The dynamic steady-state propagation of two parallel semi-infinite, mode III cracks is considered for a general, infinite, homogeneous, and isotropic linearly viscoelastic body. A Barenblatt type failure zone is introduced in order to cancel the singular stress and a formula for the energy release rate is derived which provides immediate comparisons with the corresponding single crack problem. ...

In this paper, a new kind of repairable system with repairman vacation and warning device is discussed, in which the delayed vacation rate and failure rates are functions related to system working time. The system model is established by using probability analysis method, which then is translated into a initial value problem of a class of abstract semi-linear evolution equation in a suitable Ba...

Hepatitis B virus (HBV) infection is endemic in many parts of the world. One of the characteristics of HBV transmission is the age structure of the host population. In this paper, we propose an age-structured model for the transmission dynamics of HBV. The host population is stratified by age and is divided into six subclasses: susceptible, latently infected, acutely infectious, carrier, recove...

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We study the positive steady state of a quasi-linear reaction-diffusion system in one space dimension introduced by Klausmeier and Litchman for the modelling of the distributions of phytoplankton biomass and its nutrient. The system has nonlocal dependence on the biomass function, and it has a biomass-dependent drifting term describing the active movement of the biomass towards the location of ...

this paper investigates a discrete-time impatient customer queue with bernoulli-schedule vacation interruption. the  vacation times and the service times during regular busy period and during working vacation period are assumed to follow geometric distribution. we obtain the steady-state probabilities at arbitrary and outside observer's observation epochs using recursive technique. cost an...