For a Hopf algebra H over a commutative ring k, the category MH of right Hopf modules is equivalent to the category Mk of k-modules, that is, the comparison functor −⊗k H : Mk → MH is an equivalence (Fundamental theorem of Hopf modules). This was proved by Larson and Sweedler via the notion of coinvariants McoH for any M ∈ MH . The coinvariants functor (−) coH : MH → Mk is right adjoint to the ...

Let D(H) be the quantum double associated to a finite dimensional quasi-Hopf algebra H, as in [9] and [10]. In this note, we first generalize a result of Majid [15] for Hopf algebras, and then prove that the quantum double of a finite dimensional quasitriangular quasi-Hopf algebra is a biproduct in the sense of [4].

We prove, for any n, that there is a closed connected orientable surface S so that the hyperbolic space H almost-isometrically embeds into the Teichmüller space of S, with quasi-convex image lying in the thick part. As a consequence, H quasi-isometrically embeds in the curve complex of S.

We study divisibilities between bounded holomorphic quasi-inner functions in H∞ and operator-valued bounded holomorphic quasi-inner functions in H∞(Ω, L(K)) where Ω is a bounded finitely connected region. Furthermore, we characterize these divisibilities by using rationally-invariant subspaces.

in the present paper we introduce and study the notion of pairwise weakly lindelof bitopological spaces and obtain some results. further, we also study the pairwise weakly lindelof subspaces and subsets, and investigate some of their properties. it was proved that a pairwise weakly lindelof property is not a hereditary property.

The title compound, C(13)H(18)BNO(4), was readily obtained from the reaction of methyl 4-boronobenzene acetate with ethano-lamine. A combination of inter-molecular N-H⋯O hydrogen bonds and C-H⋯π inter-actions leads to the pairwise association of mol-ecules.

In a previous paper we showed that, for any , most sets of points in are determined (up to rotations, reflections, translations and relabeling of the points) by the distribution of their pairwise distances. But there are some exceptional point configurations which are not reconstructible from the distribution of distances in the above sense. In this paper, we concentrate on the planar case and ...

The transmission over the memoryless additive white Class-A noise (AWCN) channel is considered. For uncoded transmission, an exact expression for the symbol error rate is derived. For coded transmission, the Chernoff bound on the pairwise error probability is calculated and the performance achieved on the real and the complex AWCN channels is compared. Moreover, a lowcomplexity, suboptimum deco...

In h i s paper, we introduce Quasi Serializability, a correctness criterion for concurrency control in heterogeneous distributed database environments. A global history is quasi serializable if it is (conflict) equivalent t o a quasi serial history in which global transactions are submitted serially. Quasi serializability theory is an extension of serializability. We study the relationships bet...

Six compounds based on dipicolinic acid esters have been synthesized and Hirshfeld surfaces used to investigate the structure-directing effects of functional groups in controlling their solid-state behavior. Compounds 1-4 are 4-bromo dipicolinic acid esters substituted with methyl, ethyl, propyl, and benzyl groups, respectively. The main structure-directing motif within 1-3 is a pairwise O···H ...