ON TWO CONJECTURES OF THE QUADRATIC DIFFERENTIAL SYSTEMS

ＯＮＴＷＯＣＯＮＪＥＣＴＵＲＥＳＯＦＴＨＥＱＵＡＤＲＡＴＩＣＤＩＦＦＥＲＥＮＴＩＡＬＳＹＳＴＥＭＳＺＨＡＮＧＸＩＡＮＧ＊ＡｂｓｔｒａｃｔＭａｎｕｓｃｒｉｐｔｒｅｃｅｉｖｅｄＳｅｐｔｅｍｂｅｒ２９，１９９５．＊ＩｎｓｔｉｔｕｔｅｏｆＭａｔｈｅｍａｔｉｃ...     

ASYMPTOTIC STABILITY FOR A CLASS OF NONAUTONOMOUS NEUTRAL DIFFERENTIAL EQUATIONS

ＡＳＹＭＰＴＯＴＩＣＳＴＡＢＩＬＩＴＹＦＯＲＡＣＬＡＳＳＯＦＮＯＮＡＵＴＯＮＯＭＯＵＳＮＥＵＴＲＡＬＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳ＊＊ＹＵＪＩＡＮＳＨＥ＊ＭａｎｕｓｃｒｉｐｔｒｅｃｅｉｖｅｄＪｕｌｙ４，１９９５．ＲｅｖｉｓｅｄＭａｒｃｈ２...     

INITIAL VALUE PROBLEMS FOR SECOND ORDER IMPULSIVE INTEGRO-DIFFERENTIAL EQUATIONS IN BANACH SPACES

ＩＮＩＴＩＡＬＶＡＬＵＥＰＲＯＢＬＥＭＳＦＯＲＳＥＣＯＮＤＯＲＤＥＲＩＭＰＵＬＳＩＶＥＩＮＴＥＧＲＯ┐ＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＩＮＢＡＮＡＣＨＳＰＡＣＥＳ＊＊ＧＵＯＤＡＪＵＮ＊ＡｂｓｔｒａｃｔＭａｎｕｓｃｒｉｐｔｒｅｃｅｉｖｅｄＪｕ...     

STABILITY OF MAJORLY EFFICIENT POINTS AND SOLUTIONS IN MULTIOBJECTIVE PROGRAMMING

ＳＴＡＢＩＬＩＴＹＯＦＭＡＪＯＲＬＹＥＦＦＩＣＩＥＮＴＰＯＩＮＴＳＡＮＤＳＯＬＵＴＩＯＮＳＩＮＭＵＬＴＩＯＢＪＥＣＴＩＶＥＰＲＯＧＲＡＭＭＩＮＧＧＵＧＵＯＨＵＡＡＮＤＨＵＹＵＤＡ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓａｎｄＭｅｃｈａｎｉｃｓ...     

TWO NEW CONSTRUCTIONS OF CARTESIAN AUTHENTICATION CODES FROM SYMPLECTIC GEOMETRY

ＴＷＯＮＥＷＣＯＮＳＴＲＵＣＴＩＯＮＳＯＦＣＡＲＴＥＳＩＡＮＡＵＴＨＥＮＴＩＣＡＴＩＯＮＣＯＤＥＳＦＲＯＭＳＹＭＰＬＥＣＴＩＣＧＥＯＭＥＴＲＹＧＡＯＹＯＵＡＮＤＺＯＵＺＥＮＧＪＩＡ（ＤｅｐａｒｔｍｅｎｔｏｆＢａｓｉｃＳｃｉｅｎｃｅ，Ｎｏｒｔｈｅａｓｔ...     

ESSENTIALLY NORMAL SMALL COMPAC=STRONGLY IRREDUCIBLE

ＥＳＳＥＮＴＩＡＬＬＹＮＯＲＭＡＬ＋ＳＭＡＬＬＣＯＭＰＡＣ＝ＳＴＲＯＮＧＬＹＩＲＲＥＤＵＣＩＢＬＥＪＩＪＯＵＱＩＮＧ＊ＪＡＮＧＣＨＵＮＬＡＮ＊ＷＡＮＧＺＯＮＧＹＡＯ＊＊ＡｂｓｔｒａｃｔＧｉｖｅｎａｎｅｓｓｅｎｔｉａｌｙｎｏｒｍａｌｏｐｅｒａｔｏｒＴｗ...     

NEW SYMPLECTIC MAPS： INTEGRABILITY AND LAX REPRESENTATION

ＮＥＷＳＹＭＰＬＥＣＴＩＣＭＡＰＳ：ＩＮＴＥＧＲＡＢＩＬＩＴＹＡＮＤＬＡＸＲＥＰＲＥＳＥＮＴＡＴＩＯＮ＊＊＊ＺＥＮＧＹＵＮＢＯ＊ＬＩＹＩＳＨＥＮ＊＊ＭａｎｕｓｃｒｉｐｔｒｅｃｅｉｖｅｄＪｕｎｅ２６,１９９５．＊ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭ...     

AN IMPROVEMENT OF A RESULT OF IVOCHKINA AND LADYZHENSKAYA ON A TYPE OF PARABOLIC MONGE-AMPèRE EQUATION

ＡＮＩＭＰＲＯＶＥＭＥＮＴＯＦＡＲＥＳＵＬＴＯＦＩＶＯＣＨＫＩＮＡＡＮＤＬＡＤＹＺＨＥＮＳＫＡＹＡＯＮＡＴＹＰＥＯＦＰＡＲＡＢＯＬＩＣＭＯＮＧＥ┐ＡＭＰＥＲＥＥＱＵＡＴＩＯＮＷＡＮＧＲＯＵＨＵＡＩ＊ＷＡＮＧＧＵＡＮＧＬＩ＊ＡｂｓｔｒａｃｔＭａｎｕｓｃ...     

UNIFORM STABILITY AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF 2-DIMENSIONAL MAGNETOHYDRODYNAMICS EQUATIONS

ＵＮＩＦＯＲＭＳＴＡＢＩＬＩＴＹＡＮＤＡＳＹＭＰＴＯＴＩＣＢＥＨＡＶＩＯＲＯＦＳＯＬＵＴＩＯＮＳＯＦ２－ＤＩＭＥＮＳＩＯＮＡＬＭＡＧＮＥＴＯＨＹＤＲＯＤＹＮＡＭＩＣＳＥＱＵＡＴＩＯＮＳＺＨＡＮＧＬＩＮＧＨＡＩＭａｎｕｓｃｒｉｐｔｒｅｃｅｉｖｅｄＪｕ...     

ALMOST PERIODIC SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS WITH PIECEWISE CONSTANT ARGUMENT

ＡＬＭＯＳＴＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＳＯＦＬＩＮＥＡＲＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＷＩＴＨＰＩＥＣＥＷＩＳＥＣＯＮＳＴＡＮＴＡＲＧＵＭＥＮＴＹＵＡＮＲＯＮＧＨＯＮＧＪＩＡＬＩＮＭａｎｕｓｃｒｉｐｔｒｅｃｅｉｖｅｄＪｕ...     

非退化扩散过程的水平集和极集

设X(t)(t∈R )是一个d维非退化扩散过程．本文得到了比原有结果更一般的非退化扩散过程极性的充分条件,证明了对任意u∈Rd,紧集E(0, ∞),有若d=1,则对任意紧集F(?)R, 若d≥2,则对任意紧集E ∈(0, ∞), 其中B(Rd)为Rd上的Borel σ-代数,dim和Dim分别表示Hausdorff维数和Packing 维数．     

THE SECTIONS OF ODD UNIVALENT FUNCTIONS

Let $\[{S_k}\]$ be the class of functions $\[f(z) = z + \sum\limits_{m = 1}^\infty {b_{mk + 1}^{(k)}{z^{mk + 1}}} \]$ which are regular and univalent in $\[\left| z \right| < 1\]$ and denote $\[S_n^{(k)}(z) = z + \sum\limits_{m = 1}^\infty {b_{mk + 1}^{(k)}{z^{mk + 1}}} \]$. The authors prove that the functions $\[S_n^{(2)}(z)\]$ are starlike in $\[\left| z \right| < \frac{1}{{\sqrt 3 }}\]$.     

${\mbox{\boldmath $R$}}^N$上奇异非线性多调和方程的正整体解

本文研究形如△((△nu)(p-1) )=f(|x|,u,|(?)u|)u-β,x∈RN的奇异非线性多调和方程在RN上的正整体解,此处P>1,β≥0是常数,n是自然数,f:R × R ×R →R 是一个连续函数, ξδ*:=sign(ξ)·|ξ|δ,,ξ∈R,δ>0,给出了该类方程具有无穷多个其渐进阶刚好为|x|2n的正整体解的充分条件与必要条件.这些结论可以推广到更一般的方程.     

有向跳图的生成欧拉子有向图

一个有向多重图D的跳图$J(D)$是一个顶点集为$D$的弧集,其中$(a,b)$是$J(D)$的一条弧当且仅当存在有向多重图$D$中的顶点$u_1$, $v_1$, $u_2$, $v_2$,使得$a=(u_1,v_1)$, $b=(u_2,v_2)$ 并且$v_1\neq u_2$.本文刻画了有向多重图类$\mathcal{H}_1$和$\mathcal{H}_2$,并证明了一个有向多重图$D$的跳图$J(D)$是强连通的当且仅当$D\not\in \mathcal{H}_1$.特别地, $J(D)$是弱连通的当且仅当$D\not\in \mathcal{H}_2$.进一步, 得到以下结果: (i) 存在有向多重图类$\mathcal{D}$使得有向多重图$D$的强连通跳图$J(D)$是强迹连通的当且仅当$D\not\in\mathcal{D}$. (ii) 每一个有向多重图$D$的强连通跳图$J(D)$是弱迹连通的,因此是超欧拉的. (iii) 每一个有向多重图D的弱连通跳图$J(D)$含有生成迹.     

关于p-叶星形性和强星形性的充分条件 (英)

本文利用微分从属的方法得到了单位圆盘内p-叶星形函数和强星形函数的某些充分条件．     

Oscillation Theory of $h$-fractional Difference Equations

In this paper, we initiate the oscillation theory for $h$-fractional difference equations of the form \begin{equation*} \begin{cases} _{a}\Delta^{\alpha}_{h}x(t)+r(t)x(t)=e(t)+f(t,x(t)),\ \ \ t\in\mathbb{T}_{h}^{a},\ \ 1<\alpha<2,\x(a)=c_{0},\ \ \Delta_{h}x(a)=c_{1},\ \ \ c_{0}, c_{1}\in\mathbb{R}, \end{cases} \end{equation*} where $_{a}\Delta^{\alpha}_{h}$ is the Riemann-Liouville $h$-fractional difference of order $\alpha,$ $\mathbb{T}_{h}^{a}:=\{a+kh, k\in\mathbb{Z^{+}}\cup\{0\}\},$ and $a\geqslant0,$ $h>0.$ We study the oscillation of $h$-fractional difference equations with Riemann-Liouville derivative, and obtain some sufficient conditions for oscillation of every solution. Finally, we give an example to illustrate our main results.     

奇异非线性$p-$调和方程的一类正整体解

设p>1,β≥0是常数, n是自然数, 是一个连续函数.本文研究形如的奇异非线性p-调和方程的正整体解,给出了该类方程具有无穷多个其渐近阶刚好为|x|(2n-2)(当|x|→∞时)的径向对称的正整体解的若干充分条件.     

Asymptotics of Laurent Polynomials of Odd Degree Orthogonal with Respect to Varying Exponential Weights

Let denote the linear space over spanned by . Define the (real) inner product , where V satisfies: (i) V is real analytic on ; (ii) ; and (iii) . Orthogonalisation of the (ordered) base with respect to yields the even degree and odd degree orthonormal Laurent polynomials , and . Define the even degree and odd degree monic orthogonal Laurent polynomials: and . Asymptotics in the double-scaling limit such that of (in the entire complex plane), , and (in the entire complex plane) are obtained by formulating the odd degree monic orthogonal Laurent polynomial problem as a matrix Riemann-Hilbert problem on , and then extracting the large-n behaviour by applying the non-linear steepest-descent method introduced in [1] and further developed in [2],[3].     

线性约束下Hermite-广义反Hamilton矩阵的最佳逼近问题

本文利用对称向量与反对称向量的特征性质,给出了约束矩阵集合非空的充分必要条件及矩阵的一般表达式.运用空间分解理论和闭凸集上的逼近理论,得到了任一n阶复矩阵在约束矩阵集合中的惟一最佳逼近解.     

SINGULAR BOUNDARY PROPERTIES OF HARMONIC FUNCTIONS AND FRACTAL ANALYSIS

ＳＩＮＧＵＬＡＲＢＯＵＮＤＡＲＹＰＲＯＰＥＲＴＩＥＳＯＦＨＡＲＭＯＮＩＣＦＵＮＣＴＩＯＮＳＡＮＤＦＲＡＣＴＡＬＡＮＡＬＹＳＩＳＷＥＮＺＨＩＹＩＮＧＺＨＡＮＧＹＩＰＩＮＧＭａｎｕｓｃｒｉｐｔｒｅｃｅｉｖｅｄＪａｎｕａｒｙ１１，１９９５．Ｒｅｖｉ...