In this paper, we introduce the notion of $G_\infty$-ring spectra. These are globally equivariant homotopy types with a structured multiplication, giving rise to power operations on their and cohomology groups. We illustrate structure by analysing when Moore spectrum can be endowed structure. Such $G_\infty$-structures correspond underlying ring, indexed Burnside ring. exhibit close relation be...

A set D of vertices in a graph G is 2-dominating if every vertex not in D has at least two neighbors in D and locating-dominating if for every two vertices u, v not in D, the sets N(u) ∩ D and N(v) ∩ D are non-empty and different. The minimum cardinality of a 2-dominating set (locatingdominating set) is denoted by γ2(G) (γL(G)). It is known that every tree T with n ≥ 2 vertices, leaves, s suppo...

We consider the generalized minimax programming problem (P) in which functions are locally Lipschitz (G, β)-invex. Not only G-sufficient but also G-necessary optimality conditions are established for problem (P). With G-necessary optimality conditions and (G, β)-invexity on hand, we construct dual problem (DI) for the primal one (P) and prove duality results between problems (P) and (DI). These...

For a set D of positive integers, we define a vertex set S ⊆ V (G) to be D-independent if u, v ∈ S implies the distance d(u, v) 6∈ D. The D-independence number βD(G) is the maximum cardinality of a D-independent set. In particular, the independence number β(G) = β{1}(G). Along with general results we consider, in particular, the odd-independence number βODD(G) where ODD = {1, 3, 5, . . .}.

We present a distributed approximation algorithm that computes in every graph G a matching M of size at least 2 3 β(G), where β(G) is the size of a maximum matching in G. The algorithm runs in O(log |V (G)|) rounds in the synchronous, message passing model of computation and matches the best known asymptotic complexity for computing a maximal matching in the same protocol. This improves the run...

BACKGROUND AND PURPOSE β(1) -, β(2) - and β(3) -adrenoceptors determined by functional, binding and reverse transcription polymerase chain reaction (RT-PCR) studies are present in chick astrocytes and activation of β(2) - or β(3) -adrenoceptors increase glucose uptake. The aims of the present study are to identify which β-adrenoceptor subtypes are present in mouse astrocytes, the signal transdu...

Consider a complete graph G with the edge weights satisfying the β-sharpened triangle inequality: weight(u, v) ≤ β(weight(u, x)+ weight(x, v)), for 1/2 ≤ β < 1. We study the NP-hard problem of finding a minimum weight spanning subgraph of G which is k-vertex-connected, k ≥ 2, and give a detailed analysis of an approximation quadratic-time algorithm whose performance ratio is β 1−β . The algorit...

introduction: to study the prevalence of most common β-thalassemia mutations in lorestan province and use the results for epidemiologic study and prenatal diagnosis of β_thalassemia major. material and methods: 130 chromosomes from 65 unrelated homozygous β_thalassemia patients from lorestan province of iran (west-central) were investigated for β globin gene mutations by arms pcr. results: most...

Suppose that G is a groupoid acting on a small category H in the sense of [9, Definition 4] and H ×α G is the resulting semi-direct product category (as in [9, Proposition 8]). We show that there exists a subcategory Hr ⊆ H satisfying some nice property called “regularity” such that Hr ×α G = H ×α G. Moreover, we show that there exists a so-called “quasi action” (see Definition 3.1) β of G on C...

A two-state spin system is specified by a matrix A = [ A0,0 A0,1 A1,0 A1,1 ] = [ β 1 1 γ ] where β, γ ≥ 0. Given an input graph G = (V,E), the partition function ZA(G) of a system is defined as ZA(G) = ∑