In this paper the D-BMAP/G/1 queue is considered. The goal is to derive an explicit expression for the transform of the queueing delay of the nth arriving customer, based on a transient analysis. While deriving this transform, intermediate results such as an explicit expression for the transform of the probability of having an empty system at the nth departure, are also obtained. These results ...

In this paper, we present a new algorithm and an experimental implementation for factoring elements in the polynomial nth Weyl algebra, the polynomial nth shift algebra, and Zgraded polynomials in the nth q-Weyl algebra. The most unexpected result is that this noncommutative problem of factoring partial differential operators can be approached effectively by reducing it to the problem of solvin...

In order to develop certain fractional probabilistic analogues of Taylor’s theorem and mean value theorem, we introduce the nth-order fractional equilibrium distribution in terms of the Weyl fractional integral and investigate its main properties. Specifically, we show a characterization result by which the nth-order fractional equilibrium distribution is identical to the starting distribution ...

In this set of lecture notes we focus on the point-value representation obtained by looking at a particular set of points, the nth roots of unity. In the field of complex numbers C, there are exactly n different solutions to the equation x = 1. We call these solutions the n-th roots of unity. One of these roots of unity is ωn = cos(2π/n)+ i sin(2π/n), and this is called the principal nth root o...

This report describes the preparation and partial characterization of monoclonal antibodies that are reactive specifically with the nascently produced non-triple helical form of the type IV collagen α1 chain, designated as NTH α1(IV). These antibodies were nonreactive with the α1 chain of the type IV collagen in the triple-helical conformation. Three antibodies, #141, #179 and #370, with differ...