Le Matematiche (Dipartimento di Matematica e Informatica, Università degli Studi di Catania)
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Essentially alpha-hyponormal operators with essential spectrum of area zero
No full textWe prove that essentially alpha-hyponormal operators with zero area of the essential spectrum are essentially normal
A bifurcation-type theorem for the positive solutions of a nonlinear Neumann problem with concave and convex terms
Get PDFWe consider a nonlinear elliptic Neumann problem driven by the p-Laplacian with a reaction that involves the combined effects of a “concave” and of a “convex” terms. The convex term (p-superlinear term) need not satisfy the Ambrosetti-Rabinowitz condition. Employing variational methods based on the critical point theory together with truncation techniques, we prove a bifurcation type theorem for the equation
Combined effects and degenerate phenomena in nonlinear stationary problems
Get PDFIn this survey paper we are concerned with several nonlinear stationary problems involving nonhomogeneous differential operators. We report on some recent qualitative results related with various nonlinear problems in Orlicz-Sobolev spaces. Our analysis combines spectral analysis techniques with variational methods
Probability density functions involving a generalized r–Gauss hypergeometric function
Get PDFThe aim of this paper is to study r–generalized gamma functions of a particular form.Moreover, we define a new probability density function (p.d.f) involving these new generalized functions. Some basic functions associated with the p.d.f’s, such as moment generating functions, mean residue functions and hazard rate functions are derived
On the uniqueness of limit cycles for Liénard equations: the legacy of G. Sansone
Get PDFWe give an account of the results about limit cycle’s uniqueness for Liénard equations, starting from Levinson-Smith’s one to the most recent ones. We present a new uniqueness theorem in the line of Sansone-Massera’s geometrical approach
Relazione d\u27ordine in un corpide
Get PDFA corpid is a ring (K, +, ·), different from zero, such that (K, ·) is an inverse semigroup. We define an order relation and the notion of simple element. By this we prove several results and a characterization of corpids
Factoring small 2-groups
No full textLet G be a finite abelian group and let G = A_1 · · · A_n be a factorization of G into its subsets A_1 , . . . , A_n. For a given G certain choices of the orders |A_1|, . . . , |A_n| guarantee that one of the factors is periodic. In connection with an open problem we determine such choices of orders of factors intwo special cases. In these cases |G| is either 2^5 or 2^6
Polynomial expansions for solution of wave equation in quantum calculus
Get PDFIn this paper, using the q^2 -Laplace transform early introduced by Abdi [1], we study q-Wave polynomials related with the q-difference operator ∆q,x . We show in particular that they are linked to the q-little Jacobi polynomials p_n (x; α, β | q^2 )
Properties of infinite harmonic functions relative to Riemannian vector fields
Get PDFWe employ Riemannian jets which are adapted to the Riemannian geometry to obtain the existence-uniqueness of infinite harmonic functions in Riemannian spaces. We then show such functions are equivalent to those that enjoy comparison with Riemannian cones. Using comparison with cones, we show that the Riemannian distance is a supersolution to the infinite Laplace equation, but is not necessarily a solution. We find some geometric conditions under which the Riemannian distance is infinite harmonic and under which it fails to be infinite harmonic
Stanley\u27s conjecture, cover depth and extremal simplicial complexes
Get PDFA famous conjecture by R. Stanley relates the depth of a module, an algebraic invariant, with the so-called Stanley depth, a geometric one. We describe two related geometric notions, the cover depth and the greedy depth, and we study their relations with the Stanley depth for Stanley-Reisner rings of simplicial complexes. This leads to a quest for the existence of extremely non-partitionable simplicial complexes. We include several open problems and questions.This paper is a report about a research project suggested by J. Herzog at the summer school P.R.A.G.MAT.I.C. 2008 at the University of Catania. In particular, the paper describes a direction where we expect that possible counterexamples can be found at least for a weaker version of Stanley’s conjecture