利用无穷大的比较判断正项级数的敛散性

判断正项级数的敛散性是级数理论中一个重要的基本课题.本文通过考查无穷大在某一变化过程中的快慢程度,给出一个判断正项级数敛散性的可供选择的方法.先证明如下不等式:     

判别数项级数敛散性的一些方法和技巧

基于数项级数敛散性的判别是高等数学的一个难点,其判别方法多样,技巧性也强.结合实例分别列举了利用不等式、泰勒展开式、等价量法、对数判别法等判别数项级数敛散性的一些方法和技巧.     

一个不等式在判别级数敛散性方面的应用

讨论一个不等式在幂级数和一些常数项级数敛散性判定中的应用.     

Bernoulli不等式及其应用

使用均值不等式及实数的稠密性推证Bernoulli不等式,并将其应用于证明极限、连续、单调以及其它不等式和判定级数敛散性.     

判定级数敛散性的两种初等方法

借助实例介绍针对某类级数敛散性的两种初等判定方法,即由级数通项构造相关不等式后运用比较判别法,或对级数恒等变换后再进行拆项求和.     

关于p—级数敛散性的又一证明

在级数的学习中，常常会用到户一级数：的敛散性来讨论一些级数的敛散性，一般教科书常是利用广义积分来判定p—级数的敛散性，本文主要介绍利用几何级数来判定P—级数的敛散性的一个方法。众所周知，几何级数（等比级数）当I引wtl时收敛，当卜后1时发散。为讨论产一级数的敛散性，需要下面的一个结论。命题设（。，）为递减的正项数列，那末级数2。，；与】Zn。。。。同敛散。证明设S，；和。，，；分别是级数2。。与2Zn。。。。的部分和，即如果也。，；收敛，则由（3）的第一个不等式可知｛A。｝单调增且有上界，从而AiZ’”a，。收…     

泰勒公式及泰勒级数之妙用

泰勒公式及泰勒级数是非常重要的数学工具,除了读者熟知的应用方面外,在其他问题的解决中也有妙用.举例介绍了应用泰勒公式及泰勒级数解决判断级数的敛散性、证明与积分有关的不等式等问题.     

关于交错级数的一个新的审敛准则

讨论了交错级数的敛散性,给出了判定交错级数敛散性的一个新的准则.     

含有1nn的正项级数敛散性的若干个判定方法

研究了含有1nn的正项级数的敛散性判定的常见六种方法.首先探讨研究此类级数敛散性的意义,然后通过举例说明判定含有1nn的正项级数的常见的六种方法,重点探讨利用比较法判定级数的敛散性.     

含有lnn的正项级数敛散性的若干个判定方法

研究了含有lnn的正项级数的敛散性判定的常见六种方法.首先探讨研究此类级数敛散性的意义,然后通过举例说明判定含有lnn的正项级数的常见的六种方法,重点探讨利用比较法判定级数的敛散性.     

有界线性算子非负分裂的比较

本文研究有界线性算子非负分裂的比较,建立了若干比较定理,给出了保证两个迭代算子的谱半径间严格不等式成立的一些充分条件．这些结论蕴涵并推广了Ｍａｒｅｋ 和Ｓｚｙｌｄ［２］以及作者［４］的相应结果     

Theorems of the Alternative for Inequality Systems of Real Polynomials

In this paper, we establish theorems of the alternative for inequality systems of real polynomials. For the real quadratic inequality system, we present two new results on the matrix decomposition, by which we establish two theorems of the alternative for the inequality system of three quadratic polynomials under an assumption that at least one of the involved forms be negative semidefinite. We also extend a theorem of the alternative to the case with a regular cone. For the inequality system of higher degree real polynomials, defined by even order tensors, a theorem of the alternative for the inequality system of two higher degree polynomials is established under suitable assumptions. As a byproduct, we give an equivalence result between two statements involving two higher degree polynomials. Based on this result, we investigate the optimality condition of a class of polynomial optimization problems under suitable assumptions.     

Generalized KKM theorems on hyperconvex metric spaces and some applications

In this work, we establish the intersection property for a family of admissible subsets in a hyperconvex metric space, and we apply this intersection property to get generalized KKM theorems, coincidence theorems, variational inequality theorems and minimax inequality theorems.     

复射影空间中全实子流形的刚性

本文研究了复射影空间中的全实子流形.通过使用活动标架的方法和DDVV不等式,得到了两个刚性定理和一个积分不等式,改进了相关的结果.     

Some fixed-point theorems and minimax inequalities in FC-space

By applying the existence theorem of maximal elements, some new collectively fixed-point theorems for a family of set-valued mappings defined on the product space of noncompact FC-space are proved and some new theorems about minimax inequality involving two functions are given to show the relations of fixed-point theorem and minimax inequality in FC-spaces. These results improve and generalize many important results in the recent literature.     

凸函数的Hadamard不等式的若干推广

本文获得两个定理 ,它们均是不等式f a +b2 1b -a∫baf (x) dx f (a) +f (b)2(其中 f是 [a,b]上的连续凸函数 )的推广 .     

Φ-Conjugation and noneonvex optimization. a survey (part III)

In the present paper, which is part III of our review concerning the theory of Φ-conjugate functions, we consider Lagrangians, duality theorems are proved and the connection to saddle point theorems is shown. By a fundamental inequality, duality theorems are proved and the connection to saddle point theorems is shown. By a fundamental inequality, duality theorems can be obtained, where results are modified given in part I and part II of our paper.     

对算术-几何不等式的两种推广与改进

将关于一组正数的加权算术-几何不等式推广为关于两组正数的改进型加权算术-几何不等式,其思路可为部分已有结论提供新的证明方法.突破关于自然对数的加权算术-几何不等式对具体函数的依赖,给出并证明了关于对数凸函数的加权算术-几何不等式.     

A set-valued type inequality system

A set-valued type inequality system is introduced along with two solvability questions composed of existence and perturbation, and main theorems are obtained, which include three necessary and sufficient conditions concerning the existence and a continuity property concerning the perturbation. As applications, two existence criteria with respect to a single-valued type inequality system have also been obtained.     

Comparison Theorems For Nonlinear Iterative Functional Inequality

We present two comparison theorems for inequality (1). These theorems are generalizations of similar comparison theorems proved in [1] for linear homogeneous iterative functional inequalities (see also [3] pp. 482–483).