Phase portraits of piecewise linear continuous differential systems with two zones separated by a straight line

This paper provides the classification of the phase portraits in the Poincaré disc of all piecewise linear continuous differential systems with two zones separated by a straight line having a unique finite singular point which is a node or a focus. The sufficient and necessary conditions for existence and uniqueness of limit cycles are also given.     

BOUNDEDNESS AND DISSIPATION FOR DYNAMIC EQUATIONS ON TIME SCALES

In this paper we investigate the boundedness and dissipation for dynamic equations on time scales. By using Lyapunov type function and its Dini-derivative, the boundedness and dissipation criteria for first-order IVP's are obtained. Some examples are given. Finally, we tentatively investigate convergence of the system.     

带对称齐次核的级数算子的范数刻画及其应用

对带对称齐次核K(m,n)的级数算子T:T{an}=Σ_(n=1)~∞ K(m,n)an,{an}∈lω(n),l={{an)| an≥0,Σ_(n=1)~∞ω(n)an<+∞},本文研究了T的范数刻画,并讨论其应用.     

涉及多个函数的Hardy型积分不等式

利用权系数方法和Fubini定理,研究涉及多个函数的Hardy型积分不等式,得到若干新的结果．     

On the nullity of bicyclic graphs

The nullity of a graph is the multiplicity of the eigenvalue zero in its spectrum. In this paper, we obtain the nullity set of bicyclic graphs of order n, and determine the bicyclic graphs with maximum nullity.     

Geometric ergodicity of the Gibbs sampler for the Poisson change-point model

Poisson change-point models have been widely used for modelling inhomogeneous time-series of count data. There are a number of methods available for estimating the parameters in these models using iterative techniques such as MCMC. Many of these techniques share the common problem that there does not seem to be a definitive way of knowing the number of iterations required to obtain sufficient convergence. In this paper, we show that the Gibbs sampler of the Poisson change-point model is geometrically ergodic. Establishing geometric ergodicity is crucial from a practical point of view as it implies the existence of a Markov chain central limit theorem, which can be used to obtain standard error estimates. We prove that the transition kernel is a trace-class operator, which implies geometric ergodicity of the sampler. We then provide a useful application of the sampler to a model for the quarterly driver fatality counts for the state of Victoria, Australia.     

Chaos expansion and asymptotic behavior of the Pareto distribution

We give the chaos expansion of a random variable with Pareto distribution and we analyze, by using the Malliavin calculus, the convergence in the distribution of a sequence of random variable with Pareto distribution toward the standard exponential law.     

Domain decomposition method for a system of quasivariational inequalities

We propose a domain decomposition method for a system of quasivariational inequalities related to the HJB equation. The monotone convergence of the algorithm is also established.     

两类健康评价指标的一致性研究

以我国第三次卫生服务调查中关于人群健康状况的数据为基础,研究了两类健康评价指标的一致性.一类是基于自评健康状况询问结果的主观定性数据,一类是基于包括慢性病患病率等五个指标的客观数据.一致性检验研究发现,尽管这两类指标均采用加权的方法构造,但对人群健康评价的结果却并不一致,从而提示在健康评价研究中指标选择的重要性.