In the paper, necessary and sufficient conditions are presented for a function involving a ratio of gamma functions to be logarithmically completely monotonic. This extends and generalizes the main result of Guo and Qi [Taiwanese J. Math. 7 (2003), no. 2, 239–247] and others. As applications, several inequalities involving the volume of the unit ball in R are derived, which refine, generalize a...

(1) where n ≥ 2, f is a continuous function defined on R+ × R , R+ = [0,∞), R = (−∞,∞), τi ∈ C (R+) and τi(t) ≤ t for t ∈ R+ and i = 0, 1, . . . , n− 1 . We will suppose for the simplicity that inf t∈R+ τi(t) > −∞ for i = 0, 1, . . . , n − 1. Note, that C(I), s ∈ {0, 1, . . .}, I ⊂ R+ is the set of continuous functions on I that have continuous derivatives up to the order s. A special case of e...

This vignette is an updated version of Bornkamp, Pinheiro, and Bretz (2009) and describes the MCPMod package for the R programming environment. The package implements a methodology for the design and analysis of dose-response studies that combines aspects of multiple comparison procedures and modeling approaches (Bretz, Pinheiro, and Branson 2005). The package provides tools for the analysis of...

It is established that durational and structural aspects of actions can in general not be modeled in standard interleaving semantics, even when a time-consuming action is represented by a pair of instantaneous actions denoting its start and finish. By means of a series of counterexamples it is shown that, for any n, it makes a difference whether actions are split in n or in n+1 parts. ] 1997 Ac...