SG~4上Poisson方程的Dirichlet问题

考察具有D-4对称性的立体Sierpinski垫片,定义其上的Laplacian,给出Green函数,从而解决了立体Sierpinski垫片上的Poisson方程的Dirichlet问题.     

Bakry-■mery里奇曲率下的Calabi-型定理

得到了两个关于黎曼流形上Bakry-■mery里奇曲率沿着测地线的积分估计.作为应用,得到了两个Calabi定理的推广结果,即得到了流形是紧致的充分条件.     

C~n中单位球上一般Hardy型空间的几种等价刻画

设p 0, S≥0, q+n≥0, q+s≥0,本文探讨了C~n中单位球B上一般Hardy型空间H~(p,q,s)(B)的几种等价刻画.同时,本文还给出了单位球内双变点球面积分所有情形的双向估计.     

与马猜想有关的一类不定方程

设$p$是奇素数, $b,t,r\in{\rm N}$. 1992 年, 马少麟猜想丢番图方程 $x^2=2^{2b+2}p^{2t}-2^{b+2}p^{t+r}+1$有唯一的正整数解$(x,b,p,t,r)=(49,3,5,1,2)$, 并且证明了这个猜想蕴含McFarland关于乘子为$-1$ 的阿贝尔差集的猜想.在[Ma S L, MaFarland''conjecture on Abelian difference sets with multiplier-1[J]. {\it Designs, Codes and Cryptography,} 1992, 1:321--332.]中, 马少麟证明了: 若$t\geq r$,则丢番图方程$x^2=2^{2b+2}p^{2t}-2^{b+2}p^{t+r}+1$没有正整数解. 本文证明了: 若$a>1$是奇数,$t\geq r$, 那么丢番图方程$x^2=2^{2b+2}a^{2t}-2^{b+2}a^{t+r}+1$的正整数解由$t=r=1, x+a\sqrt{2^{b+2}(2^b-1)}=(2^{b+1}-1+\sqrt{2^{b+2}(2^b-1)})^{n}$给出, 其中$n$为奇数.作者也证明了: 若$p$是奇素数, 则$(x,b,p,t,r)=(7,3,5,1,2)$是丢番图方程$x^4=2^{2b+2}p^{2t}-2^{b+2}p^{t+r}+1$的唯一正整数解.     

关于丢番图方程(an)x+(bn)y=(cn)z

设n,a,b,c是正整数,gcd(a,b,c)=1,a,b≥3,且丢番图方程a~x+b~y=c~z只有正整数解(x,y,z)=(1,1,1).证明了若(x,y,z)是丢番图方程(an)~x+(bn)~y=(cn)~z的正整数解且(x,y,z)≠(1,1,1),则yzz或xzy.还证明了当(a,b,c)=(3,5,8),(5,8,13),(8,13,21),(13,21,34)时,丢番图方程(an)~x+(bn)~y=(cn)~z只有正整数解(x,y,z)=(1,1,1).     

多线性强奇异Calderón-Zygmund算子的多线性迭代交换子的Sharp极大和加权估计

本文主要建立了由多线性强奇异Calderón-Zygmund算子和BMO函数生成的多线性迭代交换子的Sharp极大估计.作为应用,也分别得到了该类多线性迭代交换子在乘积加权Lebesgue空间和乘积变指数Lebesgue空间上的有界性.     

KAM理论与Arnol'd扩散: Hamilton系统的动力学稳定性问题

1 引言 物理、天文与力学中的许多问题的数学模型归结为Hamilton方程.这种方程由Hamilton量H=H(p,q,t)所决定: dq/dt=H/p,dp/dt=-H/q,q∈R~(2n),H一般代表能量,n是系统自由度数,p表示作用量,在许多问题中q表示角变     

Cn空间中积分表示的一种新技巧

给出Cⁿ空间中积分表示的一种新技巧.应用这种技巧,可以得到Cⁿ空间中强拟凸域上光滑函数新的积分公式和 ¶ -方程解的新的积分表示, 这些新的公式都比原有的公式简单,尤其是 ¶-方程的解更有简单的一致估计. 而且这种新的技巧, 还可进一步应用到Cn空间中任意有界域上, 使所有相应的公式都可得到简化.     

正则乘子Hopf代数上Yetter-Drinfel''d模范畴中的自同构代数

本文研究了正则乘子Hopf代数上Yetter-Drinfel''d模范畴中自同构代数的问题.利用乘子Hopf代数以及同调代数理论中的方法,获得了Yetter-Drinfel''d模范畴中两个自同构代数是同构的结果,推广了Panaite等人在Hopf代数中的结果.     

非退化Cauchy-Riemann流形上¶b复形的正则性

对于余维数大于1的CR流形M 上的一点ξ , M 在ξ 附近的CR结构可由两步幂零Lie群G_ξ的CR结构来逼近.G_ξ随ξ变化而变化.M 上的¶_b和¶_b可由两步幂零Lie群上的¶_b和¶_b逼近.用两步幂零Lie群上¶_b的拟基本解构造非退化CR流形M上¶_b的拟基本解,并定义M 上的拟距离.¶_b和¶_b复形的正则性可从M 上的调和分析得到.     

A more accurate multidimensional Hardy-Hilbert''s inequality

In this paper, by the use of the weight coefficients, the transfer formula, Hermite-Hadamard''s inequality and the technique of real analysis, a more accurate multidimensional Hardy-Hilbert''s inequality with multi-parameters and a best possible constant factor is given, which is an extension of some published results. Moreover, the equivalent forms and the operator expressions are considered.     

Fej\''{e}r type inequalities for Harmonically-convex functions with applications

In this paper, a new weighted identity involving harmonically symmetric functions and differentiable functions is established. By using the notion of harmonic symmetricity, harmonic convexity and some auxiliary results, some new Fej\''{e}r type integral inequalities are presented. Applications to special means of positive real numbers are given as well.     

Cohen-Fischman-Westreich's Double Centralizer Theorem for Almost-triangular Hopf Algebras

In this paper, the authors study the Cohen-Fischman-Westreich''s double centralizer theorem for triangular Hopf algebras in the setting of almost-triangular Hopf algebras.     

Lie symmetry analysis to Fisher''s equation with time fractional order

The aim of this letter is to apply the Lie group analysis method to the Fisher''s equation with time fractional order. We considered the symmetry analysis, explicit solutions to the time fractional Fisher''s(TFF) equations with Riemann-Liouville (R-L) derivative. The time fractional Fisher''s is reduced to respective nonlinear ordinary differential equation(ODE) of fractional order. We solve the reduced fractional ODE using an explicit power series method.     

Sub-manifold and traveling wave solutions of Ito''s 5th-order mKdV equation

In this paper, we study Ito''s 5th-order mKdV equation with the aid of symbolic computation system and by qualitative analysis of planar dynamical systems. We show that the corresponding higher-order ordinary differential equation of Ito''s 5th-order mKdV equation, for some particular values of the parameter, possesses some sub-manifolds defined by planar dynamical systems. Some solitary wave solutions, kink and periodic wave solutions of the Ito''s 5th-order mKdV equation for these particular values of the parameter are obtained by studying the bifurcation and solutions of the corresponding planar dynamical systems.     

$C_2 \oplus C_{2n}$上零和自由序列的结构

已知在任意有限循环群中, 一个零和自由序列的长度超过其Davenport常数的一半时, 该序列是光滑的. 本文给出了一类非循环阿贝尔群$C_2 \oplus C_{2n}$上 长度不小于$n+3$的零和自由序列的结构及性质.     

Rosenthal’s Inequalities for Asymptotically Almost Negatively Associated Random Variables Under Upper Expectations

In this paper, the authors generalize the concept of asymptotically almost \linebreak negatively associated random variables from the classic probability space to the upper expectation space. Within the framework, the authors prove some different types of Rosenthal''s inequalities for sub-additive expectations. Finally, the authors prove a strong law of large numbers as the application of Rosenthal''s inequalities.     

On a reverse Hardy-Littlewood-Polya''s inequality

By the use of the weight coefficients, the idea of introduced parameters and Euler-Maclaurin summation formula, a reverse Hardy-Littlewood-Polya''s inequality with parameters as well as the equivalent forms are provided. The equivalent statements of the best possible constant factor related to a few parameters and some particular cases are given.     

Effective construction of Poincar\''e--Bendixson regions

This paper deals with the problem of location and existence of limit cycles for real planar polynomial differential systems. We provide a method to construct Poincar\''e--Bendixson regions by using transversal curves, that enables us to prove the existence of a limit cycle that has been numerically detected. We apply our results to several known systems, like the Brusselator one or some Li\''{e}nard systems, to prove the existence of the limit cycles and to locate them very precisely in the phase space. Our method, combined with some other classical tools can be applied to obtain sharp bounds for the bifurcation values of a saddle-node bifurcation of limit cycles, as we do for the Rychkov system.