In this paper, we introduce the hyper-star graph HS(n, k) as a new interconnection network, and discuss its properties such as faulttolerance, scalability, isomorphism, routing algorithm, and diameter. A hyper-star graph has merits when degree × diameter is used as a desirable quality measure of an interconnection network because it has a small degree and diameter. We also introduce a variation...

In this paper we proved that every g-Riesz basis for Hilbert space $H$ with respect to $K$ by adding a condition is a Riesz basis for Hilbert $B(K)$-module $B(H,K)$. This is an extension of [A. Askarizadeh, M. A. Dehghan, {em G-frames as special frames}, Turk. J. Math., 35, (2011) 1-11]. Also, we derived similar results for g-orthonormal and orthogonal bases. Some relationships between dual fra...

Space filling curves provide several advantages for indexing spatial data. We look at the Z-curve ordering and discuss three algorithms for navigating and querying k-dimensional Z-curves. In k-dimensional space, a single hyper-’Z’-shape in a recursive Z-curve forms a hypercube with 2k quadrants. The first algorithm concerns efficient checking whether a given quadrant of a local hyper-’Z’ inters...

We study a natural generalization of the noncrossing relation between pairs of elements in [n] to k-tuples in [n] that was first considered by Petersen et al. [J. Algebra 324(5) (2010), 951–969]. We give an alternative approach to their result that the flag simplicial complex on ([n] k ) induced by this relation is a regular, unimodular and flag triangulation of the order polytope of the poset ...

introduction: hyperlipidemia is a major cardiovascular risk factor. this survey has been performed to determine the prevalence of hyperlipidemia in the 17th zone of tehran. methods: 1573 individuals 25-64 aged were recruited from the inhabitants of the 17th zone of tehran through one stage cluster sampling. standard questionnaires were filled out for all of the participants. lipid profile was c...

Let R = k[x1, ..., xn] be the polynomial ring in n independent variables, where k is a field. In this work we will study Bass numbers of local cohomology modules H I (R) supported on a squarefree monomial ideal I ⊆ R. Among them we are mainly interested in Lyubeznik numbers. We build a dictionary between the modules H I (R) and the minimal free resolution of the Alexander dual ideal I∨ that all...

Let $K$ be a locally compact hypergroup with left Haar measure and let $L^1(K)$ be the complex Lebesgue space associated with it. Let $L^infty(K)$ be the dual of $L^1(K)$. The purpose of this paper is to present some necessary and sufficient conditions for $L^infty(K)^*$ to have a topologically left invariant mean. Some characterizations of amenable hypergroups are given.

A (hyper)graph G is called k-critical if it has chromatic number k, but every proper sub(hyper)graph of it is (k− 1)-colourable. We prove that for sufficiently large k, every k-critical triangle-free graph on n vertices has at least (k−o(k))n edges. Furthermore, we show that every (k+1)-critical hypergraph on n vertices and without graph edges has at least (k−3/ 3 √ k)n edges. Both bounds diffe...