多维非退化扩散过程的多重时集与多重点集的不可能性

设dX(t)=σ(X(t))dB(t)+β(X(t))dt为一非退化d(d≥3)维扩散过程.证明了:(i)3维非退化扩散过程没有4重时集和4重点集;(ii)4维非退化扩散过程没有3重时集和3重点集;(iii)5维以上的非退化扩散过程没有2重时集和2重点集.

稳定随机游动二重时集的离散Hausdorff维数

设{Xn}n>0是d维格子点上相应于正则变差函数b（n)=n^(1/8)S_(n)则的稳定随机游动,称 A_B^d={(n,m)∈Z^2 ,Xn=Xm,n<m} 为{Xn}m>0的二重时集,本文讨论了A_β~d的离散Hausdorff维数,并且在较弱的条件下证明了:dim_H(A_β~d)=^(a.s){当d>β时 1\当d≤时 2-d/β}

A MULTI-GROUP SVEIR EPIDEMIC MODEL WITH DISTRIBUTED DELAY AND VACCINATION

In this paper, based on a class of multi-group epidemic models of SEIR type with bilinear incidences, we introduce a vaccination compartment, leading to multi-group SVEIR model. We establish that the global dynamics are completely determined by the basic reproduction number R0V which is defined by the spectral radius of the next generation matrix. Our proofs of global stability of the equilibria utilize a graph-theoretical approach to the method of Lyapunov functionals. Mathematical results suggest that vaccination is helpful for disease control by decreasing the basic reproduction number. However, there is a necessary condition for successful elimination of disease. If the time for the vaccines to obtain immunity or the possibility for them to be infected before acquiring immunity is neglected in each group, this condition will be satisfied and the disease can always be eradicated by suitable vaccination strategies. This may lead to over evaluation for the effect of vaccination.