In this paper x, X, X1, X2 are sets. Let Y be a functional set. The functor DOMS(Y ) is defined by: (Def. 1) DOMS(Y ) = ⋃ {dom f : f ranges over elements of Y }. Let us consider X. We say that X is complex-functions-membered if and only if: (Def. 2) If x ∈ X, then x is a complex-valued function. Let us consider X. We say that X is extended-real-functions-membered if and only if: (Def. 3) If x ∈...

Let ω0(G) denote the number of odd components of a graph G. The deficiency of G is defined as def(G) = maxX⊆V (G) (ω0(G−X)− |X|), and this equals the number of vertices unmatched by any maximum matching of G. A subset X ⊆ V (G) is called a Tutte set (or barrier set) of G if def(G) = ω0(G − X) − |X|, and an extreme set if def(G − X) = def(G) + |X|. Recently a graph operator, called the Dgraph D(...

with tn−→∞ as n−→∞. With N(0) def = 0, N(t) max{n : tn ≤ t} denotes the number of points that fall in the interval (0, t], and {N(t) : t ≥ 0} is called the counting process for ψ. (If t1 > t, then N(t) def = 0.) If the tn are random variables then ψ is called a random point process. We sometimes allow a point at the origin and define t0 def = 0. Xn = tn − tn−1, n ≥ 1 is called the nth interarri...

In this theoretical work, density functional theory calculations show the effect of small cobalt clusters (Con, n = 1–5) adsorbed on pristine γ-graphyne (γ-GY), and modify N-doped γ-GY monolayers (GYNs-def). Different geometrical configurations are assessed with adsorption energy, charge transfer, states. The system vacancy defects shows a large energy (19.96 eV) for Co5 cluster. This behavior ...

In this paper, the concept of pseudoconvexity and quasiconvexity for continuous~-time functions are studied and an equivalence condition for pseudoconvexity is obtained. Moreover, under pseudoconvexity assumptions, some relationships between Minty and Stampacchia vector variational inequalities and continuous-time programming problems are presented. Finally, some characterizations of the soluti...

In this paper‎, ‎the aim is to find a complex interval vector [Z] such that satisfies the complex interval linear system C[Z]=[W]‎. ‎For this‎, ‎we present a new method by restricting the general solution set via applying some parameters‎. ‎The numerical examples are given to show ability and reliability of the proposed method.

The Australian Standard for safety-critical systems development, Def(Aust) 5679, was first released in 1998. As part of the release of Issue 2 (Department of Defence 2008) of the Standard, guidance material has been prepared to assist those who need to apply the Standard. The guidance is made up of three main parts: a case study that demonstrates how the Standard can be applied to an example sa...