ON THE NUMBER OF LIMIT CYCLES OF A POLYNOMIAL DIFFERENTIAL SYSTEM

In this paper, we employ qualitative analysis and methods of bifurcation theory to study the maximum number of limit cycles for a polynomial system with center in global bifurcation.     

EXISTENCE OF POSITIVE SOLUTIONS TO SINGULAR SUBLINEAR SEMIPOSITONE NEUMANN BOUNDARY VALUE PROBLEM

The existence of positive solutions to a singular sublinear semipositone Neumann boundary value problem is considered. In this paper,the nonlinearity term is not necessary to be bounded from below and the function q(t) is allowed to be singular at t = 0 and t = 1.     

重积分和线面积分中的一个典型题目

针对授课班级出错率较高的一道曲面积分题目,给出四种解法.分析出错的原因在于练习不够外,主要是对重积分概念理解不够透彻.     

On the Ferrers property of valued interval orders

We study the relationship between the Ferrers property and the notion of interval order in the context of valued relations. Given a crisp preference structure without incomparability, the strict preference relation satisfies the Ferrers property if and only if the associated weak preference relation does. These conditions characterize a total interval order. For valued relations the Ferrers property can be written in two different and non-equivalent ways. In this work, we compare these properties by finding the kind of completeness they imply. Moreover, we study whether they still characterize a valued total interval orders.     

A centrosymmetric chaos

Symmetry plays an important part in the research of the dynamical behavior of nonlinear system. It is proved in this paper that, for a class of centrosymmetric systems with parametric excitation, chaos behaves in centrosymmetric manner, which implies that chaos need not to be an unsymmetric dynamical state. The project supported by National Natural Science Foundation of China     

Boundedness of higher order commutators of generalized fractional integral operators on Hardy spaces

Let Tμ,b,m be the higher order commutator generated by a generalized fractional integral operator Tμ and a BMO function b. In this paper, we will study the boundedness of Tμ,b,m on classical Hardy spaces and Herz-type Hardy spaces.     

ON J-SELFADJOINT EXTENSION OF THE PRODUCT OF TWO nTH-ORDER J-SYMMETRIC ORDINARY DIFFERENTIAL OPERATORS ON [a,b]

The problem of J-selfadjointness of the product of two nth-order J-symmetric operators on [a,b] is studied. We give a condition to ensure that the product operator is a J-selfadjoint extension.     

Entangled network and quantum communication

A theoretical scheme is introduced to generate entangled network via Dzyaloshinskii-Moriya (DM) interaction. The dynamics of entanglement between different nodes, which is generated by direct or indirect interaction, is investigated. It is shown that, the direction of (DM) interaction and the locations of the nodes have a sensational effect on the degree of entanglement. The minimum entanglement generated between all the nodes is quantified. The upper and lower bounds of the entanglement depend on the direction of DM interaction, and the repetition of the behavior depends on the strength of DM. The generated entangled nodes are used as quantum channel to perform quantum teleportation, where it is shown that the fidelity of teleporting unknown information between the network members depends on the locations of the members.     

Banks’ criterion and symmetric stable laws with index of stability between one-half and one

In this paper we compare the sample mean and the sample median of independent and identically distributed data that come from a symmetric stable distribution using Banks’ (1997) criterion, which is an alternative to Pitman’s (1937) criterion for comparing estimators of a parameter of interest. For data from a symmetric stable distribution with index of stability between one half and one and odd sample size, we show that Banks’ criterion choses the sample median as an estimator of the location parameter of the distribution. For data from a normal distribution with even sample size, we show that Banks’ criterion favours the sample mean (thus “complementing” a similar result about odd sample sizes in Karunaratne and Hadjicostas (2009)). In the process, we prove some trigonometric inequalities, which are interesting in their own right.     

Ap和Hp空间的乘子

给出了关于Ａ^p和Ｈ^p空间系数乘子的一些结果