查询词典 reciprocity theorem

By using these convergence theorems,it presents the Silverman-To-eplitz regular theorem and Samaratunga-Sember theorem on the Abelian topologicalgroups,the Vitali-Hahn-Saks theorem on algebras and the weak sequentially completenesstheorem of 〓-dual spaces of sequence spaces,etc.

这是抽象分析中的两个基本定理。作为应用，给出了Abelian拓扑群上的Silverman-Toeplitz正则性定理、Samaratunga-Sember定理、代数上的Vitali-Hahn-Saks定理，以及序列空间的〓对偶空间之弱序列完备性定理等。

Theorem 1 constructs a set of universal measure zero using continuous extension; Theorem 2 verifies absolutely continuous function being of good property under some condition; Theorem 3 reveals some relation between real function and meager.

定理1 主要运用了连续延拓构造了一个泛测度零集；定理2 证明绝对连续函数在一定条件下具有良好的性质；定理3 揭示了实函数与第一纲集的某种关系。

For some special cases, the paper gives some important identical theorems, and then establishes a valuable relation between the uniformly almost periodic functions and the trigonometric polynomials.Secondly, on the basis of the identical theorem, the paper investigates the Fourier series of the uniformly B2 almost periodic functions, and further proves that the series is unique.Thirdly, the paper discusses the Parseval equation of the uniformly B2 almost periodic functions, which establishes the relation between these functions and the coefficients of their Fourier series; and next investigates an important approximation theorem-Riesc-Fischer theorem, about the uniformly B2 almost periodic functions and the trigonometric polynomials.

并给出了特殊情况下的几个重要的恒同定理，将一致概周期函数与有限三角多项式联系起来；第二，在恒同定理的基础上，给出了一致B~2概周期函数的Fourier级数，并且级数是唯一的；第三，讨论了一致B~2概周期函数的Parseval方程，建立了函数与其Fourier级数的系数之间的联系；接着给出了关于一致B~2概周期函数和三角多项式之间的一个重要近似定理—Riesc-Fischer定理。

Then we deeply studied the completeness of LP . Consequently, we established:(1) The completeness theorem of LP with truth-value in finite Lukasiewiczchain;(2) The completeness theorem of LP with truth-value in complete and atomic lattice implication algebras;(3) The completeness theorem of LP with truth-value in injective lattice implication algebras.

建立了：（1）基于Lukasiewicz有限链的格值命题逻辑系统LP的完备性定理；（2）基于完备的且原子的格蕴涵代数的格值命题逻辑系统LP的完备性定理；（3）基于内射的格蕴涵代数的格值命题逻辑系统LP的完备性定理。

Based on the view that the theorem of closed mested interval is an axiom,this paper deduces the essential limit of monotonic bounded sequence of number and the Dedekind theorem,and proves the general theorem of bull closed nested interval of real number .

以通常所说的闭区间套定理作为公理推出单调有界数列存在极限和Dedekind定理，并且证明了通常所说的实数满闭区间套定理

We give a brief proof of the existence theorem of Supremum and Infimum of a bounded set of fuzzy numbers given by Wu cong-xin and Wu chong in [30] . It is used to establish the monotone convergence theorem and the nest theorem of closed intervals on E〓,τ

给出了吴从忻、吴冲[30]得到的模糊数集的确界存在定理的一个简洁证明，并利用此定理在空间E〓，τ(l中建立了模糊数序列的单调收敛定理和闭区间套定理。

Theorem C: The commutator algebra of so *(2 n ) is its own, and the commutator algebra ofand the commutator algebra of Theorem D: The Cartan subalgebra ofand the Cartan subalgebra of Theorem E: The structural formula of

定理C so *(2 n )的换位子代数就是其本身， g *(2 n， S ， C )的换位子代数为g *(2 n + 1， S ， C)的换位子代数为定理D so *(2 n )和g *(2 n ， S ， C )的Cartan子代数是定理E so *(2 n )和g * m， S ，(来源：AB78C论文网www.abclunwen.comC 的结构公式都是来源：A6bBCe9论文网www.abclunwen.com

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"。

You can do some assertiveness training.

你可以进行一些自信训练。

We were well on the path to making a rear-wheel-drive global platform," says Mays."

我们正致力于建立一个后轮驱动的平台，"Mays这样说道。"