the cases of the linear interconnected systems with all its subsystems are one dimension, a theorem to judge the properties of single loop interactions has been given; the study also indicated that the properties of interactions cann't independent of the properties of subsystems in the multi-loop interaction conditions, and a all field root locus method has been proposed to decide the properties of interactions; a interaction stabilizable theorem has been given, and the efficacy of interactions with respect to the interconnected systems has been configured, Some primary results are reported which are induced by using a method of computer aided test to study block interactions, the stationary feedback efficacy of closed loop interactions have been discussed and a stability guess has been proposed.

本文提出互连系统的合作稳定性概念及其原理，给出了互连系统的本原稳定度、稳定中心、回路关连的级数以及关连的性质等基本定义；并在此基础上对线性互连系统进行关连分析，给出了一系列涉及到关连与互连系统稳定性关系的命题、引理、定理及其证明；其中，在子系统都是一维的线性定常互连系统情况，得出了单回路关连性质判断的定理；并指出在多回路关连条件下，关连的性质不能独立于子系统的性质，以及用全域根轨迹法判断关连性质的方法；给出了关连可稳定理，并对关连对互连系统的影响作用进行了分析。本文还用机辅试验的方法研究块阵关连并给出一些初步结果，本中还探讨了回路关连的静态反馈作用并提出一个判稳猜想。

Theorem （convergence Theorem , Dirichlet Condition

定理（收敛定理，狄利克雷充分条件）设是周期为的周期函数，如果它满足

Listen,point and check your answers.

听，指出并且检查你的答案。

Warming needle is one of effective treatment methods for knee arthralgia aggravated by cold,and it is simple,safety,so it should be developed in clinical acupuncture and moxibustion extensively.

但以本院科针灸门诊在2005年1月—2006年6月期间共收治膝痛患者100余例，经过临床的诊断后，其中施以温针治疗的48例，疗效显著，报道如下。1临床资料本组病例48