Le Matematiche (Dipartimento di Matematica e Informatica, Università degli Studi di Catania)
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On the Hilbert function and the minimal free resolution of the GF(q)-points of Del Pezzo surfaces of P^n
Get PDFHere we study the Hilbert function of the points rational over a fixed finite field GF(q), q = pe of some Del Pezzo surfaces and of the Veronese plane. This work is motivated by the equivalence (due to Moorhouse) between the knowledge of the Hilbert function of a finite set of a projective space over GF(q) and the p-rank of its incidence matrix
On fractional deviation operators
Get PDFThe so called fractional deviation operators are introduced. This class of integral transforms appears naturally from the study of iteration of fractional integrals of Riemann-Liouville type. Since B. Ross\u27 formulation on fractional iteration process, among other problems selected by T. Osler [5] toward 1974, several authors have been working on this subject. In particular, are worth mentioning contributions of B. Rubin [7] that allowed an intrinsic connection between fractional integrals with different limits of integration (Love\u27s question, see [5] also) and the corresponding Ross\u27 problem for Chen fractional integrals, handled by A. Nahushev [4] and M. Salahitdinov, with broad applications to non local boundary value problems. In this article we consider deviation operators as integral transforms, their connection with operators of Rubin type and mapping properties between classical and weighted Lebesgue spaces
Strong solvability for a class of nonlinear parabolic equations
Get PDFExistence of strong solutions to Cauchy-Dirichlet problem for nonlinear parabolic equation is established. The nonlinear operator is prescribed by Carathéodory\u27s function which satisfies an ellipticity condition due to S. Campanato. The main results are reached through Aleksandrov-Bakel\u27man-Pucci type maximum principle and topological fixed point theorem
Contributo alle iperstrutture matroidali
Get PDFIn this paper we continue the investigation of matroidal hyperstructures, introduced in [8], [9], [15], [17], [22]. In the first section, we define the sub-hypergroupoid [A] generated by a subset A of an hypergroupoid (H, •). We introduce the notion of defect and optimal defect of [A] and nvestigate their properties.In the following sections, we define the class of M_λ -hypergroups, attached to an action of a group on a set M . We give necessary, and necessary and sufficient conditions for a M_λ -hypergroupoid to be matroidal. The most significant case is given by the canonical action of the multiplicative group K^∗ of a field K on the set V − {0}, where V is a K-vector space. Moreover, we determine necessary conditions under which the defect of a sub-hypergroupoid [A] of a M_λ -hypergroupoid is optimal; we also give examples of non-commutative matroidal hypergroupoids. In the last section, we continue the investigation of finite non-commutative exchange groups
A new generalization of generalized hypergeometric functions
Get PDFIn this paper a natural generalization of the familiar H -function of Fox namely the I -function is proposed. Convergence conditions, various series representations, elementary properties and special cases for the I -function have also been given
Necessary and sufficient conditions for Hölder continuity of solutions of degenerate Schrödinger operators
Get PDFIn this paper it is studied the Hoelder-continuity of solutions of a linear degenerate elliptic equation of the form (∗) -Sum_ {i, j =1}^n (a_{i j} u_{x_i} )_{x_j} + V u = 0.It is proved that the solutions of (∗) are Hoelder-continuous if the coefficient V belongs to an appropriate "degenerate" Morrey space. Under some additional assumptions on the weight giving the degeneracy, the previous condition is also necessary
A very ampleness result
Get PDFLet (M, L) be a polarized manifold. The aim of this paper is to establish a connection between the generators of the graded algebra oplus_{i≥1} H^0(M, i L) and the very ampleness of the line bundle r L . Some applications are given
On tail asymptotics for L^1-norm of centered brownian bridge
Get PDFAsymptotics of the tail probability for L^1 -norm of the centered Brownian bridge is obtained
Algebraic and geometric automorphisms of hypergroupoids
Get PDFTwo concepts of automorphism of a hypergroupoid are introduced; the first one preserve the algebraic structure of a hypergroupoid, the second one preserve the geometric structure that one can associate naturally to a hypergroupoid. The groups of such automorphisms are studied, in particular in the case that the geometric space associated to a hypergroupoid is a Steiner system