Le Matematiche (Dipartimento di Matematica e Informatica, Università degli Studi di Catania)
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New Ostrowski type inequalities for co-ordinated s-convex functions in the second sense
Get PDFIn this paper some new Ostrowski type inequalities for co-ordinated s-convex functions in the second sense are obtained
The cone of Hilbert functions in the non-standard graded case
Get PDFWe describe the cone of Hilbert functions of artinian graded modules finitely generated in degree 0 over the polynomial ring R = k[x, y] with the non-standard grading deg(x) = 1 and deg(y) = n, where n is any natural number
On the Betti numbers of some semigroup rings
Get PDFFor any numerical semigroup S, there are infinitely many numerical symmetric semigroups T such that S = T/2 (see below for the definition of T/2) is their half. We are studying the Betti numbers of the numerical semigroup ring K[T ] when S is a 3-generated numerical semigroup or telescopic. We also consider 4-generated symmetric semigroups and the so called 4-irreducible numerical semigroups
The cones of Hilbert functions of squarefree modules
Get PDFIn this paper, we study different generalizations of the notion of square freeness for ideals to the more general case of modules. We describe the cones of Hilbert functions for squarefree modules in general and those generated in degree zero. We give their extremal rays and defining inequalities. For squarefree modules generated in degree zero, we compare the defining inequalities of that cone with the classical Kruskal-Katona bound, also asymptotically
Analytic study on linear systems of distributed order fractional differential equations
Get PDFIn this paper we introduce the distributed order fractional differential equations (DOFDE) with respect to the nonnegative density function. We generalize the inertia and characteristics polynomial concepts of pair with respect to the nonnegative density function. We also give generalization of the invariant factors of a matrix and some inertia theorems for analyzing the stability of the DOFDE systems
Univalent harmonic functions defined by Salagean integral operator with respect to symmetric points
Get PDFIn this paper, we define and investigate a subclass of univalent harmonic functions defined by Salagean integral operator with respect to symmetric points. We obtain coefficient conditions, extreme points, distortion bounds, convex combinations for this family of harmonic univalent functions
Generalized fractional integration of the \overline{H}-function
No full textA significantly large number of earlier works on the subject of fractional calculus give interesting account of the theory and applications of fractional calculus operators in many different areas of mathematical analysis (such as ordinary and partial differential equations, integral equations, special functions, summation of series, et cetera). In the present paper, we study and develop the generalized fractional integral operators given by Saigo. First, we establish two Theorems that give the images of the product of H-function and a general class of polynomials inSaigo operators. On account of the general nature of the Saigo operators, H-function and a general class of polynomials a large number of new and known Images involving Riemann-Liouville and Erdélyi-Kober fractional integral operators and several special functions notably generalized Wright hypergeometric function, generalized Wright-Bessel function, the polylogarithm and Mittag-Leffler functions follow as special cases of our main findings
Marichev-Saigo-Maeda fractional integration operators of the Bassel functions
Get PDFIn this paper, we apply generalized operators of fractional integration involving Appell’s function F_3 (.) due to Marichev-Saigo-Maeda, to the Bessel function of first kind. The results are expressed in terms of generalized Wright function and hypergeometric functions _pF_q . Special cases involving this function are mentioned. Results given recently by Kilbas and Sebastian follow as special cases of the theorems establish here
On the relation between Betti numbers of an Arf semigroup and its blowup
Get PDFIn this note we prove the relation between Betti numbers of an Arf semigroup S and its blowup S in the case when they have the same multiplicity n
The h-vector of the union of two sets of points in the projective plane
Get PDFGiven two h-vectors, h and h\u27, we study which are the possible h-vectors for the union of two disjoint sets of points in P^2 , respectively associated to h and h\u27 and how they can be constructed. We will give some bounds for the resulting h-vector and we will show how to construct the minimal h-vector of the union among all possible ones