We study the problem of comparing ageing patterns lifetimes k-out-of-n systems with i.i.d. components. Mathematically, this reduces to being able decide about a stochastic ordering relationship between different order statistics. discuss such relationships respect second-order dominance, obtaining characterizations through verification relative convexity suitably chosen reference distribution f...

The m-order connectivity index mχ(G) of a molecular graph G is the sum of the weights (di1di2 · · · dim+1) 1 2 , where di1di2 · · · dim+1 runs over all paths of length m in G and di denotes the degree of vertex vi. Dendrimer is a polimer molecule with a distinctive structure that resembles the crown of a tree. In this paper we compute second-order and third-order connectivity indices of an infi...

The new mechanism for obtaining a nonlinear phase shift has been proposed and the schemes are described for its implementation. As it is shown, the interference of two waves with intensity-dependent amplitude ratio coming from the second harmonic generation should produce the nonlinear phase shift. The sign and amount of nonlinear distortion of a beam wavefront is dependent of the relative phas...

Decomposition is a common tool for synthesis of many physical systems. It is also used for analyzing large scale systems which then known as fearing and reconstruction. On the other hand, commutativity of cascade connected systems have gained a grate deal of interest and its possible benefits have been pointed out in the literature. In this paper, the necessary and sufficient conditions for dec...