查询词典 replacement theorem

Secondly,we firstly study the properties of functions with values in a uni-versal Clifford algebra 〓,and we obtain the following very important basictheorems in universal Clifford analysis:Cauchy's integral formula,Cauchy's inte-gral theorem,the mean value theorem,the three versions of the maximum mod-ulus theorem,the Taylor's expansion,the Laurent's expansion and the residuetheorem etc..All of these results generalized the classical results.

第二，本文所讨论的各种函数性质以及所得的结果都在泛Clifford代数〓上所做的工作，它一方面包含了从前在泛Clifford代数〓上所做的工作，所得到的结果更广泛、更漂亮、更自然，另一方面，本文也是迄今为止第一次建立起来了在泛Clifford分析中与经典函数论相对照处基础地位的LR正则函数在特异边界上的Cauchy积分公式、Cauchy积分定理、平均值定理、极大模原理的三种表达形式、Taylor展式、Laurent展式留数定理等深刻的结果。

Second,we introduce some important theorems we use in this paper,that is traverse theorem,martingale central limit theorem and slutsky theorem.

此外，还介绍了本文中所应用的主要定理，例如遍历定理，鞅中心极限定理以及slutsky定理等。

The key concepts are "isomorphism" and "symmetric isomorphism" which are used to describe the relation between two search domains, the key results are "Structure Theorem","Isomorphism Theorem" and "Isomorphism Classification Theorem".

核心的概念是非常重要的用于描述搜索域之间相互关系的"同构"与"对称同构"，核心结果是"结构定理"，"同构定理"和"同构类定理"。

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。

Nowadays, most of research are to build a transmutative Petri Nets through adding controlling place sets, controlling arc sets and controlling policy to the basic Petri Nets, while the Controlled Petri Nets could be used to argue many controlling theory problems conveniently and to induce many logically and physically supervisory and solve the Event Feedback Controlling Problems and State Feedback Controlling Problem in DEDS supervisory theory.

目前大多数的研究表现为在变形后的受控Petri网基础上，利用各种方法求得各种逻辑型、结构型控制器，解决DEDS监控理论中的事件反馈控制问题与状态反馈控制问题。

On one hand, there are discussions with the works council and union about extension of short time working up to the end of September.

一方面，有讨论，工程理事会和联盟关于延长工作时间短至9月底。