It is well-known in ruin theory that the expected present value of penalty at ruin satisfies a defective renewal equation in the Erlang-n renewal risk model. This paper presents a new matrix operator approach to derive a parallel defective renewal equation for the expected present value of total operating costs in a phase-type renewal risk model and hence provides explicit matrix analytic solut...

The most commonly used models for the failure process of a repairable system are nonhomogeneous Poisson processes, corresponding to minimal repairs, and renewal processes, corresponding to perfect repairs. This paper studies a more general model for recurrent events, called the Trend-Renewal Process (TRP). This is a time transformed renewal process, having both the ordinary renewal process and ...

Renewal-anomalous-heterogeneous files are solved. A simple file is made of Brownian hard spheres that diffuse stochastically in an effective 1D channel. Generally, Brownian files are heterogeneous: the spheres’ diffusion coefficients are distributed and the initial spheres’ density is non-uniform. In renewal-anomalous files, the distribution of waiting times for individual jumps is exponential ...

Some problems of point and interval prediction in a trend-renewal process (TRP) are considered. TRP’s, whose realizations depend on a renewal distribution as well as on a trend function, comprise the non-homogeneous Poisson and renewal processes and serve as useful reliability models for repairable systems. For these processes, some possible ideas and methods for constructing the predicted next...

We consider the problem of seeking the optimal time to sell a stock, subject to a fixed sale cost and an exponential discounting rate ρ. We assume that the price of the stock fluctuates according to the equation dYt = Yt (μdt+σ ξ(t) dt), where (ξ(t)) is an alternating Markov renewal process with values in {±1}, with an exponential renewal time. We determine the critical value of ρ under which t...

Human tissues continually replace dying cells with newborn cells. However, the rate of renewal varies by orders of magnitudes between blood cells, which are renewed every day and neurons, for which renewal is non-existent or limited to specific regions of the brain. Between those extreme are many tissues that turn over on a time scale of years, although no direct measurements have been done. We...

this paper examines the structure and form of the alley spaces in kampala central businessdistrict, with purpose to examine their uses, and the potential for urban renewal. the study employed multiplemethodological approaches and procedures including document review, case study approaches and analysis anddeduction of empirical findings, and explanation building. the study findings reveal that a...

Nestin knockout leads to embryonic lethality and self-renewal deficiency in neural stem cells (NSCs). However, how nestin maintains self-renewal remains uncertain. Here, we used the dosage effect of nestin in heterozygous mice (Nes+/-) to study self-renewal of NSCs. With existing extracellular signaling in vivo or in vitro, nestin levels do not affect proliferation ability or apoptosis when com...

Spermatogonial stem cells (SSCs) are required for spermatogenesis. Earlier studies showed that glial cell line-derived neurotrophic factor (GDNF) was indispensable for SSC self-renewal by binding to the GFRA1/RET receptor. Mice with mutations in these molecules showed impaired spermatogenesis, which was attributed to SSC depletion. Here we show that SSCs undergo GDNF-independent self-renewal. A...