In this paper, we define the higher Frobenius-Schur (FS-)indicators for finite-dimensional modules of a semisimple quasi-Hopf algebra H via the categorical counterpart developed in a 2005 preprint. When H is an ordinary Hopf algebra, we show that our definition coincides with that introduced by Kashina, Sommerhäuser, and Zhu. We find a sequence of gauge invariant central elements of H such that...

Let G and H be connected graphs and let G ∗ H be the strong product of G by H. We show that every retract R of G ∗ H is of the form R = G′ ∗ H ′, where G′ is a subgraph of G and H ′ one of H. For triangle–free graphs G and H both G′ and H ′ are retracts of G and H, respectively. Furthermore, a product of finitely many finite, triangle–free graphs is retract–rigid if and only if all factors are ...

Many NLP tasks can be regarded as a selection problem from set of options, such classification tasks, multi-choice question answering, etc. Textual entailment (TE) has been shown the state-of-the-art (SOTA) approach to dealing with those problems. TE treats input texts premises (P), options hypotheses (H), then handles by modeling (P, H) pairwise. Two limitations: first, pairwise is unaware oth...

Given two hypergraphs H and H ′ on a common vertex set, we write H < H ′ if each edge of H is contained in an edge of H ′. Given H < H ′, either find an acyclic hypergraph A between them, H < A < H ′, or claim that there is no such A. This problem is referred to as the Acyclic Hypergraph Sandwich Problem (AHSP) (H,H ′). We show that one can assume without loss of generality that H is a graph. T...

We de ne fuzzy h-subhemiring, fuzzy h-ideals and fuzzy generalized h-biideals with thresholds, and characterize h-hemiregular and h-intra-hemiregular hemirings by the properties of their fuzzy h-ideals, fuzzy h-bi-ideals and fuzzy h-quasi-ideals with thresholds.

The steady state distribution of quasi-birth-death pro esses an be eÆ iently obtained by matrix-geometri (MG) methods. Sin e a number of tele ommuni ation problems are modelled by pro esses with bat h arrivals, the extension of MG methods for these pro esses has pra ti al importan e. This paper presents an extension of MG methods whi h is e e tive for the analysis of quasi-birth-death pro esses...

The aim of this paper is to study induced (quasi-)uniformities in Kramosil and Michalek's fuzzy metric spaces. Firstly, $I$-uniformity in the sense of J. Guti'{e}rrez  Garc'{i}a and $I$-neighborhood system in the sense of H"{o}hle and u{S}ostak are induced by the given fuzzy metric. It is shown that the fuzzy metric and the induced $I$-uniformity will generate the same $I$-neighborhood system. ...

We show that Ambro–Kawamata’s non-vanishing conjecture holds true for a quasi-smooth WCI X which is Fano or Calabi-Yau, i.e. we prove that, if H is an ample Cartier divisor on X , then |H | is not empty. If X is smooth, we further show that the general element of |H | is smooth. We then verify Ambro–Kawamata’s conjecture for any quasi-smooth weighted hypersurface. We also verify Fujita’s freene...