The factor refinement principle turns a partial factorization of integers (or polynomials) into a more complete factorization represented by basis elements and exponents, where basis elements are pairwise coprime. There are many applications of this refinement technique such as simplifying polynomial systems and, more generally, to algebraic algorithms generating redundant expressions during in...

The multivalency approach to generalized Nevanlinna functions established in Wietsma (Indag Math 29:997–1008, 2018) is here extended the related class of Schur giving thereby rise new characterizations for this as well a straightforward function-theoretical proof its factorization. In particular, explains how well-known factorizations two mentioned classes differ from each other. Indeed, by fac...

We find necessary and sufficient conditions for a complete local (Noetherian) ring containing the rationals to be completion of countable excellent domain. Furthermore, we noncatenary domain, as well it unique factorization

We give a precise average-case analysis of a complete polynomial factorization chain over nite elds by methods based on generating functions and singularity analysis. Polyn^ omes al eatoires et factorisation de polyn^ omes R esum e Nous donnons une analyse en moyenne pr ecise d'une cha^ ne compl ete de factorisation de polyn^ omes sur les corps nis par des m ethodes fond ees sur les fonctions g...

Given a one-factorization F of the complete bipartite graph Kn,n, let pf(F) denote the number of Hamiltonian cycles obtained by taking pairwise unions of perfect matchings in F . Let pf(n) be the maximum of pf(F) over all one-factorizations F of Kn,n. In this work we prove that pf(n) > n2/4, for all n > 2. 1 Perfect one-factorizations A one-factorization of a graph G is a partition of its set o...

Let L = Q[α] be an abelian number field of prime degree q, and let a be a nonzero rational number. We describe an algorithm which takes as input a and the minimal polynomial of α over Q, and determines if a is a norm of an element of L. We show that, if we ignore the time needed to obtain a complete factorization of a and a complete factorization of the discriminant of α, then the algorithm run...

Results for the complete NLO electroweak corrections to Standard Model Higgs production via gluon fusion are included in the total cross section for hadronic collisions. Artificially large threshold effects are avoided working in the complex-mass scheme. The numerical impact at LHC (Tevatron) energies is explored for Higgs mass values up to 500 GeV (200 GeV). Assuming a complete factorization o...

We pose and solve the existence of 2-factorizations of complete graphs and complete bipartite graphs that have the number of cycles per 2-factor varying, called pancomponented. Such 2-factorizations exist for all such graphs. The pancomponented problem requires a slight generalization of the methods used to solve pancyclic 2-factorization problem, by building 2-factors from cyclically generated...

The factor refinement principle turns a partial factorization of integers (or polynomials) into a more complete factorization represented by basis elements and exponents, with basis elements that are pairwise coprime. There are lots of applications of this refinement technique such as simplifying systems of polynomial inequations and, more generally, speeding up certain algebraic algorithms by ...