Le Matematiche (Dipartimento di Matematica e Informatica, Università degli Studi di Catania)
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ACM Bundles on Del Pezzo surfaces
Get PDFACM 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
SELF-VERIFIED EXTENSION OF AFFINE ARITHMETIC TO ARBITRARY ORDER
Get PDFAffine Arithmetic (AA) is a self-verifying computational approach that keeps track of first-order correlation between uncertainties in the data and intermediate and final results.In this paper we propose a higher-order extension satisfying the requirements of genericity, arbitrary-order and self-verification, comparing the resulting ethod with other well-known high-order extensions of AA.Affine Arithmetic (AA) is a self-verifying computational approachthat keeps track of first-order correlation between uncertainties in the data and intermediate and final results. In this paper we propose a higher-order extension satisfying the requirements of genericity, arbitrary-order and self-verification, comparing the resulting method with other well-known high-order extensions of AA
GEOMETRIC GROUP PRESENTATIONS: A COMBINATORIAL APPROACH
Get PDFIn this paper we obtain combinatorial conditions for the geometricity of group presentations; such a criterion holds both for orientable and for non-orientable manifolds.In this paper we obtain combinatorial conditions for the geometricityof group presentations; such a criterion holds both for orientable and fornon-orientable manifolds
INFINITELY MANY SOLUTIONS TO THE DIRICHLET PROBLEM FOR QUASILINEAR ELLIPTIC SYSTEMS INVOLVING THE P(X) AND Q(X)-LAPLACIAN
Get PDFIn this paper we consider the Dirichlet problem involving the p(x) and q(x) -Laplacian of the type−∆p(x)u = f (u,v) in Ω−∆q(x)v = g(u,v) in Ωu = 0 on ∂Ωv = 0 on ∂Ωand, by applying a critical point variational principle obtained by Ricceri as a consequence of a more general variational principle, we prove the existence of infinitely many solutions.In this paper we consider the Dirichlet problem involving the p(x) andq(x) -Laplacian of the type−∆p(x)u = f (u,v) in Ω−∆q(x)v = g(u,v) in Ωu = 0 on ∂Ωv = 0 on ∂Ωand, by applying a critical point variational principle obtained by Riccerias a consequence of a more general variational principle, we prove theexistence of infinitely many solutions
CUMULATIVE HIERARCHIES AND COMPUTABILITY OVER UNIVERSES OF SETS
Get PDFVarious metamathematical investigations, beginning with Fraenkel’s historical proof of the independence of the axiom of choice, called for suitable definitions of hierarchical universes of sets. This led to the discovery of such important cumulative structures as the one singled out by von Neumann (generally taken as the universe of all sets) and Godel’s universe of the so-called constructibles. Variants of those are exploited occasionally in studies concerning the foundations of analysis (according to Abraham Robinson’s approach), or concerning non-well-founded sets. We hence offer a systematic presentation of these many structures, partly motivated by their relevance and pervasiveness in mathematics. As we report, numerous properties of hierarchy-related notions such as rank, have been verified with the assistance of the ÆtnaNova proof-checker.Through SETL and Maple implementations of procedures which effectively handle the Ackermann’s hereditarily finite sets, we illustrate a particularly significant case among those in which the entities which form a universe of sets can be algorithmically constructed and manipulated; hereby, the fruitful bearing on pure mathematics of cumulative set hierarchies ramifies into the realms of theoretical computer science and algorithmics.Various metamathematical investigations, beginning with Fraenkel’shistorical proof of the independence of the axiom of choice, called forsuitable definitions of hierarchical universes of sets. This led to the discovery of such important cumulative structures as the one singled out by von Neumann (generally taken as the universe of all sets) and Godel’s universe of the so-called constructibles. Variants of those are exploited occasionally in studies concerning the foundations of analysis (according to Abraham Robinson’s approach), or concerning non-well-founded sets. We hence offer a systematic presentation of these many structures, partly motivated by their relevance and pervasiveness in mathematics. As we report, numerous properties of hierarchy-related notions such as rank, have been verified with the assistance of the ÆtnaNova proof-checker.Through SETL and Maple implementations of procedures which effec-tively handle the Ackermann’s hereditarily finite sets, we illustrate a particularly significant case among those in which the entities which forma universe of sets can be algorithmically constructed and manipulated;hereby, the fruitful bearing on pure mathematics of cumulative set hierarchies ramifies into the realms of theoretical computer science and algorithmics
USING ÆTNANOVA TO FORMALLY PROVE THAT THE DAVIS-PUTNAM SATISFIABILITY TEST IS CORRECT
Get PDFThis paper reports on using the ÆtnaNova/Referee proof-verification system to formalize issues regarding the satisfiability of CNF-formulae of propositional logic. We specify an “archetype” version of the Davis-Putnam-Logemann-Loveland algorithm through the THEORY of recursive functions based on a well-founded relation, and prove it to be correct.Within the same framework, and by resorting to the Zorn lemma, we develop a straightforward proof of the compactness theorem.This paper reports on using the ÆtnaNova/Referee proof-verificationsystem to formalize issues regarding the satisfiability of CNF-formulaeof propositional logic. We specify an “archetype” version of the Davis-Putnam-Logemann-Loveland algorithm through the THEORY of recursive functions based on a well-founded relation, and prove it to be correct.Within the same framework, and by resorting to the Zorn lemma, we develop a straightforward proof of the compactness theorem
COHOMOLOGICAL SUPPORT LOCI FOR ABEL-PRYM CURVES
Get PDFFor an Abel-Prym curve contained in a Prym variety, we determine the cohomological support loci of its twisted ideal sheaves and the dimension of its theta-dual.For an Abel-Prym curve contained in a Prym variety, we determine thecohomological support loci of its twisted ideal sheaves and the dimension of its theta-dual
ON THE EXISTENCE OF MILD SOLUTIONS OF SEMILINEAR FUNCTIONAL DIFFERENTIAL INCLUSIONS
Get PDFIn this paper the existence of local and global mild solution of a semi-linear functional differential inclusion in the case when the kernel is not necessarily compact is proved. Also, some topological properties of the solution set are obtained.In this paper the existence of local and global mild solution of a semi-linear functional differential inclusion in the case when the kernel is notnecessarily compact is proved. Also, some topological properties of thesolution set are obtained
A CHARACTERIZATION OF JACOBIANS BY THE EXISTENCE OF PICARD BUNDLES
Get PDFBased on the Matsusaka-Ran criterion we give a criterion to characterize when a principal polarized abelian variety is a Jacobian by the existence of Picard bundles.Based on the Matsusaka-Ran criterion we give a criterion to characterize when a principal polarized abelian variety is a Jacobian by the existence of Picard bundles
ITERATED DIRICHLET PROBLEM FOR THE HIGHER ORDER POISSON EQUATION
Get PDFConvoluting the harmonic Green function with itself consecutively leads to a polyharmonic Green function suitable to solve an iterated Dirichlet problem for the higher order Poisson equation. The procedure works in any regular domain and is not restricted to two dimensions. In order to get explicit expressions however the situation is studied in the complex plane and sometimes in particular the unit disk is considered.Convoluting the harmonic Green function with itself consecutivelyleads to a polyharmonic Green function suitable to solve an iterated Dirichlet problem for the higher order Poisson equation. The procedure works in any regular domain and is not restricted to two dimensions. In order to get explicit expressions however the situation is studied in the complex plane and sometimes in particular the unit disk is considered