asthma is a chronic inflammatory and remodeling disorder of the airways, in which many cells, cellular elements, and cytokines play important roles. the role of tumor necrosis factor- α (tnf-α) in asthma is unclear in pakistani population. the aim of this study was to assess the relationship between tnf-α -308 polymorphism and asthma.polymorphism of tnf-α (g-308-a locus; rs 1800629) in 329 asth...

Let α(G) and χ(G) denote the independence number and chromatic number of a graph G respectively. Let G×H be the direct product graph of graphs G and H . We show that if G and H are circular graphs, Kneser graphs, or powers of cycles, then α(G ×H) = max{α(G)|V (H)|, α(H)|V (G)|} and χ(G×H) = min{χ(G), χ(H)}. AMS Classification: 05C15, 05C69.

background: herpes simplex viruses (hsv) are human pathogens that establish lytic and latent infections. reactivation from latency occurs intermittently, which represents a life-long source for recurrent infection. the role of immune factors in the control of recurrent symptomatic hsv lesions is complex and the exact role of cytokines remains unclear. objective: to assess the levels of tumor ne...

The stability number of a graph G, denoted by α(G), is the cardinality of a stable set of maximum size in G. If α(G − e) > α(G), then e is an α-critical edge, and if μ(G − e) < μ(G), then e is a μ-critical edge, where μ(G) is the cardinality of a maximum matching in G. G is a König-Egerváry graph if its order equals α(G) + μ(G). Beineke, Harary and Plummer have shown that the set of α-critical ...

For a graph G without isolated vertices and a real α = 0, we introduce a new graph invariant s∗α (G)the sum of the αth power of the non-zero normalized Laplacian eigenvalues of G. Recently, the cases α = 2 and −1 have appeared in various problems in the literature. Here, we present some lower and upper bounds of s∗α (G) for a connected graph G, where α = 0, 1. We also discuss the case α = −1.

A bipartite graph G is called (α, β)-biregular if all vertices in one part of G have the degree α and all vertices in the other part have the degree β. An edge coloring of a graph G with colors 1, 2, 3, . . . , t is called an interval t-coloring if the colors received by the edges incident with each vertex of G are distinct and form an interval of integers and at least one edge of G is colored ...

3. The restriction K|gα×g−α , i.e. K(a, b) with a ∈ gα and b ∈ g−α, is non-degenerate, so it induces a pairing between gα and g−α. In particular, we have dim gα = dim g−α. 4. The restriction K|h×h is non-degenerate, hence we have an isomorphism ν : h → h∗ given by ν(h)(h′) = K(h, h′) for all h, h′ ∈ h. The map ν induces a bilinear form on h∗ by K(α, β) = β ( ν−1(α) ) = α ( ν−1(β) ) for all α, β...

For a connected graph G on n vertices, recall that the reciprocal distance signless Laplacian matrix of is defined to be RQ(G)=RT(G)+RD(G), where RD(G) matrix, RT(G)=diag(RT1,RT2,⋯,RTn) and RTi degree vertex vi. In 2022, generalized which by RDα(G)=αRT(G)+(1−α)RD(G),α∈[0,1], was introduced. this paper, we give some bounds spectral radius RDα(G) characterize its extremal graph. addition, also li...

In this article we introduce and study the concept of characteristic degree of a subgroup in a finite group. We define the characteristic degree of a subgroup H in a finite group G as the ratio of the number of all pairs (h,α) ∈ H×Aut(G) such that h^α∈H, by the order of H × Aut(G), where Aut(G) is the automorphisms group of G. This quantity measures the probability that H can be characteristic ...

In 1990, Comfort asked: is there, for every cardinal number α≤2c, a topological group G such that Gγ countably compact all cardinals γ<α, but Gα not compact? A similar question can also be asked pracompact groups: which α there pracompact? this paper we construct in the case α=ω, assuming existence of c incomparable selective ultrafilters, and α=κ+, with ω≤κ≤2c, 2c ultrafilters. particular, und...