This report contains revision and extension of some results about RBO from [14]. RBO is a simple and efficient broadcast scheduling of n = 2 uniform frames for battery powered radio receivers. Each frame contains a key from some arbitrary linearly ordered universe. The broadcast cycle – a sequence of frames sorted by the keys and permuted by k-bit reversal – is transmitted in a round robin fash...

We study the relationship between operators, orthonormal basis of subspaces and frames of subspaces (also called fusion frames) for a separable Hilbert space H. We get sufficient conditions on an orthonormal basis of subspaces E = {Ei}i∈I of a Hilbert space K and a surjective T ∈ L(K,H) in order that {T (Ei)}i∈I is a frame of subspaces with respect to a computable sequence of weights. We also o...

This article builds on work by Bolander and Blackburn [7] on terminating tableau systems for the minimal hybrid logic K. We provide (for the basic uni-modal hybrid language) terminating tableau systems for a number of non-transitive hybrid logics extending K, such as the logic of irreflexive frames, antisymmetric frames, and so on; these systems don’t employ loop-checks. We also provide (for hy...

For a given class F of uniform frames of fixed redundancy we define a Grassmannian frame as one that minimizes the maximal correlation |〈fk, fl〉| among all frames {fk}k∈I ∈ F . We first analyze finite-dimensional Grassmannian frames. Using links to packings in Grassmannian spaces and antipodal spherical codes we derive bounds on the minimal achievable correlation for Grassmannian frames. These ...

We show that modal logic over universally first-order definable classes of transitive frames is decidable. More precisely, let K be an arbitrary class of transitive Kripke frames definable by a universal first-order sentence. We show that the global and finite global satisfiability problems of modal logic over K are decidable in NP, regardless of choice of K. We also show that the local satisfi...

Recently, fusion frames and for operators were considered as generalizations of in Hilbert spaces. In this paper, we generalize some the known results frame theory to related a linear bounded operator K which call K-fusion frames. We obtain new by considering with class construct from given ones. also study stability under small perturbations. further give characterizations atomic systems subsp...