An irregularity index IR(Γ) of a graph Γ is nonnegative numeric quantity (i.e., IR(Γ)≥0) such that IR(Γ)=0 iff regular graph. In this paper, we show IRC closely correlates with the normal boiling point Tbp and standard heat formation ΔHfo lower benzenoid hydrocarbons. The correlation models fit data efficiently for both are linear. We develop further mathematical properties by calculating its e...

Let K/Q be a number field with ring of integers O . Let Γ ⊂ SLn(O) be a finite index subgroup, and let ν be the virtual cohomological dimension of Γ. That is, if Γ ⊂ Γ is any finite index torsion-free subgroup, then H (Γ,M) = 0 for i > ν and any ZΓ-module M . Let M be the free abelian group generated by the symbols [v1, . . . , vn], where the vi are nonzero points in K , modulo the following re...

In this paper we will introduce a new index of interactivity between marginal possibility distributions A and B of a joint possibility distribution C. The starting point of our approach is to equip each γ-level set of C with a uniform probability distribution, then the probabilistic correlation coefficient between its marginal probability distributions is interpreted as an index of interactivit...

This paper is concerned with the general atom-bond sum-connectivity index ABSγ, which a generalization of recently proposed index, where γ any real number. For connected graph G more than two vertices, number ABSγ(G) defined as sum (1−2(dx+dy)−1)γ over all edges xy G, dx and dy represent degrees vertices x y respectively. −10≤γ≤10, significance ABSγ examined on data set twenty-five benzenoid hy...

 First principle calculations of nanolayered ZnO polymorphs (Wurzite–, Zincblende–, Rocksalt–structures) in the scheme of density functional theory were performedwith the help of full potential linear augmented plane wave (FP-LAPW) method. Theexchange - correlation potential is described by generalized gradient approximation asproposed by Perdew–Burke–Ernzrhof (GGA–PBE) and modified Becke–Johns...

We study a general k dimensional infinite server queues process with Markov switching, Poisson arrivals and where the service times are fat tailed index α∈(0,1). When arrival rate is sped up by factor nγ, transition probabilities of underlying chain divided nγ n, we identify two regimes (”fast arrivals”, when γ>α, and” equilibrium”, γ=α) in which prove that properly rescaled converges pointwise...

A topological index is a numeric quantity associated with chemical structure that attempts to link the various physicochemical properties, reactivity, or biological activity. Let R be commutative ring identity, and Z*(R) set of all non-zero zero divisors R. Then, Γ(R) said zero-divisor graph if only a·b=0, where a,b∈V(Γ(R))=Z*(R) (a,b)∈E(Γ(R)). We define a∼b a·b=0 a=b. ∼ always reflexive symmet...

In this paper we make a survey of some recent developments of the theory of Sobolev spaces W (X, d,m), 1 < q < ∞, in metric measure spaces (X, d,m). In the final part of the paper we provide a new proof of the reflexivity of the Sobolev space based on Γ-convergence; this result extends Cheeger’s work because no Poincaré inequality is needed and the measure-theoretic doubling property is weakene...

By looking at the Γ-convergence of some easy functionals in terms of underlying Young measures, we emphasize the connection of this issue with the Monge-Kantorovich mass transfer problem. After exploring this relationship, we study a typical example in periodic homogenization to realize the difference between the Monge-Kantorovich problem and the usual cell-problem. We also state a version of t...

We investigate the limiting description for a finite-difference approximation of a singularly perturbed Allen–Cahn type energy functional. The key issue is to understand the interaction between two small length-scales: the interfacial thickness ε and the mesh size of spatial discretization δ. Depending on their relative sizes, we obtain results in the framework of Γ-convergence for the (i) subc...