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...

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...

This paper discusses some details of Vachaspati’s particle-monopole correspondence and their relation to a dual standard model. We show that contained within his correspondence are several sub-correspondences relating to electroweak, strong and hypercharge interactions. Associated with each of these we propose an analogous dual model; the use of these being to examine in isolation specific feat...

Hypercubes and star graphs are widespread topologies of interconnection networks. The class of hyper-stars was introduced as a new type of interconnection network to compete with both hypercubes and star graphs, and the class of folded hyper-stars is a strengthened variation of hyperstars with additional links to connect nodes with complemented 0/1-strings. Constructing independent spanning tre...

The double copy relates scattering amplitudes and classical solutions in Yang-Mills theory, gravity, related field theories. Previous work has shown that this an explicit realisation self-dual YM where the equation of motion can be written a form maps directly to Pleba\'nski's heavenly for gravity. involves area-preserving diffeomorphism algebra, two copies which appear equation. In paper, we s...