This paper presents majorization results for PH-generators. Based on the majorization results, bounds on the moments and Laplace-Stieltjes transforms of phase-type distributions are found. Exponential distributions and Coxian distributions are identified to be extremal PH-distributions with respect to all the moments and Laplace-Stieltjes transforms for certain subsets of PH-distributions. UN C...

This paper presents a formal proof of the Riesz representation theorem in the PVS theorem prover. The Riemann Stieltjes integral was defined in PVS, and the theorem relies on this integral. In order to prove the Riesz representation theorem, it was necessary to prove that continuous functions on a closed interval are Riemann Stieltjes integrable with respect to any function of bounded variation...

The Stieltjes coefficients γk(a) arise in the expansion of the Hurwitz zeta function ζ(s, a) about its single simple pole at s = 1 and are of fundamental and long-standing importance in analytic number theory and other disciplines. We present an array of exact results for the Stieltjes coefficients, including series representations and summatory relations. Other integral representations provide...

We establish a hierarchy of weighted majorization relations for the singularities of generalized Lamé equations and the zeros of their Van Vleck and Heine-Stieltjes polynomials as well as for multiparameter spectral polynomials of higher Lamé operators. These relations translate into natural dilation and subordination properties in the Choquet order for certain probability measures associated w...

We analyze a family of queueing systems where the interarrival time I n+1 between customers n and n + 1 depends on the service time B n of customer n. Speciically, we consider cases where the dependency between I n+1 and B n is a proportionality relation, and B n is an exponentially distributed random variable. Such dependencies arise in the context of packet-switched networks which use rate po...

FOREWORD SEVERAL YEARS AGO, Karl Narr asked me to write an article summarizing the recently discovered data of Southeast Asian prehistory for publication in German in Saeculum. In the fall of 1977, I finally did this in the context of an examination of a number of Heine-Ge1dern's hypotheses on Southeast Asian prehistory. I titled the paper "New data on late Southeast Asian prehistory and their ...