For a random process (X(t), t ≥ 0), suppose that there is a cost fx associated with being in state x. This paper is concerned with evaluating the distribution and the expected value of the total cost Γ over the life of the process. The existing literature contains results for particular classes of process and particular choices of f , usually linear functions of the state. We will describe a me...

in the present research, friction stir welding (fsw) process was used for butt joining of pure copper plate to 316l stainless steel plate. mechanical properties and microstructural characteristics of the joint were evaluated by microhardness and tensile tests as well as optical and scanning electron microscope (sem). it was found that microstructure of the weld nugget (wn) has fine grains where...

We investigate a neutral model for speciation and extinction, the constant rate birth-death process. The process is conditioned to have n extant species today, we look at the tree distribution of the reconstructed trees--i.e. the trees without the extinct species. Whereas the tree shape distribution is well-known and actually the same as under the pure birth process, no analytic results for the...

We investigate a neutral model for speciation and extinction, the constant rate birth-death process. The process is conditioned to have n extant species today, we look at the tree distribution of the reconstructed trees– i.e. the trees without the extinct species. Whereas the tree shape distribution is well-known and actually the same as under the pure birth process, no analytic results for the...

In this paper, we investigate the emergence of a predator-prey model with Beddington-DeAngelistype functional response and reaction-diffusion. We derive the conditions for Hopf and Turing bifurcation on the spatial domain. Based on the stability and bifurcation analysis, we give the spatial pattern formation via numerical simulation, i.e., the evolution process of the model near the coexistence...

Large-scale phylogenies provide a valuable source to study background diversification rates and investigate if the rates have changed over time. Unfortunately most large-scale, dated phylogenies are sparsely sampled (fewer than 5% of the described species) and taxon sampling is not uniform. Instead, taxa are frequently sampled to obtain at least one representative per subgroup (e.g. family) and...

A fractional generalized pure birth process is studied based on the master equation approach. The exact analytic solution of the generating function of the probability density for the process is given in terms of the Gauss hypergeometric function. The expressions of moments are also obtained in an explicit form. The effects of fixed and distributed initial conditions are also elucidated. The ef...