Showing papers in "Le Matematiche in 2009"

ACM Bundles on Del Pezzo surfaces

Abstract: ACM rank 1 bundles on del Pezzo surfaces are classified in terms of the rational normal curves that they contain. A complete list of ACM line bundles is provided. Moreover, for any del Pezzo surface X of degree less or equal than six and for any n ≥ 2 we construct a family of dimension ≥ n − 1 of non-isomorphic simple ACM bundles of rank n on X .

Graded Betti numbers of ideals with linear quotient

Abstract: In this paper we show that every ideal with linear quotients is componentwise linear. We also generalize the Eliahou-Kervaire formula for graded Betti numbers of stable ideals to homogeneous ideals with linear quotients.

An algorithm to compute the Stanley depth of monomial ideals

Abstract: In this article we describe an algorithm to compute the Stanley depth of I=J where I and J are monomial ideals. We describe also an implementation in CoCoA.

Some remarks on the Stanley depth for multigraded modules

Abstract: We show that Stanley’s conjecture holds for any multigraded module M over S , with sdepth(M) = 0 , where S = K[x_1; ... ; x_n] . Also, we give some bounds for the Stanley depth of the powers of the maximal irrelevant ideal in S .

Common fixes points in ordered Banach spaces

Abstract: In this paper we introduce the notion of g-weak isotone mappings in an ordered Banach space and we extend some common fixed point theorems of Dhage, O’Regan and Agarwal [1].

Derived categories of toric Fano 3-folds via the Frobenius morphism

Abstract: In [8, Conjecture 3.6], Costa and Miro-Roig state the following conjecture: Every smooth complete toric Fano variety has a full strongly exceptional collection of line bundles. The goal of this article is to prove it for toric Fano 3-folds.

Derived category of toric varieties with picard number three

Abstract: We construct a full, strongly exceptional collection of line bundles on the variety X that is the blow up of the projectivization of the vector bundle O_{Pn−1} ⊕ O_{Pn−1}(b_1) along a linear space of dimension n − 2, where b_1 is a non-negative integer.

Dimension, depth and zero-divisors of the algebra of basic k-covers of a graph

Abstract: We study the basic k -covers of a bipartite graph G ; the algebra A(G) they span, first studied by Herzog, is the fiber cone of the Alexander dual of the edge ideal. We characterize when A(G) is a domain in terms of the combinatorics of G ; it follows from a result of Hochster that when A(G) is a domain, it is also Cohen-Macaulay. We then study the dimension of A(G) by introducing a geometric invariant of bipartite graphs, the “graphical dimension”. We show that the graphical dimension of G is not larger than dim(A(G)) , and equality holds in many cases (e.g. when G is a tree, or a cycle). Finally, we discuss applications of this theory to the arithmetical rank.

Mammographic density - a useful biomarker for breast cancer risk in epidemiologic studies

Abstract: We describe mammographic density and how it is associated with breast cancer risk, what mammographic density represents biologically, as well as evidence that it is associated with breast cancer risk factors and is modifiable. Mammographic density has a large unused potential in mammographic screening programs. Currently mammographic density is being used as a biomarker or surrogate endpoint for breast cancer risk in a number of studies, and we discuss the rationale for doing this, as well as the challenges involved. A major challenge is the need for an automated method that can yield an even more precise estimate of the dense areas in the breast. Currently the most widely used methods are various computer-assisted methods. These are reader intensive, but so far the methods that yield the highest estimates for breast cancer risk. Once a robust automated method for assessing mammographic density or breast density is developed, this measure will probably become even more widely used, not just in epidemiology, but also in screening programs and in clinical practice.

Stanley's conjecture, cover depth and extremal simplicial complexes

Abstract: A 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.

Componentwise linearity of ideals arising from graphs

Abstract: Let G be a simple undirected graph on n vertices. Francisco and Van Tuyl have shown that if G is chordal ...

Betti numbers of powers of ideals

Abstract: Let A=K[x1, ..... ,xn] be a standard graded polynomial ring over a field K , let M = (x_1, .... , x_n) be the graded maximal ideal and I a graded ideal of A . For each i the Betti numbers b_i(I^k ) of I^k are polynomial functions for k>>0 . We show that if I is M -primary, then these polynomial functions have the same degree for all i .

Second order evolution inclusions governed by sweeping process in Banach spaces

Abstract: In this paper we prove two existence theorems concerning the existence of solutions for second order evolution inclusions governed by sweeping process with closed convex sets depending on time and state in Banach spaces. This work extends some recent existence theorems cncerning sweeping process from Hilbert spaces to Banach spaces.

Adendum to Self-verified extension of affine arithmetic to arbitrary order

Abstract: Le MatematicheVol. LXIII (2008 - Fasc. I, pp. 15–30)For a technical mistake this article appeared without references and citations. Here we add the references and, page by page, the necessary citations in order of appearance. We apologize for this inconvenient.

Gotzmann lexsegment ideals

Abstract: In this paper we characterize the componentwise lexsegment ideals which are componentwise linear and the lexsegment ideals generated in one degree which are Gotzmann.

On the non-existence of orthogonal instanton bundles on P^{2n+1}

Abstract: In this paper we prove that there do not exist orthogonal instanton bundles on P ^{2n+1} . In order to demonstrate this fact, we propose a new way of representing the invariant, introduced by L. Costa and G. Ottaviani, related to a rank 2n instanton bundle on P ^{2n+1}.

A characterization of ACM 0-dimensional schemes in Q.

Abstract: Let X ⊂ Q = P ^1 × P ^1 be a reduced 0-dimensional subscheme of the quadric Q and let P ∈ X be any point. Using the separating degree of P for X we give a sufficient condition so that X is ACM. This result, together with the previous ones (see [9]) gives a new characterization of ACM 0-dimensional schemes of Q by using separators.

Henstock integral and Dini-Riemann theorem

Abstract: In [5] an analogue of the classical Dini-Riemann theorem related to non-absolutely convergent series of real number is obtained for the Lebesgue improper integral. Here we are extending it to the case of the Henstock integral.

Notes on symmetric and exterior depth and annihilator numbers

Abstract: We survey and compare invariants of modules over the polynomial ring and the exterior algebra. In our considerations, we focus on the depth. The exterior analogue of depth was first introduced by Aramova, Avramov and Herzog. We state similarities between the two notion of depth and exhibit their relation in the case of squarefree modules. Work of Conca, Herzog and Hibi and Trung, respectively, shows that annihilator numbers are a meaningful generalization of depth over the polynomial ring. We introduce and study annihilator numbers over the exterior algebra. Despite some minor differences in the definition, those invariants show common behavior. In both situations a positive linear combination of the annihilator numbers can be used to bound the symmetric and exterior graded Betti numbers, respectively, from above.

Properties of infinite harmonic functions relative to Riemannian vector fields

Abstract: We 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.

A note on the Serrin problem in the plane

Abstract: We investigate the stability of the radial symmetry for the overdetermined Serrin problem in a planar convex set. More precisely, we prove that, whenever we properly perturb both the boundary conditions and the data, then a convex solution is “close” to a suitable paraboloid and the domain is “close” to a ball with respect to the Hausdorff metric.

On the dimension of the minimal vertex cover semigroup ring of an unmixed bipartite graph

Abstract: In a paper in 2008, Herzog, Hibi and Ohsugi introduced and studied the semigroup ring associated to the set of minimal vertex covers of an unmixed bipartite graph. In this paper we relate the dimension of this semigroup ring to the rank of the Boolean lattice associated to the graph.

Studio di una classe notevole di anelli dotata di inverso generalizzato

Abstract: We study a remarkable class of rings, which we call corpids, that is the rings, different from zero, (K;+; .); such that (K; .) is an inverse semi-group (or groupid, which is the name given by G. Tallini [4]). The inverse semigroup has been defined and called generalized group, indipendently by Viktor Vladimirovich Vagner [6] in the Soviet Union and by Gordon Preston in the Great Britain [3].

One parameter dual lorentzian spherical motions and ruled surfaces

Abstract: In this work, we first introduced one parameter dual Lorentzian spherical motions in three dimensional dual Lorentz space D^3_1 and spacelike and timelike ruled surfaces in three dimensional Lorentz space IR^3_1 corresponding to dual curves on dual Lorentz unit sphere S^2_1 . After that we have given the relations on the velocities and instantaneous rotation axis for one parameter Lorentzian spherical motions in dual Lorentz space D^3_1 , with some examples on these timelike and spacelike ruled surfaces. Finally we have obtained the theorem related to the acceleration, acceleration centres and acceleration axis for these one parameter dual Lorentzian spherical motions.

Enhancement of high-energy distribution tail in Monte Carlo semiconductor simulations using a Variance Reduction Scheme

Abstract: The Multicomb variance reduction technique has been introduced in the Direct Monte Carlo Simulation for submicrometric semiconductor devices. The method has been implemented in bulk silicon. The simulations show that the statistical variance of hot electrons is reduced with some computational cost. The method is efficient and easy to implement in existing device simulators.

Splitting criteria for vector bundles on the symplectic isotropic Grassmannian

Abstract: We extend a theorem of Ottaviani on cohomological splitting criterion for vector bundles over the Grassmannian to the case of the symplectic isotropic Grassmanian. We find necessary and sufficient conditions for the case of the Grassmanian of symplectic isotropic lines. For the general case the generalization of Ottaviani’s conditions are sufficient for vector bundles over the symplectic isotropic Grassmannian. By a calculation in the program LiE, we find that Ottaviani’s conditions are necessary for Lagrangian Grassmannian of isotropic k-planes for k ≤ 6, but they fail to be necessary for the case of the Lagrangian Grassmannian of isotropic 7-planes. Finally, we find a related set of necessary and sufficient splitting criteria for the Lagrangian Grassmannian.

The standard graded property for vertex cover algebras of quasi-trees

Abstract: In [5] the authors characterize the vertex cover algebras which are tandard graded. In this paper we give a simple combinatorial criterion for the standard graded property of vertex cover algebras in the case of quasi-trees. We also give an example of how this criterion works and compute the maximal degree of a minimal generator in that case.

Existence of solutions for some degenerate quasilinear elliptic equations

Abstract: In this paper we are interested in the existence of solutions for Dirichlet problem associated to the degenerate quasilinear elliptic equations

Extended solutions of a system of nonlinear integro-differential equations

Abstract: This paper deals with extended solutions of a system of nonlinear integro-differential equations. This system is obtained in the process of applying the Galerkin method for some initial-boundary value problems.

A model of recreation services in local government

Abstract: The purpose of this study is to define an applicable model for organizing human resources, customer expectations, and service quality in recreational activities for local governments. Sportive recreation is one of the areas that people spend their money on. Health consciousness is the main reason underneath. Government should support such kind of activities. Municipality is the main part of local government. This is the reason that municipalities are the main services provider for public. The local government should provide healthy, reliable, satisfactory, safe recreational activities. The success of recreation units depends on the skilled stuff who know the wishes, interest and hopes of the society and who have been educated to hold the philosophy, concept and aims of recreation. The purpose is to enable the local governments to be professional institutions about recreational activities and is to establish a certain model. To reach the defined aim; it is to state recreational activities, applied education, to serve tutorial help to the amateur and professional practitioners, to contribute to the organizations like festival, exhibition, exposition, etc., to establish a concept by making practitioners and experts come together.