ON THE EXISTENCE OF GLOBAL GENERAL SOLUTIONS OF POLYNOMIAL SYSTEMS

ＯＮＴＨＥＥＸＩＳＴＥＮＣＥＯＦＧＬＯＢＡＬＧＥＮＥＲＡＬＳＯＬＵＴＩＯＮＳＯＦ　ＰＯＬＹＮＯＭＩＡＬＳＹＳＴＥＭＳＺＨＡＯＸＩＡＯＱＩＡＮＧ（赵晓强）（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ｔｈｅＣｈｉｎｅｓｅＡｃａｄｅｍｙｏ...     

A NOTE ON THE GLOBAL SOLUTIONS OF A SEMILINEAR REACTION DIFFUSION SYSTEM

ＡＮＯＴＥＯＮＴＨＥＧＬＯＢＡＬＳＯＬＵＴＩＯＮＳＯＦＡＳＥＭＩＬＩＮＥＡＲＲＥＡＣＴＩＯＮＤＩＦＦＵＳＩＯＮＳＹＳＴＥＭ（王明新，吴永辉）￥ＷａｎｇＭｉｎｇｘｉｎ（Ｄｅｐｔ．ｏｆＭａｔｈｅｍａｔｉｃｓＭｅｃｈａｎｉｃｓ，ＳｏｕｔｈｅａｓｔＵｎｉｖ，...     

GLOBAL ANALYSIS OF AN EBENMAN＇S MODEL OF POPULATION WITH TWO COMPETING AGE CLASSES

ＧＬＯＢＡＬＡＮＡＬＹＳＩＳＯＦＡＮＥＢＥＮＭＡＮ＇ＳＭＯＤＥＬＯＦＰＯＰＵＬＡＴＩＯＮＷＩＴＨＴＷＯＣＯＭＰＥＴＩＮＧＡＧＥＣＬＡＳＳＥＳＬＩＵＷＥＩＭＩＮ（刘为民）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃａｌＳｃｉｅｎｃｅｓ，Ｉｎｄｉａｎａ...     

BOUNDARY LAYER ESTIMATION OF A SINGULAR PROBLEM WITH LIMIT EQUATION OF ORDER 2

ＢＯＵＮＤＡＲＹＬＡＹＥＲＥＳＴＩＭＡＴＩＯＮＯＦＡＳＩＮＧＵＬＡＲＰＲＯＢＬＥＭＷＩＴＨＬＩＭＩＴＥＱＵＡＴＩＯＮＯＦＯＲＤＥＲ２ＨＥＣＨＥＮＧ（何成）ＺＨＡＮＧＷＥＩＴＡＯ（张维弢）（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，Ｃｈｉｎｅ...     

ADMISSIBILITY OF LINEAR ESTIMATE OF REGRESSION COEFFICIENTS IN GROWTH CURVE MODEL UNDER MATRIX LOSS

ＡＤＭＩＳＳＩＢＩＬＩＴＹＯＦＬＩＮＥＡＲＥＳＴＩＭＡＴＥＯＦＲＥＧＲＥＳＳＩＯＮＣＯＥＦＦＩＣＩＥＮＴＳＩＮＧＲＯＷＴＨＣＵＲＶＥＭＯＤＥＬＵＮＤＥＲＭＡＴＲＩＸＬＯＳＳＷＡＮＧＸＵＥＲＥＮ（王学仁）（ＤｅｐａｒｔｍｅｎｔｏｆＳｔａｔｉｓｔｉｃｓ，...     

TOPOLOGICAL CLASSIFICATION OF NONAUTONOMOUS LINEAR SYSTEMS

ＴＯＰＯＬＯＧＩＣＡＬＣＬＡＳＳＩＦＩＣＡＴＩＯＮＯＦＮＯＮＡＵＴＯＮＯＭＯＵＳＬＩＮＥＡＲＳＹＳＴＥＭＳＳｈｉＪｉｎｌｉｎ（史金麟）（ＦｕｚｈｏｕＵｎｉｖｅｒｓｉｔｙ，福州大学，邮编：３５０００２）Ａｂｓｔｒａｃｔ：Ｔｏｐｏｌｏｇｉｃａｌｃｌａｓｓ...     

SPECTRAL SEQUENCES OF COHOMOLOGIES OF SINGULARITIES OF C∞ MAPPINGS

ＳＰＥＣＴＲＡＬＳＥＱＵＥＮＣＥＳＯＦＣＯＨＯＭＯＬＯＧＩＥＳＯＦＳＩＮＧＵＬＡＲＩＴＩＥＳＯＦＣ∞ＭＡＰＰＩＮＧＳＸＩＡＯＥＲＪＩＡＮＡｂｓｔｒａｃｔＴｗｏｓｐｅｃｔｒａｌｓｅｑｕｅｎｃｅｓａｒｅｄｅｆｉｎｅｄｒｅｓｐｅｃｔｉｖｅｌｙｆｏｒｃｏｈ...     

DISTRIBUTION OF THE (0,∞) ACCUMULATIVE LINES OF MEROMORPHHIC FUNCTIONS

ＤＩＳＴＲＩＢＵＴＩＯＮＯＦＴＨＥ（０，∞）ＡＣＣＵＭＵＬＡＴＩＶＥＬＩＮＥＳＯＦＭＥＲＯＭＯＲＰＨＨＩＣＦＵＮＣＴＩＯＮＳ￥ＷＵＳＨＥＮＧＪＩＡＮ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＢｅｉｊｉｎｇＵｎｉｖｅｒｓｉｔｙ，ＢｅｉＪｉｎｇ１...     

GLOBAL ATTRACTIVITY OF LINEAR NON－AUTONOMOUS NEUTRAL DIFFERENTIAL－DIFFERENCE EQUATIONS

ＧＬＯＢＡＬＡＴＴＲＡＣＴＩＶＩＴＹＯＦＬＩＮＥＡＲＮＯＮ－ＡＵＴＯＮＯＭＯＵＳＮＥＵＴＲＡＬＤＩＦＦＥＲＥＮＴＩＡＬ－ＤＩＦＦＥＲＥＮＣＥＥＱＵＡＴＩＯＮＳＨＥＸＵＥＺＨＯＮＧ（何学中）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，Ｎｉｎｇｘｉ...     

OPTIMAL GLOBAL RATES OF CONVERGENCE OF M－ESTIMATES FOR MULTIVARIATE NONPARAMETRIC REGRESSION

ＯＰＴＩＭＡＬＧＬＯＢＡＬＲＡＴＥＳＯＦＣＯＮＶＥＲＧＥＮＣＥＯＦＭ－ＥＳＴＩＭＡＴＥＳＦＯＲＭＵＬＴＩＶＡＲＩＡＴＥＮＯＮＰＡＲＡＭＥＴＲＩＣ　ＲＥＧＲＥＳＳＩＯＮＳＨＩＰＥＩＤＥ（施沛德）（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，ｔｈ...     

Dynamics of a Function Related to the Primes

Let n = p1p2 ··· pk, where pi(1 ≤ i ≤ k) are primes in the descending order and are not all equal. Let Ωk(n) = P(p1 + p2)P(p2 + p3) ··· P(pk-1+ pk)P(pk+ p1), where P(n) is the largest prime factor of n. Define w0(n) = n and wi(n) = w(wi-1(n)) for all integers i ≥ 1. The smallest integer s for which there exists a positive integer t such thatΩs k(n) = Ωs+t k(n) is called the index of periodicity of n. The authors investigate the index of periodicity of n.     

关于杨全会和陈永高提出的一个问题

对任意的正整数与集合,令为解的个数.杨全会和陈永高证明了:若整数且,则不存在集合使得对所有充分大的整数成立,其中.对整数和,定义为满足对所有整数成立的集合的个数.杨全会和陈永高证明了是有限的,且.同时,他们问对任意整数,是否存在使得对所有整数成立.在本文中,我们给出了在时的准确公式.从而推出在时成立.     

一类限制m元over-分拆同余式

We discuss a family of restricted m-ary overpartition functions bm,j （n）, which is the number of m-ary overpartitions of n with at most i ＋ j copies of the non-overlined part m^i allowed, and obtain a family of congruences for bm,lm-1 （n）.     

UNIFORM STRONG CONVERGENCE RATE OF NEAREST NEIGHBOR DENSITY ESTIMATION

Based on [3] and [4],the authors study strong convergence rate of the k_n-NNdensity estimate f_n(x)of the population density f(x),proposed in [1].f(x)>0 and fsatisfies λ-condition at x(0<λ≤2),then for properly chosen k_nlim sup(n/(logn)~(λ/(1 2λ))丨_n(x)-f(x)丨C a.s.If f satisfies λ-condition,then for propeoly chosen k_nlim sup(n/(logn)~(λ/(1 3λ)丨_n(x)-f(x)丨C a.s.,where C is a constant.An order to which the convergence rate of 丨_n(x)-f(x)丨andsup 丨_n(x)-f(x)丨 cannot reach is also proposed.     

LIMIT CYCLES OF THE GENERALIZED POLYNOMIAL LINARD DIFFERENTIAL SYSTEMS

Using the averaging theory of first and second order we study the maximum number of limit cycles of generalized Linard differential systems{x = y + εh_l~1(x) + ε~2h_l~2(x),y=-x- ε(f_n~1(x)y~(2p+1) + g_m~1(x)) + ∈~2(f_n~2(x)y~(2p+1) + g_m~2(x)),which bifurcate from the periodic orbits of the linear center x = y,y=-x,where ε is a small parameter.The polynomials h_l~1 and h_l~2 have degree l;f_n~1and f_n~2 have degree n;and g_m~1,g_m~2 have degree m.p ∈ N and[·]denotes the integer part function.     

ON A MULTILINEAR OSCILLATORY SINGULAR INTEGRAL OPERATOR （I）

ＯＮＡＭＵＬＴＩＬＩＮＥＡＲＯＳＣＩＬＬＡＴＯＲＹＳＩＮＧＵＬＡＲＩＮＴＥＧＲＡＬＯＰＥＲＡＴＯＲ（Ｉ）ＣＨＥＮＷＥＮＧＵＨＵＧＵＯＥＮＬＵＳＨＡＮＺＨＥＮＭａｎｕｓｃｒｉｐｔｒｅｃｅｉｖｅｄＯｃｔｏｂｅｒ１８，１９９４．ＲｅｖｉｓｅｄＤｅｃｅ...     

Higher Order Turán Inequalities

The celebrated Turán inequalities , where denotes the Legendre polynomial of degree , are extended to inequalities for sums of products of four classical orthogonal polynomials. The proof is based on an extension of the inequalities , which hold for the Maclaurin coefficients of the real entire function in the Laguerre-Pólya class, .

     

A Note on Bounds for the Supremum Metric for Discrete Random Variables

For positive or negative integer-valued random variables X and Y with finite second moments the inequality sup \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop {\sup }\limits_n |\Pr \{ X \le n\} - \Pr \{ Y \le n\} |\, \le \,|EX - EY| + \frac{1}{2}(EX(EX - 1) + (EY(Y - 1)) $\end{document} is established by elementary manipulation, and shown to be tight. Use of generating functions and an inversion formula yields the larger bound with 1/2 replaced by 2/π.     

Boundedness Characterization of Maximal Commutators on Orlicz Spaces in the Dunkl Setting

On the real line, the Dunkl operators$$D_{\nu}(f)(x):=\frac{d f(x)}{dx} + (2\nu+1) \frac{f(x) - f(-x)}{2x}, ~~ \quad\forall \, x \in \mathbb{R}, ~ \forall \, \nu \ge -\tfrac{1}{2}$$are differential-difference operators associated with the reflection group $\mathbb{Z}_2$ on $\mathbb{R}$, and on the $\mathbb{R}^d$ the Dunkl operators $\big\{D_{k,j}\big\}_{j=1}^{d}$ are the differential-difference operators associated with the reflection group $\mathbb{Z}_2^d$ on $\mathbb{R}^{d}$.In this paper, in the setting $\mathbb{R}$ we show that $b \in BMO(\mathbb{R},dm_{\nu})$ if and only if the maximal commutator $M_{b,\nu}$ is bounded on Orlicz spaces $L_{\Phi}(\mathbb{R},dm_{\nu})$. Also in the setting $\mathbb{R}^{d}$ we show that $b \in BMO(\mathbb{R}^{d},h_{k}^{2}(x) dx)$ if and only if the maximal commutator $M_{b,k}$ is bounded on Orlicz spaces $L_{\Phi}(\mathbb{R}^{d},h_{k}^{2}(x) dx)$.     

SOME GENERALIZATION OF GRONWALL-BIHARI INTEGRAL INEQUALITIES AND THEIR APPLICATIONS

The interest of this paper lies in the estimates of solutions of the three kinds of Gronwail-Bihari integral inequalities:(Ⅰ) y(x)≤f(x) sum from i=1 to n(g_i(x)integral from n=0 to x(h_i(d)y(s)ds)),(Ⅱ) y(x)≤f(x) g(x)φ(integral from n=0 to x(h(s)w(y(s))ds))(Ⅲ) y(x)≤f(x) sum from i=1 to n(g_i(x)integral from n=0 to a(h_i(s)y(s)ds g_(n 1)φ(integral from n=0 to x(h_(n 1)(s)w(y(t))ds)).The results include some modifications and generalizations of the results of D. Willett, U. D. Dhongade and Zhang Binggen. Furthermore, applying the conclusion on the above inequalities to a Volterra integral equation and a differential equation, the authors obtain some new better results.