基于分解测度的模糊积分及收敛定理Mamadou Traore

为了解决一些收敛定理,我们给出基于半环([0,1],, )的伪可加分解测度的积分这种模糊积分被深入研究.在给出这种积分的性质的基础上,我们得到一些收敛定理,它们是经典收敛定理的扩张,同时我们得到关于这种模糊测度的Egorof定理.     

HAKOPIAN插值的弱收敛性

1　引　　言在 1 982年 ,Ｈａｋｏｐｉａｎ[1 ]提出了一种新的多元插值 这种插值是Ｋｅｒｇｉｎ插值的一种发展 ( [2 - 4 ]) 王和来 [5]在 1 984年给出了这种插值的余项估计 梁在 [6 ]的基础上于 86年给出了二元Ｈａｋｏｐｉａｎ插值的Ｌａｇｒａｎｇｅ型表达式并对定义于单位圆盘上足够光滑的插值函数给出了它的收敛速度估计 [7] 圆盘上的二元Ｈａｋｏｐｉａｎ插值的导数收敛性在 [8]中进行了讨论 最近 ,在 97年 ,梁和吕 [9]进一步研究了Ｈａｋｏｐｉａｎ插值的积分收敛性 我们在这篇文章中对Ｈａｋｏｐｉａｎ插值的弱收敛性进行了研…     

无穷限积分的控制收敛理论

本文根据有限区间上Ｒｉｅｍａｎｎ积分的Ａｒｚｅｌａ控制收敛定理［１］，给出无穷限积分的控制收敛定理，并做了相应的推广。     

积分型Hilbert定理的改进与应用

本文建立如下权函数的不等式ｗ （ｘ） ＝ ∫∞０１ｘ ＋ ｙ ＋ １（ｘ ＋ １ｙ ＋ １）１／２ｄｙ ≤π［１ － １ － ２／π（ｘ ＋ １）１／２］　（ｘ ∈［０,∞））,这里,常数１－ ２／π是最佳值,从而改进了积分型Ｈｉｌｂｅｒｔ定理,作为应用,建立一个Ｈｉｌｂｅｒｔ类积分不等式及其加强式;并改进推广了Ｈａｒｄｙ－Ｌｉｔｔｅｗ ｏｏｄ 积分不等式．     

THE LSRS PROPERTY AND THE CONVERGENCE THEOREM OF HENSTOCK-KURZWEIL INTEGRAL

1Introducti0nandPreliminariesIn19571958,J.KurzweilandR.Henst0ckindependentlygaveaRiemannc0mpletetypeintegral,calledtl1eKurzweil-Henstockintegral(0rKH-integral/H-integral)['].Itisan0n-absoluteinterga1anditsdefinitiondoesn0tneedthemeasuretlieory.lthasbeenprovedthatthisintegralisequivalenttothespecialDenjoyilltegral['].Theref0retlieH-integralc0ntainstl1eNewton,ffiemann,Improper-fuemannandLebesgueintegrals.In1985,P.Y.LeeandT.S.ChewgavetheC0ntr0lledC0nvergenceTheorem,andmadetheH-integraJ…     

基于凸优函数的Newton类方法的收敛定理

本文研究了求解Banach空间上非线性算子方程f(x)=0的Newton类方法的收敛性.利用优函数原理,在A(x0)1f满足关于某一凸优函数的广义Lipschitz条件下,得到了Newton类方法的一个半局部收敛定理.同时,当f和A(x)及初始点x0给定时,针对广义Lipschitz条件构造了相应的优函数,推广了Newton类方法的相关结果.     

关于"圆盘定理的改进与弱连对角占优矩阵"一文的注记

本文指出《应用数学学报》中一文的错误,分析了产生错误的原因,同时给出修正的矩阵谱包含域及特征值定理,推广与改进了佟文廷（１９７７）以及叶伯英（１９８５）的相应结果。     

ON THE TITCHMARSH-WEYL THEORY OF ORDINARY SYMMETRIC ODD-ORDER DIFFERENTIAL EXPRESSIONS AND A DIRECT CONVERGENCE THEOREM

Abstract

In this paper the odd-order differential equation M[y] λ wy on the interval (O,∞), associated with the symmetric differential expression M of (2k-1)st order (k ≥ 2) with w a positive weight function and λ a complex number, is shown to possess k-Titchmarsh-Weyl solutions for every non-real λ in the underlying Hilbert space L² _w(O, ∞) having identical representation for every non-real λ. In terms of these solutions the Green's function associated with the singular boundary value problem is shown to possess identical representation for all non-real λ which has been further made use of in the third-order case to establish a direct convergence eigenfunction expansion theorem. The symmetric spectral matrix appearing in the expansion theorem has been characterized in terms of the Titchmarsh-Weyl m-coefficients.     

关于Lax-Milgram定理和Cea定理的一个注记

本文研究抽象变分问题（不必要求具有强制性）的Galerhin方法，利用泛函分析理论证明了：若变分问题的Galerkin逼近问题存在唯一解，那么它本身的解存在唯一且可由Galerhin逼近解无限逼近的充要条件是其Galerkin逼近格式具有某种稳定性．此结果是对Lax-Milgram定理和Cea定理的补充，可以应用于不必具有强制性的变分问题．     

A THEOREM ON THE CONVERGENCE OF SUMS OF INDEPENDENT RANDOM VARIABLES

1 IntroductionThroughout this paperl {X., n 2 1} is assumed to be a sequence of independent randomvariables. Fn denotes the distribution function of the partial surns S. = Z Xk. As is known,k = 1oothe series Z X. is said to be essentially convergent (a.s.) if there exists a sequence of constantsn = 1oo{b., n 2 1} such that Z (X. -- 6.) a.s. converges. When this happens we writeClearlyFn(x) = G.(x -- B.). (l.2)Our problem stems from an old conjecture in Probabilistic Number Theory sugges…     

WEAK ORLICZ SPACE AND ITS CONVERGENCE THEOREMS

In this article, a class of weak Orlicz function spaces is defined and their basic properties are discused. In particular, for the sequences in weak Orlicz space, we establish several basic convergence theorems including bounded convergence theorem, control convergence theorem and Vitali-type convergence theorem and so on. Moreover, the conditional compactness of its subsets is also discussed.     

一类推广的控制收敛定理及其应用

本文研究了一类推广的控制收敛定理及其应用,利用对控制函数满足条件的修改,建立了推广的控制收敛定理,获得其在弱奇异性积分算子中的应用,简化了经典结论的证明.     

弱型及加权弱拟(1,1)型算子的有界性

在这篇文章中 ,我们介绍了拟 (1 ,1 )型算子T ,给出了它的弱有界性和加权弱有界性     

适应性滤波器的强收敛速度

适应性滤波器的收敛性问题已经被许多学者研究.问题可以叙述如下.设{y_n}和{(?)_n}分别是输出信号和参考信号,欲求一序列{x_n},使其在每一时刻 n,y_n 被 x_n 加权,并且在     

SOME RESEARCHES ON WEAK CONVERGENCE OF KERGIN INTERPOLATION

The aim of this paper is to study the weak integral convergence of Kergin interpolation. The results of the weighted integral convergence and the weighted （partial） derivatives integral convergence of Kergin interpolation polynomial for the smooth functions on the unit disk were obtained in the paper. Those generalized Liang＇s main results were acquired in 1998 to the more extensive situation. At the same time, the estimation of convergence rate of Kergin interpolation polynomial is given by means of introducing a new kind of smooth norm.     

Gerschgorin型定理与奇异束特征值的扰动

Wilkinson曾举例说明,微小扰动可以任意地改变一个奇异束的特征值;同时他又举出下面的例子,说明事情的另一个方面。 例1.1.考虑矩阵对     

弱Hopf代数上的Militaru-Stefan提升定理

本文研究了弱Hopf-Galois扩张的扩张模.利用忠实平坦的弱Hopf-Galois扩张理论,研究了弱Hopf代数上的Militaru-Stefan提升定理,推广了文献[10]中的相应结果.进一步地,通过诱导模的自同态环的cleft扩张刻画了弱稳定模.     

ON THE RATES OF CONVERGENCE IN THE CENTRAL LIMIT THEOREM FOR TWO－PARAMETER MARTINGALE DIFFERENCES

ＯＮＴＨＥＲＡＴＥＳＯＦＣＯＮＶＥＲＧＥＮＣＥＩＮＴＨＥＣＥＮＴＲＡＬＬＩＭＩＴＴＨＥＯＲＥＭＦＯＲＴＷＯ－ＰＡＲＡＭＥＴＥＲＭＡＲＴＩＮＧＡＬＥＤＩＦＦＥＲＥＮＣＥＳ￥（龙红卫）ＬｏｎｇＨｏｎｇｗｅｉ（ＩｎｓｔｉｔｕｔｅｏｆＭａｔｈｅｍａｔｉｃａｌ...     

ON CONVEX SOBOLEV INEQUALITIES AND THE RATE OF CONVERGENCE TO EQUILIBRIUM FOR FOKKER-PLANCK TYPE EQUATIONS

It is well known that the analysis of the large-time asymptotics of Fokker-Planck type equations by the entropy method is closely related to proving the validity of convex Sobolev inequalities. Here we highlight this connection from an applied PDE point of view.

In our unified presentation of the theory we present new results to the following topics: an elementary derivation of Bakry-Emery type conditions, results concerning perturbations of invariant measures with general admissible entropies, sharpness of convex Sobolev inequalities, applications to non-symmetric linear and certain non-linear Fokker-Planck type equations (Desai-Zwanzig model, drift-diffusion-Poisson model).     

Calderon-Zygmund型算子在加权Herz型Hardy空间上的弱型估计

本文引入了加权弱Herz型Hardy空间，并证明了当a=n(1-1/q) δ时，胡国恩和陆善镇等在文[1]中所考虑的两类Calderon-Zygmund型算子分别连续地映加权Herz型Hardy空间到加权弱Herz空间和加权弱Herz型Hardy空间。