Abstract Priority queueing models have been commonly used in telecommunication systems. The development of analytically tractable models to determine their performance is vitally important. The discrete time batch Markovian arrival process (DBMAP ) has been widely used to model the source behavior of data traffic, while phase-type (PH) distribution has been extensively applied to model the serv...

1 Phase-Type Distributions 2 1.1 Continuous Phase-Type Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Discrete Phase-Type Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Closure Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.4 Further Closure Properties for Continuous Distributions . . . . . . . . . ....

Let I be a square-free monomial ideal of projective dimension one. Starting with the Taylor complex on generators $$I^r$$ , we use discrete Morse theory to describe CW that supports minimal free resolution . To do so, concretely acyclic matching faces complex.

Aharoni, R. and I. Ben-Arroyo Hartman, On Greene-Kleitman’s theorem for general digraphs, Discrete Mathematics 120 (1993) 13-24. Linial conjectured that Greene-Kleitman’s theorem can be extended to general digraphs. We prove a stronger conjecture of Berge for digraphs having k-optimal path partitions consisting of ‘long’ paths. The same method yields known results for acyclic digraphs, and exte...

This paper introduces a unified approach to phase-type approximation in which the discrete and the continuous phase-type models form a common model set. The models of this common set are assigned with a non-negative real parameter, the scale factor. The case when the scale factor is strictly positive results in Discrete phase-type distributions and the scale factor represents the time elapsed i...

We studied the influence of the aromatic sidewalls on the ability of acyclic CB[n]-type molecular containers (1a-1e) to act as solubilizing agents for 19 insoluble drugs including the developmental anticancer agent PBS-1086. All five containers exhibit good water solubility and weak self-association (Ks ≤ 624 M(-1)). We constructed phase solubility diagrams to extract Krel and Ka values for the...

an acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. the acyclic chromatic index of a graph $g$ denoted by $chi_a '(g)$ is the minimum number $k$ such that there is an acyclic edge coloring using $k$ colors. the maximum degree in $g$ denoted by $delta(g)$, is the lower bound for $chi_a '(g)$. $p$-cuts introduced in this paper acts as a powerfu...

An acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. The acyclic chromatic index of a graph $G$ denoted by $chi_a '(G)$ is the minimum number $k$ such that there is an acyclic edge coloring using $k$ colors. The maximum degree in $G$ denoted by $Delta(G)$, is the lower bound for $chi_a '(G)$. $P$-cuts introduced in this paper acts as a powerfu...