查询词典 radon nikodym theorem

The structure theorem is obtained by defining "ternary ordered partition method" which is used to choose the test-sets of the first $k$ tests, and by defining two operations and two relations on feedback sequences; The isomorphism classification theorem is strictly proved by virtue of the structure theorem, thus the complicated problem of discussing $3^k$ possible search domains is reduced to the relatively easy problem on $k+1$ representative search domains; By the techniques of "super-coin construction method" and "image-union method", the search problem on $k+1$ representative search domains is reduced to the simple verification of several conditions on finite space of small cardinality.

通过引入用于选取前$k$次试验的试验集的"三元有序剖分法"以及关于反馈序列的两种运算和两种关系，得到了结构定理；基于结构定理严格地证明了同构类定理，从而将必须针对$3^k$个搜索域的复杂问题转变为讨论$k+1$个具代表性的搜索域的相对简单的问题；通过"构造超币法"和"并像法"等技术手段，将关于$k+1$个具代表性的搜索域的搜索问题转化为简单的关于势非常小的有限空间的几个条件的验证问题。

Topics include: mathematical definition and properties of information; source coding theorem, lossless compression of data, optimal lossless coding; noisy communication channels, channel coding theorem, the source-channel separation theorem, multiple access channels, broadcast channels, Gaussian noise, and time-varying channels.

课程主题包括：针对「资讯」的明确数学定义及性质描述；信源编码理论、无失真资料压缩技术、最佳化无错误编码；杂讯干扰的通讯频道解析、频道编码理论、资讯来源-通道编码分离理论、多重存取频道解析，广播型态频道解析、高斯杂讯及多变量时间频道解析。

The cohomology of q-polynomial coalgebras with coefficients in trivialcomodule K are also determined(see Theorem 6.3.11).Having obtained Theorem 5.2.3 andTheorem 5.2.4,we determine(see Theorem 7.2.6)all the nonzero 〓.

对于这一类q-多项式余代数，我们决定了（见定理6.3.11）系数在它的平凡余模K中的上同调，有了定理5.2.3与定理5.2.4以后，我们决定了（见定理7.2.6）所有非零的〓。

In part 1, we explore some properties of solution y of a backward stochastic differential equation, such as comparison theorem, reverse comparison theorem and uniqueness theorem of generator.

第一部分研究了倒向随机微分方程的解中y的性质，其中包括解的比较定理，逆比较定理，生成元的唯一性定理。

By mean of the method of upper and lower solutions, we will obtain a existence theorem like Kazdan-Warners. Using this theorem, we will study the vortex equation in holomorphic line bundle over complex manifold and prove a theorem of existence of Hermitian metric with a prescribed holomorphic section.

在本论文的最后部分，我们在紧复流形上讨论一类Kazdan-Warner型方程，用上下解方法得到了光滑解存在的Kazdan-Warner型定理，并将其用于研究全纯线丛的涡旋方程，得到了一个具有预定全纯截面的厄米度量的存在定理。

Helling and Jorgensen established the algebraic convergence theorem,limit theorem and convergence theorem in plane,respectively.

Helling、Jorgensen分别建立了平面Mobius群列的极限定理、代数收敛性定理和收敛性定理等等。

Invariant theorem of the operator series multiplier convergent. Using operator series multiplier convergent,AK-space of concept ,we obtained the theorem of operator series multiplier convergent invariant and the old theorem of general series multiplier convergent invariant is looked as special case.

第三章 算子级数乘数收敛的不变性：利用算子级数乘数收敛、AK—空间的定义，得到了算子级数乘数收敛的不变性定理，从而将以往的普通级数乘数收敛的不变性定理作为特殊情况。

This paper investigates the converse theorem of rectangular projection theorem in descriptive geometry,and furthermore supplements and confirms another converse theorem,If the projection of two lines intersecting vertically fo rms a rectangle on a certain projecting plane,at least one line of the two lines is parallel to the projecting plane.

通过对《画法几何学》中直角投影定理的逆定理的研究，得出："若垂直相交的两直线在某一投影面上投影成直角，则该两直线至少有一条直线平行于该投影面"的推论。

All the following process was done on the sub image. Second, the morphology gradient theorem and its converse theorem were both proved. And the DGT reverse theorem was used to look for the regional maxima points of the sub image. In the improved region growing method, the seeds were those regional maxima points.

然后证明了数学形态学的膨胀梯度定理(dilation gradient theorem， DGT)及其逆定理，并利用DGT逆定理查找图像的局部极大值点，将灰度值不为0的局部极大值点作为区域生长法的种子点。

In the following, we list the main works in our paper:(1) We introduce briefly the concepts of fuzzy mathematics and three fundamental principles—decomposition theorem, representation theorem and extension theorem. We also present the concepts of fuzzy number and some simple properties.

本文主要内容包括以下几个方面：(1)简要地介绍了模糊数学中基本概念和三大基本定理--分解定理，表现定理和扩展定理，模糊数的概念、性质以及比较两个模糊数的方法。

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