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...

This paper presents a method based on the simplex algorithm to evaluate real or complex polynomials, having scalar or interval coeecients. The aim of this method is not to nd exactly the set P(X) where P is a polynomial and X a real interval or a complex disk but to obtain a set which surely contains P(X). Evaluation de polyn^ omes avec l'agorithme du Simplexe. R esum e : Nous pr esentons ici u...

This paper gives a new and eecient algorithm in order to compute some characteristic polynomials using Cauchy modules. This algorithm is used for the computation of absolute resolvents and multi-resolvents which are essential tools in constructive Galois theory. formation de facteurs parasites, le polyn^ ome caract eristique d'un endomorphisme multi-plicatif associ e a un invariant quelconque d...

The natural projection from the moduli space of polynomials of degree n is not surjective if n ≥ 4. We give explicit parametric representation of the exceptional set when n = 4 and 5. And we describe degeneration which occurs above the exceptional set when n = 4. Also we show that the preimage of a point generally consists of (n − 2)! points, where (n − 2)! is the maximum when the preimage is a...

1.1 Définitions élémentaires Définition 1. Soit P ∈ k[X ] et a ∈ k. On dit que a est une racine de P si P (a) = 0, ou de manière équivalente si X − a divise P . On appelle multiplicité de a le plus grand entier μ tel que (X − a) divise P . Proposition 1. Si P ∈ k[X ] admet a1, . . . , al pour racines, de multiplicités respectives μ1, . . . , μl, alors il existe Q ∈ k[X ] tel que P = Q∏(X − ai)i...

We propose a restarted Arnoldi's method with Faber polynomials and discuss its use for computing the rightmost eigenvalues of large non hermitian matrices. We illustrate, with the help of some practical test problems, the beneet obtained from the Faber acceleration by comparing this method with the Chebyshev based acceleration. M ethode d'Arnoldi-Faber pour les probl emes aux valeurs propres no...

The concern of this paper is the study of automated deduction methods for propositional modal logics. We use tableau proof-systems to show that Fitting's translation of the transitive modal logic S4 into T can be constructed in deterministic polynomial time. Moreover, we establish a polynomial bound to the length of branches in both tableau and sequent proof search for the transitive logics S4 ...

Cellular behavior is frequently influenced by the cell's history, indicating that single cells may memorize past events. We report that budding yeast permanently escape pheromone-induced cell-cycle arrest when experiencing a deceptive mating attempt, i.e., not reaching their putative partner within reasonable time. This acquired behavior depends on super-assembly and inactivation of the G1/S in...

The study of the topological classiication of complex polynomials began in the XIX-th century by Luroth (1871), Clebsch (1873) and Hurwitz (1891). In the works of Zdravkovska 23] and Khovanskii and Zdravkovska 17] the problem is reduced to a purely combinatorial one, that of the study of a certain action of the braid groups on a class of tree-like gures that we, following 14], call \cacti". Usi...

Ferromagnetic iron oxide nanoparticles of about 33nm in diameter were synthesized by hightemperature decomposition of an iron–oleate complex, using octadecene as the solvent. These particles were subsequently coated with polyN-isopropylacrylamide (pNIPAAm) by a surfactant exchange method. Temperature-sensitive behavior of these particles was studied using ac susceptibility and dynamic light sca...