The edge Szeged index is a new molecular structure descriptor equal to the sum of products mu(e)mv(e) over all edges e = uv of the molecular graph G, where mu(e) is the number of edges which its distance to vertex u is smaller than the distance to vertex v, and nv(e) is defined analogously. In this paper, the edge Szeged index of one-pentagonal carbon nanocone CNC5[n] is computed for the first ...

The second Zagreb coindex is a well-known graph invariant defined as the total degree product of all non-adjacent vertex pairs in a graph. The second Zagreb eccentricity coindex is defined analogously to the second Zagreb coindex by replacing the vertex degrees with the vertex eccentricities. In this paper, we present exact expressions or sharp lower bounds for the second Zagreb eccentricity co...

Recent advances in understanding bacterial cell-cycle regulation suggest circuit control mechanisms that operate analogously to those in the eukaryotic cell cycle.

the edge szeged index is a new molecular structure descriptor equal to the sum of products mu(e)mv(e) over all edges e = uv of the molecular graph g, where mu(e) is the number of edges which its distance to vertex u is smaller than the distance to vertex v, and nv(e) is defined analogously. in this paper, the edge szeged index of one-pentagonal carbon nanocone cnc5[n] is computed for the first ...

We show that the maximal linear extension theorem for well partial orders is equivalent over RCA0 to ATR0. Analogously, the maximal chain theorem for well partial orders is equivalent to ATR0 over RCA0.

a) 0 = FX,Y (−∞, y) = S(FX(−∞), FY (y)) = S(0, v) where v ∈ Ran FY , and analogously S(u, 0) = 0 for u ∈ Ran FX . b) FY (y) = FX,Y (+∞, y) = S(FX(+∞), FY (y)) = S(1, v) where v = FY (y), and analogously S(u, 1) = u where u = FX(x) for some x ∈ R. c) 0 ≤ P (x1 < X ≤ x2 , y1 < Y ≤ y2) = FX,Y (x2, y2)−FX,Y (x2, y1)−FX,Y (x1, y2)+ FX,Y (x1, y1) and therefore by (1) we have that S(u2, v2)− S(u2, v1)...

Some structural aspects of mixtures, in general, have been previously investigated by the author in [I] and [2]. The aim of this article is to investigate some important structural properties of the special cases of Poisson and binomial mixtures in detail. Some necessary and sufficient conditions are arrived at for different modality and divisibility properties of a Poisson mixture based o...

Abstract We give some characterizations of commutative objects in a subtractive category and central morphisms regular category. In particular, we show that objects, i.e., internal unitary magmas, are the same as abelian groups analogously, centrality has an alternative description terms so-called “subtractors”