Let us consider a 3-numerical semigroup S = 〈a, b,N 〉. Given m ∈ S, the triple (x, y, z) ∈ N3 is a factorization of m in S if xa+ yb+ zN = m. This work is focused on finding the full set of factorizations of any m ∈ S and as an application we compute the catenary degree of S. To this end, we relate a 2D tessellation to S and we use it as a main tool.

We introduce F-IVM, a unified incremental view maintenance (IVM) approach for a variety of tasks, including gradient computation for learning linear regression models over joins, matrix chain multiplication, and factorized evaluation of conjunctive queries. F-IVM is a higher-order IVM algorithm that reduces the maintenance of the given task to the maintenance of a hierarchy of increasingly simp...

Abstract For a peculiar family of double braid knots there is remarkable factorization formula for the coefficients differential (cyclotomic) expansion (DE), which nowadays widely used to construct exclusive Racah matrices S and $${\bar{S}}$$ S ¯ </mml:math...

In this paper we find necessary and sufficient conditions for the existence of a group divisible design GDD(n, m) of index (*1 , *2) in which n=2 or m=2, thereby completing the solution of the existence problem for all n, m, *1 , and *2 . In the process, necessary and sufficient conditions are found for the existence of an x-regular partial triple system whose complement in *Kn has a 1-factoriz...

We review the application of perturbative QCD to diffractive processes. We introduce the two gluon exchange model to describe diffractive q ¯ q and q ¯ qg production in deep inelastic scattering. We study the triple Regge limit and briefly consider multiple gluon exchange. We discuss diffractive vector meson production at HERA both at t = 0 and large |t|. We demonstrate the non-factorization of...

In this paper, we define a new concept of factorization for a bounded bilinear mapping $f:Xtimes Yto Z$, depended on  a natural number $n$ and a cardinal number $kappa$; which is called $n$-factorization property of level $kappa$. Then we study the relation between $n$-factorization property of  level $kappa$ for $X^*$ with respect to $f$ and automatically boundedness and $w^*$-$w^*$-continuity...

In standard Regge theory, the contribution of the tripe-pomeron amplitude to the t = 0 differential cross section for single diffraction dissociation has the form dσ/dMdt|t=0 ∼ (s/s0)IP (0)−1]/(M2)αIP (0), where αIP (t) is the pomeron trajectory. For αIP (0) > 1, this form, which is based on factorization, does not scale with energy. From an analysis of pp and p̄p data from fixed target to colli...

The most important consequence of Pomeron being a pole is the factorization property. However, due to Pomeron intercept being greater than 1, the extrapolated single diffraction dissociation cross section based on a classical triple-Pomeron formula is too large leading to a potential unitarity violation at Tevatron energies, which has been referred to as “Dino’s paradox”. We review our resoluti...

Most collaborative filtering (CF) models estimate missing ratings with an implicit assumption that the are missing-at-random, which may cause biased rating estimation and degraded performance since recent deep exploration shows likely be missing-not-at-random (MNAR). To debias MNAR estimation, we introduce item observability user selection to depict generation of propose a tripartite CF (TCF) f...