Henstock积分问题的一个注记

本文证明了如果X是不含c0的Banach空间，f是定义在区间I0包含R^m上取值于Panach空间X的函数，并且，在I0上Henstock可积，则总存在I0的一个非退化子区间J，使得f在J上McShane可积，从而对Kartak的一个问题作出了肯定的回答．     

对称性在积分中的应用

本讨论了在各类积类中利用对称性解题的技巧的使用方法。     

向量值函数的Mcshane积分

本文讨论了向量值函数的Ｍｃｓｈａｎｅ积分的性质．例如收敛定理和原函数的性质等．     

关于重积分与线面积分内容体系的探讨

本文将二重积分、三重积分、第一类曲线积分及第一类曲面积分统一为多元数量值函数的积分，并且用第一类曲线、曲面积分定义第二类曲线、曲面积分。     

A NEGATIVE ANSWER TO A PROBLEM OF FREMLIN AND MENDOZA

This article studies some convergence results for the McShane integral of func- tions mapping the interval[0,1]into a Banach space X from the point of view of an open problem propose by D.H.Fremlin and J.Mendoza in[2].also the anthors give a negative answer to this open problem.     

对称性在积分学中的应用

如果能充分利用积分区域的对称性和被积函数的奇偶性,高等数学中许多积分的计算过程将得到简化.总结并借助实例说明对称性在高等数学定积分、重积分以及曲线与曲面积分计算中的应用.     

积分凸性及其应用

该文在Banach空间中通过向量值函数的Bochner积分引进集合与泛函的积分凸性以及集合的积分端点等概念. 文章主要证明有限维凸集、开凸集和闭凸集均是积分凸集，下半连续凸泛函与开凸集上的上半连续凸泛函均是积分凸的, 非空紧集具有积分端点, 对紧凸集来说其积分端点集与端点集一致, 最后给出积分凸性在最优化理论方面的两个应用.     

含有积分的一些极限问题的解法

在处理积分极限问题时 ,若将积分计算出来再求极限 ,有时候难以办到 ,如 ex2 、sinxx 、 cosx2等函数的原函数不能用初等函数表示 ,所以无法先积分再求极限 .实际上 ,往往也不需要如此 ,本文介绍几种处理此类问题的方法 .一、利用积分中值定理利用积分中值定理将积分号去掉 ,然后再求极限 ,这是一种常用方法 .例 1　求 limn→∞∫n ansinxx dx　 (a >0 ) .解　因 sinxx 在 [n,n a]连续 ,故依积分中值定理 ,存在ξn ∈ [n,n a],使得limn→∞∫n ansinxx dx =limn→∞ (a .sinξnξn) =limξn→∞ (a .sinξnξn) =0 .　　例 2　设函数 …     

Rm上Banach-值函数的强McShane积分

在本文中,我们定义和研究了I0Rm到Banach空间X中函数的强McShane积分,直接证明了强Mcshane积分与Bochner积分是等价的,McShane积分与强Mcshane积分等价当且仅当Banach空间X有限维. 从而部分地回答了R.A.Gordon的一个公开问题.     

正交变换在曲线,曲面积分计算中的应用

正交变换在曲线、曲面积分计算中的应用林元重（江西萍乡高等专科学校３３７０５５）对于三维空间的曲线积分与曲面积分，如果知道其积分曲线或积分曲面的参数形式，一般可按数学分析教材所介绍的公式计算．但是，对于某些曲线、曲面积分，要把积分曲线或曲面用适当的参数...     

Precise Asymptotics in the Law of the Iterated Logarithm of Moving-Average Processes

In this paper, we discuss the moving-average process Xk = ∑i=-∞ ^∞ ai＋kεi, where {εi;-∞ 〈 i 〈 ∞} is a doubly infinite sequence of identically distributed ψ-mixing or negatively associated random variables with mean zeros and finite variances, {ai;-∞ 〈 i 〈 -∞） is an absolutely solutely summable sequence of real numbers.     

Wavelets and Geometric Structure for Function Spaces

Abstract With Littlewood–Paley analysis, Peetre and Triebel classified, systematically, almost all the usual function spaces into two classes of spaces: Besov spaces and Triebel–Lizorkin spaces ; but the structure of dual spaces of is very different from that of Besov spaces or that of Triebel–Lizorkin spaces, and their structure cannot be analysed easily in the Littlewood–Paley analysis. Our main goal is to characterize in tent spaces with wavelets. By the way, some applications are given: (i) Triebel–Lizorkin spaces for p = ∞ defined by Littlewood–Paley analysis cannot serve as the dual spaces of Triebel–Lizorkin spaces for p = 1; (ii) Some inclusion relations among these above spaces and some relations among and L ¹ are studied. Supported by NNSF of China (Grant No. 10001027)     

Hoermander＇s Multipliers for the Weighted Herz-type Hardy Spaces

In this article, we apply the molecular characterization of the weighted Hardy space developed by the first two authors to show the boundedness of Hormander multiplier on the weighted Herz-type Hardy spaces HK^α,p 2（｜x｜^t; ｜x｜^t） and HK^α,P 2（｜x｜^t; ｜x｜^t）.     

Multilinear Singular Integrals with Rough Kernel

For a class of multilinear singular integral operators T _A ,

A Nontrivial Product of Filtration s ＋ 5 in the Stable Homotopy of Spheres

In this paper, some groups Ext A^s.t （Zp, Zp） with specialized s and t are first computed by the May spectrM sequence. Then we make use of the Adams spectral sequence to prove the existence of a new nontrivial family of filtration s＋5 in the stable homotopy groups of spheres πpnq＋（s＋3）pq＋（s＋1）q-5S which is represented （up to a nonzero scalar） by β＋2bohh∈ExtA^s＋5,P^nq＋（n＋3）pq＋（n＋1）q＋s（Zp, Zp） in the Adams spectral sequence, where p ≥ 5 is a prime number, n ≥3, 0≤ s 〈 p - 3, q = 2（p - 1）.     

Some generalizations of Knopp's identity*

For integers a, b and n > 0, define

On the Order of Magnitude of the Divisor Function

Let D be an increasing sequence of positive integers, and consider the divisor functions： d（n, D） =∑d｜n,d∈D,d≤√n1, d2（n,D）=∑[d,δ]｜n,d,δ∈D,[d,δ]≤√n1, where [d,δ]=1.c.m.（d,δ）. A probabilistic argument is introduced to evaluate the series ∑n=1^∞and（n,D） and ∑n=1^∞and2（n,D）.     

Blow-up Solutions for Mixed Nonlinear Schrodinger Equations

This paper is concerned with the initial boundary-value problem for the following nonlinear evolution equation: Фt=iαФxx βФ^2Ф^-x γ|Ф|^2Фx ig(|Ф|^2)Ф Under certain conditions on the initial data and the function g(s),we study the existence and nonexistence of global solution for this equation.The blow-up solution and the blow-up time are also investigated.     

On the Convergence of Products γ^-sh1hn in the Adams Spectral Sequence

Abstract Let A be the mod p Steenrod algebra and S the sphere spectrum localized at p, where p is an odd prime. In 2001 Lin detected a new family in the stable homotopy of spheres which is represented by （b0hn-h1bn-1）∈ ExtA^3,（p^n＋p）q（Zp,Zp） in the Adams spectral sequence. At the same time, he proved that i.（hlhn） ∈ExtA^2,（p^n＋P）q（H^＊M, Zp） is a permanent cycle in the Adams spectral sequence and converges to a nontrivial element ξn∈π（p^n＋p）q-2M. In this paper, with Lin＇s results, we make use of the Adams spectral sequence and the May spectral sequence to detect a new nontrivial family of homotopy elements jj′j^-γsi^-i′ξn in the stable homotopy groups of spheres. The new one is of degree p^nq ＋ sp^2q ＋ spq ＋ （s - 2）q ＋ s - 6 and is represented up to a nonzero scalar by hlhnγ-s in the E2^s＋2,＊-term of the Adams spectral sequence, where p ≥ 7, q = 2（p - 1）, n ≥ 4 and 3 ≤ s 〈 p.     

Regularity of Weak Solutions of Nonlinear Equations with Discontinuous Coefficients

In this paper, we prove that the weak solutions u∈Wloc^1, p （Ω） （1 〈p〈∞） of the following equation with vanishing mean oscillation coefficients A（x）： -div[（A（x）△↓u·△↓u）p-2/2 A（x）△↓u＋│F（x）│^p-2 F（x）]=B（x, u, △↓u）, belong to Wloc^1, q （Ω）（A↓q∈（p, ∞）, provided F ∈ Lloc^q（Ω） and B（x, u, h） satisfies proper growth conditions where Ω ∪→R^N（N≥2） is a bounded open set, A（x）=（A^ij（x）） N×N is a symmetric matrix function.