This paper is concerned with properties of the algebraic degree of the Laplace–Stieltjes transform of phase-type (PH) distributions. The main problem of interest is: given a PH generator, how do we find the maximum and the minimum algebraic degrees of all irreducible PH representations with that PH generator? Based on the matrix exponential (ME) order of ME distributions and the spectral polyno...

A digraph D is supereulerian if D has a spanning directed eulerian subdigraph. Hong et al. proved that δ(D) + δ(D) ≥ |V (D)| − 4 implies D is supereulerian except some well-characterized digraph classes if the minimum degree is large enough. In this paper, we characterize the digraphs D which are not supereulerian under the condition d+D (u) + d−D (v) ≥ |V (D)| − 4 for any pair of vertices u an...

Recently, a mixed hybrid operator, generalizing the well-known Phillips operators and Baskakov-Szász type operators, was introduced. In this paper, we study Bézier variant of these new operators. We investigate the degree of approximation of these operators by means of the Lipschitz class function, the modulus of continuity, and a weighted space. We study a direct approximation theorem by means...

the time evaluation of quantum entropy in a four-level double- type atomic system is theoretically investigated. quantum entanglement of the atom and its spontaneous emission fields is then discussed via quantum entropy. it is found that the degree of entanglement can be increased by the quantum interference induced by spontaneous emission. the phase dependence of the atom-field entanglement is...

the probability that the commutator of two group elements is equal to a given element has been introduced in literature few years ago. several authors have investigated this notion with methods of the representation theory and with combinatorial techniques. here we illustrate that a wider context may be considered and show some structural restrictions on the group.

Splashing of splat particles is one of the most important phenomena in industrial processes such as thermal spray coating. The data relative to the degree of splashing of splats sprayed with a normal angle are commonly characterized by the Weibull distribution function. In this present study, an effort has been made to show that the Burr distribution is better than the Weibull distribution for ...