We define the notion of factorizable quasi-Hopf algebra by using a categorical point of view. We show that the Drinfeld double D(H) of any finite dimensional quasi-Hopf algebra H is factorizable, and we characterize D(H) when H itself is factorizable. Finally, we prove that any finite dimensional factorizable quasi-Hopf algebra is unimodular. In particular, we obtain that the Drinfeld double D(...

bivariate features, obtained from multichannel electroencephalogram (eeg) recordings, quantify the relation between different brain regions. studies based on bivariate features have shown optimistic results for tackling epileptic seizure prediction problem in patients suffering from refractory epilepsy. a new bivariate approach using univariate features is proposed here. differences and ratios ...

A (loopless) digraph H is strongly immersed in a digraph G if the vertices of H are mapped to distinct vertices of G, and the edges of H are mapped to directed paths joining the corresponding pairs of vertices of G, in such a way that the paths used are pairwise edge-disjoint, and do not pass through vertices of G that are images of vertices of H. A digraph has cutwidth at most k if its vertice...

The faithful quasi-dual H and strict quasi-dual H ′ of an infinite braided Hopf algebra H are introduced and it is proved that every strict quasi-dual H ′ is an HHopf module. The connection between the integrals and the maximal rational Hsubmodule H of H is found. That is, H ∼= ∫ l H ⊗H is proved. The existence and uniqueness of integrals for braided Hopf algebras in the Yetter-Drinfeld categor...

We study the problem of computing h-quasi planar drawings in linear area; in an h-quasi planar drawing the number of mutually crossing edges is bounded by a constant h. We prove that every n-vertex partial k-tree admits a straight-line h-quasi planar drawing in O(n) area, where h depends on k but not on n. For specific sub-families of partial k-trees, we present ad-hoc algorithms that compute h...

Security communication is an important requirement in many sensor network applications. A new kind of pairwise key establishment scheme based on hierarchical hypercube model H(k,u,m,v,n) for clustersdeployed sensor networks distribution model is presented. Theoretic analysis and experimental figures show that the new pairwise key model has better performance and provides higher possibilities fo...

Let r > 1 be an integer. An h-hypergraph H is said to be r-quasi-linear (linear for r = 1) if any two edges of H intersect in 0 or r vertices. In this paper it is shown that r-quasi-linear paths P h,r m of length m > 1 and cycles C h,r m of length m > 3 are chromatically unique in the set of h-uniform r-quasi-linear hypergraphs provided r > 2 and h > 3r − 1.

The title compound, C15H12N2O4S, is V-shaped with the isoindoline ring system (r.m.s. deviation = 0.006 Å) inclined to the benzene ring by 84.27 (13)°. In the crystal, inversion dimers are formed via pairwise N-H⋯O hydrogen bonds. These dimers associate further into corrugated ribbons, via pairwise N-H⋯O and C-H⋯O hydrogen bonds, propagating along the a-axis direction and lying parallel to (001).

An (N ;n,m, {w1, . . . , wt})-separating hash family is a set H of N functions h : X −→ Y with |X| = n, |Y | = m, t ≥ 2 having the following property. For any pairwise disjoint subsets C1, . . . , Ct ⊆ X with |Ci| = wi, i = 1, . . . , t, there exists at least one function h ∈ H such that h(C1), h(C2), . . . , h(Ct) are pairwise disjoint. Separating hash families generalize many known combinator...

We introduce strong separation axioms in bitopological spaces. We also introduce the notion of strong pairwise compactness.