Dynamical behavior of a hybrid switching SIS epidemic model with vaccination and Lévy jumps

In this paper, the dynamical behavior of a hybrid switching SIS epidemic model with vaccination and Lévy jumps is considered. Besides a standard geometric Brownian motion, another two driving processes are taken into account: a stationary Poisson point process and a continuous time finite-state Markov chain. Firstly, we establish sufficient conditions for persistence in the mean of the disease. Then we obtain sufficient conditions for extinction of the disease. In addition, we also establish sufficient conditions for the existence of positive recurrence of the solutions to the model by constructing a suitable stochastic Lyapunov function with regime switching.     

Enumerating words with forbidden factors

This presentation is an exposition of an application of the theory of recurrence relations to enumerating strings over an alphabet with a forbidden factor (consecutive substring). As an illustration we examine the case of binary strings with a forbidden factor of k consecutive symbols 1 for given k, using generating function techniques that deserve to be better known.This allows us to derive a known upper bound for the number of prefix normal binary words: words with the property that no factor has more occurrences of the symbol 1 than the prefix of the same length. Such words arise in the context of indexed binary jumbled pattern matching.     

混合方程递推公式的直接列写法

本文导出了混合方程递推公式的直接列写法。由于该方法的导出，使得计算机用暂态伴随模型法求解动态电路时，可以直接形成电路在不同时刻的混合方程。避免了重复、繁琐的矩阵运算，从而大大减少了计算工作量、节省了机时和内存，使暂态伴随模型法有更加广泛的使用价值。     

Character sums and nonlinear recurrence sequences

We obtain upper bounds on character sums and autocorrelation of nonlinear recurrence sequences over arbitrary finite rings.     

Fibonacci数的一类和数列的性质

文中用组合分析中的计算方法得到了关于Fibonacci数的一类和数列的性质。     

On a generalization of duality triads

Some aspects of duality triads introduced recently are discussed. In particular, the general solution for the triad polynomials is given. Furthermore, a generalization of the notion of duality triad is proposed and some simple properties of these generalized duality triads are derived.     

偶极子在径向非均匀介质中的电磁场分布

提出了柱状多层介质中的磁偶极子在任意介质层中的电磁场的递推算法，给出了磁偶极子产生的电磁波在柱状多层介质中的反射、透射系数和广义反射系数，从而得到了任意介质层中满足各层界面边界条件的电磁场解析表达式．     

等差型方程k∑i=0aiyn-i=δn的特解解法

给出求k阶等差型方程k∑i=0 aiyn-i=δn的特解的一种解法.     

独立渐进随机环境中随机行走

讨论了一类独立但不一定同分布随机环境中随机行走的常返性和非常返性，进而研究了常返性中的正常返，以及在它们基础上逃逸速度的极限性质，从而推广了Solmn的理论框架。     

Path Collapse for an Inhomogeneous Random Walk

On an open interval we follow the paths of a Brownian motion which returns to a fixed point as soon as it reaches the boundary and restarts afresh indefinitely. We determine that two paths starting at different points either cannot collapse or they do so almost surely. The problem can be modelled as a spatially inhomogeneous random walk on a group and contrasts sharply with the higher dimensional case in that if two paths may collapse they do so almost surely.