Schur不等式和Hoelder不等式及其应用

Schur不等式和Hoelder不等式是两个重要的不等式，本讲我们介绍Schur不等式和Hoelder不等式及其应用．     

Wiener过程在Hoelder范数下的泛函重对数定律

本文借助于Hoelder范数在函数空间中诱导出的强拓扑下的大偏差公式，得到了Wiener过程在Hoelder范数下的泛函重对数定律．     

Regularity for P-Harmonic Type Systems with the Gradients below the Controllable Growth

In this paper, we shall establish that each weak solution of p-harmonic type systems with the gradients below the controllable growth belongs to, Holder continuity spaces with any HSlder exponent α∈ [0, 1）. Furthermore, we can obtain that the gradients of the corresponding weak solutions also belong to locally Hoelder continuity spaces with some Hoelder exponent. Keywords controllable growth, p-harmonic systems, full regularity MR（2000） Subject Classification 35J60, 35B65     

Ap权反向Hoelder不等式的注记

本文指出[1]中关于Ap权反向Hoelder不等式的证明有误并给出一个正确的证明．     

一类非齐次A-调和方程组很弱解的性质

该文应用Hodge分解定理，得到了非齐次A—调和方程组-Di(A^ij(x,Du)) Difj(i(x)=0,j=1,…，m的很弱解是弱解，进一步，利用Morrey空间法与Campanato空间法以及齐次化方法，作者得出了该方程的很弱解是局部Hoelder连续的，并且得出了Hoelder连续指数μ与λ之间的多值函数关系式．     

三角形退缩椭园组弱解的全局正侧性

In this paper,using direct method,we prove the golbal Hoelder continuiy of teak solutions to degenerate eliptic systems in triangular form.     

非线性渗流方程分界面的正则性

本文用Harnack不等式研究了具有非线性源和对流项的一般渗流方程正解分界面的Hoelder连续性。     

关于耦合反应扩散系统解的整体存在性

利用对偶性技巧及Hoelder不等式，证明了一类耦合反应扩散系统解的整体存在性，推广了相关结果．     

Functional Modulus of Continuity for Brownian Motion in Holder Norm

The author establishes a large deviation for κ-dimensional Brownian motion B in stronger topology, by which the functional modulus of continuity for B in Hoelder norm can be obtained.     

Koch曲线的级数展开式

本文给出Koch曲线的级数展开式，利用这一展开式证明了Koch曲线满足指数为α=log3/log4的Hoelder条件和处处不可微。     

一类分形函数及其维数估计

本文作者首先借助于b进制分数及无穷级数构造了一类分形函数,然后研究了这些函数图象的分形维数及其Hoelder性质,得到了一些维数结果。     

一阶Hoelder条件下带参数的修正型Euler—Halley迭代族的局部收敛性

The convergence problem of the family of the deformed Euler-Halley iterations with parameters for solving nonlinear operator equations in Banach spaces are studied. Under the assumption that the derivative of an operator satisfies the Hoelder condition， the local convergence of order 1 p of the family of the deformed Euler-Halley iterations are established.     

一类具有脉冲的时滞神经网络模型周期解的存在性和稳定性

By using the continuation theorem of Mawhin＇s coincidence degree theory, Hoelder inequality and some analysis techniques, some effective results are obtained ensuring existence and global exponential stability of periodic solutions in delayed cellular neural networks with impulses. An illustrative example is given to demonstrate the effectiveness of the obtained results.     

无界区域上Cauchy型奇异积分算子的性质

On the basis of introducing the modified Cauchy kernel, we discuss the Hoelder continuity of the Cauchy-type singular integral operator on unbounded domains for regular functions by dividing into the following three cases： two points are on the boundary of region; one point is on the boundary and another point is in the interior（or exterior） of the region; two points are in the interior （or exterior） of the region.     

A-调和逼近方法和具有可控增长条件的非线性椭圆方程组最优内部部分正则性

考虑具有可控增长条件的非线性椭圆方程组弱解的部分正则性．利用Duzaar和Grotowski引进的弱解部分正则性证明的新方法，该方法是建立在调和逼近技巧一般形式的基础上的，我们把前人的结果由自然增长条件推广到了可控增长条件，并且所得到的弱解导数的Hoelder指标是最优的．     

ON THE GENERALIZATIONS OF KALANDIA＇S LEMMA

Based on Bernstein＇s Theorem, Kalandia＇s Lemma describes the error estimate and the smoothness of the remainder under the second part of Hoelder norm when a HSlder function is approximated by its best polynomial approximation. In this paper, Kalandia＇s Lemma is generalized to the cases that the best polynomial is replaced by one of its four kinds of Chebyshev polynomial expansions, the error estimates of the remainder are given out under Hoeder norm or the weighted HSlder norms.     

THE NAGUMO EQUATION ON SELF－SIMILAR FRACTAL SETS

The Nagumo equationut ut=△u+bu(u-a)(1-u),t＞0 is investigated with initial data and zero Neumann boundary conditions on post-critically finite (p.c.f.) self-similar fractals that have regular harmonic structures and satisfy the separation condition. Such a nonlinear diffusion equation has no travelling wave solutions because of the“pathological” property of the fractal. However, it is shown that a global Hoelder continuous solution in spatial variables exists on the fractal considered. The Sobolev-type inequality plays a crucial role, which holds on such a class of p.c.f self-similar fractals. The heat kernel has an eigenfunction expansion and is well-defined due to a Weyl‘s formula. The large time asymptotic behavior of the solution is discussed, and the solution tends exponentially to the equilibrium state of the Nagumo equation as time tends to infinity if b is small.     

有循环极大子群的素数幂阶群的作用是边传递的图(II)

假定Γ是一个有限的、单的、无向的且无孤立点的图,G是Aut(Γ)的一个子群.如果G在Γ的边集合上传递,则称Γ是G-边传递图.我们完全分类了当G为一个有循环的极大子群的素数幂阶群时的G-边传递图.结果为:设图Γ含有一个阶为pn(p是素数,n≥2)的自同构群,且G有一个极大子群循环,则Γ是G-边传递的,当且仅当Γ同构于下列图之一1)pmK1,pn-1-m,0≤m≤n-1;2)pmK1,pn-m,0≤m≤n;3)pmKp,pn-m-1,0≤m≤n-2;4)pn-mCpm,pm≥3,m＜n;5)2n-2K1,1;6)pn-1-mCpm,pm≥3,m≤n-1;7)2pn-mCpm,pm≥3,m≤n-1;8)2pn-mK1,pm,0≤m≤n;9)pn-mK1,2pm,0≤m≤n;10)pn-mK2,pm,0＜m≤n;11)C(2pn-m,1,pm);12)pkC(2pm-k,1,pn-m),0＜k＜m,0＜m≤n;13)(t-s,2m)C(2m 1/(t-s,2m),1,2n-1-m),其中0≤m≤n-1,2n-2(s-1)≡0(mod 2m),t≡1(mod 2),s(≠)t(mod 2m),1≤s≤2m,1≤t≤2n-1;14)∪p i=1 Ci p n-1,其中Ci p n-1=Ca1a1 [1 (i-1)pn-2]a 1 2[1 (i--1)p n-2]…a 1 (pn-1-1)[1 (i-1)p n-2]≌Cp n-1,i=1,2,…,p;15)∪2 i=1 Ci 2n-1,其中Ci 2n-1=Ca1a 1 [1 (i-1)(2n-2-1)]a1 2[1 (i-1)(2n-2-1)]…a1 (2n-1-1)[1 (i-1)(2n-2-1)]≌C2n-1,i=1,2.     

从一道课本例题开始的研究性学习

在高中数学课本的《圆》这一章节中 ,有这么一道例题 :已知圆C的方程是x2 +y2 =r2 ,求证 :经过圆C上一点M(x1 ,y1 )的切线的方程是x1 x+y1 y=r2 .课本上给出的证明是 :方法一 :当OM与坐标轴都不垂直时 ,设直线OM的斜率为k1 ,切线斜率为k,根据圆的切线性质 ,得k=- 1k1 .因为k1 =y1 x1 ,所以k=- x1 y1 .于是经过点M(x1 ,y1 )的切线方程是 y-y1 =- x1 y1 (x-x1 ) .经过整理 ,得xx1 +yy1 =r2 .当OM垂直于x轴时 ,经过点M(x1 ,y1 )的切线方程是x =x1 ;当OM垂直于 y轴时 ,经过点M(x1 ,y1 )的切线方程是 y=y1 .显然分别是在y1 =0或x1 =0时 ,方…     

替换法巧解初中数学竞赛题

<正>2014年7月,我带领学生参加了由江苏省数学学会主办的初中数学奥林匹克培训班,学习了很多关于数学竞赛方面的知识,受益匪浅.通过整理、归纳,发现替换法可以巧解一些计算题,这种解题思路非常重要,下面看几个例子.一、相同的部分替换例1计算(1-1/2-1/3-1/4-1/5)(1/2+1/3+1/4+1/5+1/6)-(1-1/2-1/3-1/4-1/5-1/6)(1/2+1/3+1/4+1/5).分析本题如果直接运用乘法公式,展开的式子项比较多,非常复杂,书写起来也非常不方便,注意到这个题目里有相同的式子