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.

這是抽象分析中的兩個(gè)基本定理人人插人人妻。作為應(yīng)用日本ā片免费观看网站，給出了Abelian拓?fù)淙荷系腟ilverman-Toeplitz正則性定理在线高清日本不卡网站、Samaratunga-Sember定理在线国产馆、代數(shù)上的Vitali-Hahn-Saks定理，以及序列空間的〓對(duì)偶空間之弱序列完備性定理等成年片色大黄全免费网站久久。

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.

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Main work follows:(1) In the first part of this paper, a historical development of the number theory before Gauss is reviewed.Based on the systematic analysis of Gauss"s work in science and mathematics, inquiry into the mathematical background that Disquisitiones Arithmeticae appeals and Gauss"s congruent theory;(2) The development process of Fermat"s little theorem and its important function in the compositeness test is elaborated through original literature.we think that the first three section of Disquisitiones Arithmeticae is a summary and development for ancestors" work about Fermat"s little theorem,show that Fermat"s little theorem played an important role in the elementary number theory;(3) With the two main sources of the quadratic reciprocity law, investigating Fermat,Euler,Lagrange,Legendre, until the related work of Gauss,the way to realize the laws huge push to the development of algebraic number theory in 19 centuries.

本文主要做了以下工作：(1)首先回顧了高斯之前的數(shù)論研究狀況，在系統(tǒng)分析高斯的科學(xué)與數(shù)學(xué)成就的基礎(chǔ)上国产成人无码调教AV，探討了《算術(shù)研究》出現(xiàn)的數(shù)學(xué)背景和高斯的同余理論一级视频在线观看免费播放；(2)通過(guò)對(duì)原始文獻(xiàn)的系統(tǒng)解讀，深入分析了費(fèi)馬小定理發(fā)現(xiàn)發(fā)展的歷程以及在素性檢驗(yàn)中的重要作用欧美亚洲另类专区，指出《算術(shù)研究》前三節(jié)是高斯在總結(jié)并發(fā)展了前人對(duì)該定理研究的基礎(chǔ)上形成的https国产黄视免费，并揭示了費(fèi)馬小定理在初等數(shù)論定理證明中的核心地位；(3)以二次互反律的兩個(gè)主要來(lái)源為線索日韩AV毛片精品簧片无码，詳細(xì)考察了費(fèi)馬亚洲精品精品熟妇熟妇，歐拉亚洲人成人一二区在线观看，拉格朗目，勒讓德国产色视频在线观看香蕉，直到高斯的相關(guān)工作日韩成人网址播放视频在线播放免费，揭示了該定律對(duì)十九世紀(jì)數(shù)論發(fā)展的巨大推動(dòng)作用。

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.

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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有限鏈的格值命題邏輯系統(tǒng)LP的完備性定理手机看片1024乱伦；（2）基于完備的且原子的格蘊(yùn)涵代數(shù)的格值命題邏輯系統(tǒng)LP的完備性定理；（3）基于內(nèi)射的格蘊(yùn)涵代數(shù)的格值命題邏輯系統(tǒng)LP的完備性定理免费色网。

Chapter 2 deals with some refinements of the central limit theorem for a class of non-uniformly hyperbolic dynamical systems called Young\'s system, such as local central limit theorem and so-called Berry-Esseen theorem giving the rate of convergence in the central limit theorem.

在第二多人操逼视频、三章中，我們考慮一類重要的非一致雙曲動(dòng)力系統(tǒng)的統(tǒng)計(jì)性質(zhì)-中心極限定理国内特一级A片黄片，及其進(jìn)一步的精細(xì)結(jié)果如局部中心極限定理亚洲一区免费观看，帶有收斂速度的中心極限定理。

On the other hand , illuminated by close relation between harmonic maps and sumanifold theory, we have also researched in-depth about some relative problems in submanifolds theory which include: the estimate of heat kernel and eigenvalue and it geometric application of submanifolds with or without boundary; many kinds of pinching problem of submanifolds which include the rigidity theorem, topological sphere theorem, differential sphere theorem and topological finite theorem.

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The positive periodic solution of functional differential equation with infinite delay is deeply concentrated these years, some scholars study this subject by means of Lyapunov theorem, Schauder fixed point theorem, and cone extending and compression theorem (from thesis -[5]), and they obtain the existence theorem of positive periodic solution.

近年來(lái)，無(wú)窮時(shí)滯泛函微分方程的周期解問(wèn)題受到廣泛關(guān)注日本女孩高潮，一些學(xué)者應(yīng)用Lyapunov泛函方法欧美A特级人成视频，Schauder不動(dòng)點(diǎn)方法，以及非線性泛函分析中的錐拉伸錐壓縮方法(見[1]-[5])黄网欧美日韩一区，研究了無(wú)窮時(shí)滯泛函微分方程的周期解的存在性問(wèn)題欧美综合自拍亚洲综合第一页。

In addition, by utilizing Jacobi two square numbers theorem and Lagrange four square numbers theorem and some theta function identities, we also prove the known results of number theory: two triangular number theorem, four triangular number theorem, and the number of representations of a positive integer by various quadratic forms in terms of divisor functions

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And guided by Schur theorem, many of the Schur theorem inference arises, formed a complete theoretical system Schur theorem. Schur theorem and put many of its reasoning applied to the unitary matrix and the similarity matrix eigenvalue of proof onto.

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