We study the problem of estimating the size of independent sets in a graph G defined by a stream of edges. Our approach relies on the Caro-Wei bound, which expresses the desired quantity in terms of a sum over nodes of the reciprocal of their degrees, denoted by β(G). Our results show that β(G) can be approximated accurately, based on a provided lower bound on β. Stronger results are possible w...

In this paper, we find the best proximity point in G-metric spaces for G-generalized ζ-β-T contraction mappings and verify existence uniqueness of complete G metric space using idea an approximatively compact set. addition, example is provided to illustrate outcome.

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...

G protein-coupled receptor (GPR) 30 is a novel estrogen receptor. Recent studies suggest that activation of the GPR30 confers rapid cardioprotection in isolated rat heart. It is unknown whether chronic activation of GPR30 is beneficial or not for heart failure. In this study we investigated the cardiac effect of sustained activation or inhibition of GPR30. Female Sprague-Dawley rats were divide...

The effect of an invasive voltage probe on the phase-coherent conduction through a ballistic chaotic cavity is investigated by random-matrix theory. The entire distribution P (G) of the conductance G is computed for the case that the cavity is coupled to source and drain by two point contacts with a quantized conductance of 2e2/h, both in the presence (β = 1) and absence (β = 2) of time-reversa...

We study the asymptotics of fundamental solutions of p-adic pseudodifferential equations of type (f(∂, β) + λ)u = g, where f(∂, β) is a pseudo-differential operator with symbol |f | K , β > 0, f is a form of arbitrary degree with coefficients in a p−adic field, λ ≥ 0, and g is a Schwartz-Bruhat function.

We consider the multiplicity of nontrivial solutions of the following quasilinear elliptic system -div(|x|(-ap)|∇u|(p-2)∇u) + f₁(x)|u|(p-2) u = (α/(α + β))g(x)|u| (α-2) u|v| (β) + λh₁(x)|u| (γ-2) u + l₁(x), -div(|x|(-ap) |∇v| (p-2)∇v) + f₂(x)|v| (p-2) v = (β/(α + β))g(x)|v|(β-2) v|u|(α) + μh 2(x)|v|(γ-2)v + l 2(x), u(x) > 0, v(x) > 0, x ∈ ℝ(N), where λ, μ > 0, 1 < p < N, 1 < γ < p < α + β < p* ...

A set of vertices S resolves a connected graph G if every vertex is uniquely determined by its vector of distances to the vertices in S. The metric dimension of G is the minimum cardinality of a resolving set of G. Let Gβ,D be the set of graphs with metric dimension β and diameter D. It is well-known that the minimum order of a graph in Gβ,D is exactly β + D. The first contribution of this pape...

We prove a number of Turán and Ramsey type stability results for cycles, in particular, the following one: Let n be sufficiently large, 0 < β < 2 × 10 −7 , and the edges of K ⌊(2−β)n⌋ be 2-colored so that no mononchromatic C n exists. Then, for some q ∈ ((1 − β) n, n) , we may drop a vertex v so that in K ⌊(2−β)n⌋ −v one of the colors induces K q,⌊(2−β)n⌋−q−1 , while the other one induces K q ∪...