Sur le troisième invariant d''une forme quadratique

Résumé Nous étudions un invariant à valeurs dans un sous-quotient deK ₃.

---

On the third invariant of a quadratic form

We study an invariant with values in a subquotient ofK ₃.

---

     

Chaînes alternées

Résumé Je caractérise les combinaisons booléennes de parties finales d'un ordre partiel P au moyen d'une limitation de la façon dont elles peuvent alterner sur les chaînes de P.

---

I characterize the Boolean combinations of final segments of an ordered set by restricting the way they alternate on the chains of P.

     

Comportement moyen du cardinal de certains ensembles de facteurs premiers

Letn be a positive integer andS _n a particular set of prime divisors ofn. We establish the average order off(n) wheref(n) stands for the cardinality ofS _n . Thek-ary,k-free, semi-k-ary prime factors ofn are some of the classes of prime divisors studied in this paper.

     

Sulle superficie di ordine 2n con una conica multipla di ordinen.

Riassunto Costruzione della immagine di una involuzione ciclica appartenente ad, una superficie di ordine 2n con una conica multipla di ordinen.

---

Résumé Construction de l'image d'une involution cyclique appartenant à une surface d'ordre 2n ayant une conique multiple d'ordren.

     

Sur le rang de la jacobienne des systèmes linéaires de quadriques

A necessary and sufficient condition is shown in order that a linear system of quadrics inS _r, joined of first and second kind, has a Jacobian with rankr— k.

     

Sur la suite de polynômes orthogonaux associée à la formeu=δ c +λ(x−c) −1 L

We show that, ifL is regular, semi-classical functional, thenu is also regular and semi-classical for every complex λ, except for a discrete set of numbers depending onL andc. We give the second order linear differential equation satisfied by each polynomial of the orthogonal sequence associated withu. The cases whereL is either a classical functional (Hermite, Laguerre, Bessel, Jacobi) or a functional associated with generalized Hermite polynomials are treated in detail.

     

Una nota sui gruppi policiclici che ammettono un automorfismo con numero di Reidemeister finito

LetG be a group and ϕ an automorphism ofG. Two elementsx, y ∈ G are called ϕ-conjugate if there existsg ∈ G such thatx=g ⁻¹ yg ^θ. It is easily verified that the ϕ-conjugation is an equivalence relation; the numberR(ϕ) of ϕ-classes ofG is called the Reidemeister number of the automorphism ϕ. In this paper we prove that if a polycyclic groupsG admits an automorphism ϕ of ordern such thatR(ϕ)<∞, thenG contains a subgroup of finite index with derived length at most 2 ⁿ⁻¹ .

     

On zero dimensional subschemes of scrolls

Here we consider cohomological properties of zero-dimensional subschemes of a scrollS⊂P ^N . We study them proving cohomological results forS. The main tool is the degeneration ofS to a suitable union of linear subspaces ofP ^N .

---

Sunto In questo lavoro siamo interessati alle proprietà coomologiche dei sottoschemi di dimensione 0 di uno scrollS⊂P ^N . Per il loro studio si provano in questo lavoro risultati coomologici perS usando degenerazioni diS ad unioni di sottospazi lineari diP ^N .

     

Almost topological spaces

Summary Convergence spaces are studied from a geometrical point of view. In many cases we may construct a topological space VirtX, which can be considered as the resolution of the topological singularities ofX.

---

Riassunto Spazi di convergenza vengono studiati da un punto di vista geometrico. In molti casi possiamo costruire uno spazio topologico VirtX che può essere considerato come la risoluzione delle singolarità diX.

     

Soluzioni periodiche di equazioni ellittiche totalmente non lineari

Sunto In questo lavoro dimostriamo due teoremi di esistenza di soluzioni periodiche per due classi di equazioni ellittiche totalmente non lineari.

---

Summary Existence theorems for periodic solutions of totaly non linear elliptic equations are given.

---

---

Lavoro eseguito nell'ambito del G.N.A.F.A. del C.N.R.     

On the divisor class groups of localizations,completions and veronesean subrings of z-graded krull domains

Summary LetR be aZ-graded, noetherian, integral domain. This paper deals mainly with the divisor class groups of localizations and completions with respect to an α-adic topology (α homogeneous) ofR. Some technical results are used to study the Veronesean subrings ofR.

---

Riassunto SiaR un dominioZ-graduato, noetheriano. Questo articolo tratta principalmente il gruppo di classi di divisori di localizzazioni e completamenti rispetto ad una topologia α-adica (α omogeneo) diR. Alcuni risultati tecnici vengono applicati allo studio dei sottoanelli Veronesiani diR.

     

Prolégomènes à l'étude des polynômes orthogonaux semi-classiques

Résumé On établit une théorie générale des suites de polynômes orthogonaux dont la suite des dérivées est une suite quasi-orthogonale.

---

Summary One deals with general theory of orthogonal polynomials sequences whose derivatives sequence is quasi-orthogonal.

     

Existence results for some free boundary filtration problems

Summary A suitable extension of the pressure junction allows to formulate quite general free boundary filtration problems in terms of a non-standard variational inequality, both for the stationary and the evolution situations. Existence results are proved.

---

Sunto Un opportuno prolungamento della funzione pressione permette di formulare problemi di filtrazione a frontiera libera alquanto generali in termini di una disequazione variazionale di tipo non standard. Si dimostrano risultati di esistenza, sia per il caso stazionario che per quello di evoluzione.

     

Anneaux extrémaux dans les surfaces de Riemann

Let X be a closed hyperbolic surface, and let c be a disjoint union of simple closed geodesics on X. A sharp upper bound for the injectivity radius of c is given in terms of the total length of c and of the Euler-Poincaré characteristic of X.

---

Résumé Soit X une surface hyperbolique fermée et soit c une réunion disjointe de géodésiques fermées simples de X. Nous établissons une majoration optimale du rayon d’injectivité de c en fonction de sa longueur totale et de la caractéristique d’Euler-Poincaré de X.

     

Sur Les Partitions en Chaînes du Graphe Divisoriel

On path partitions of the divisor graph. Let D(x) be the graph with vertices {1, 2, ..., ⌊x⌋} whose edges come from the division relation, and let D(x, y) be the subgraph restricted to the integers with prime factors less than or equal to y. We give sufficient conditions on x and y for the graph D(x, y) to be Hamiltonian. We deduce an asymptotic formula for the number of paths in D(x) needed to partition the set of vertices {1, 2, ..., ⌊x⌋}.

     

On the absolute continuity of the roots of some algebraic equations

We prove that for every polynomial of degreem≤3, with coefficients depending smoothly on a real parametert, it is possible to select am-tuple of roots absolutely continuous int.

---

Sunto Proviamo che per ogni polinomio di gradom≤3, i cui coefficienti dipendano con sufficiente regolarità da un parametro realet, si possono selezionarem radici (indipendenti) che sono assolutamente continue int.

     

A note on well-posedness of the displacement problem in linear elastostatics

It is proved that thedisplacement problem of homogeneous linear elastostatics in exterior domains iswell-posed in the Hilbert space of all vector-valued functions having afinite Dirichlet integral, provided theelasticity tensor is strongly elliptic.

---

Sommario Si dimonstrano dei teoremi dibuona posizione per ilproblema di posto dell'elastostatica lineare omogenea ed isotropa in domini esterai. Si ambienta il problema nello spazio di Hilbert costituito dalle funzioni vettoriali aventiintegrale di Dirichlet finito e si assume ehe iltensore elatico siafortemente ellittico.

     

Rami di varietà lungo sottovarietà da un punto di vista topologico

Summary A topological definition is given of « branch of a complex algebraic variety along a subvariety ». Comparisons are made with classical algebraic branch theory.     

Sui connettivi tra eventi e l’impostazione assiomatica del calcolo delle probabilità

Riassunto Ammesso il connettivoaut sull’insieme degli eventi, si mostra come risultano definiti i connettivivel edet. Si deducono quindi i teoremi delle probabilità totali e delle probabilità composte.

---

Résumé Admis le connectifaut sur l’ensemble des événements, on montre comme résultent définis les connectifvel etet. On déduit de là les théorèmes des probabilités totales et des probabilités composées.

     

Application du prolongement analytique au problème inverse du potentiel

Sommaire Le but de cet article est établir quelques résultats nouveaux sur le problème inverse du potentiel newtonien. Nous démontrons deux théorèmes d'unicité: pour les polyédres convexes dansR ⁿ et pour les lemniscates dansR ². L'instrument principal est un lemme basé sur une idée de V. Kondrachkov rarement utilisé malgré sa puissance. Nous montrons son efficacité en liaison avec la méthode du prolongement analytique des potentiels.

---

The goal of this paper is to establish some new results in the inverse Newtonian potential problem. We prove two uniqueness theorems: for convex polyhedra inR ⁿ and for lemniscates inR ². The main tool is a lemma based upon an idea of V. Kondrashkov which, though powerful, is rarely used. We show its efficiency applied together with the method of analytic continuation of potentials.