Transition probabilities within a birth and death process are difficult to find analytically. As a consequence pure birth and pure death processes are considered in seperate systems and it is found that both systems can be fully specified from intensity specifications. In a linear continuous-time Markovian pure death process it is found that optional death times are independent. Faddy (1985) co...

This note is motivated by connections between the online and offline problems of selecting a possibly long subsequence from Poisson-paced sequence uniform marks under either monotonicity or sum constraint. The problem with constraint amounts to counting Poisson arrivals before their total exceeds certain level. A precise asymptotics for mean count obtained coupling nonlinear pure birth process.

The constant rate birth-death process is a popular null model for speciation and extinction. If one removes extinct and non-sampled lineages, this process induces 'reconstructed trees' which describe the relationship between extant lineages. We derive the probability density of the length of a randomly chosen pendant edge in a reconstructed tree. For the special case of a pure-birth process wit...

in this research, aluminizing packs containing naf and nh4cl activators were used for aluminizing of pure titanium samples at 1100 ºc. the results showed that the layers of tial3, tial2, γ-tial, α2-ti3al, and α-solid solution are formed on titanium samples in both cases. however, the weight gain and the thickness of tial3 layer in treated samples with nh4cl activator are greater than those when...