Le Matematiche (Dipartimento di Matematica e Informatica, Università degli Studi di Catania)
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Oscillation estimates relative to p-homogeneous forms and Kato measures data
No full textWe state pointwise estimate for the positive subsolutions associated to a p-homogeneous form and nonnegative Radon measures data. As a by-product we establish an oscillation’s estimate for the solutions relative to Kato measures data
On some positive embedding of P^d
Get PDFWe prove that any two embeddings P^d ∼ Y → X_1 , P^d ∼ Y → X_2 , d ≥ 3, in two n-folds projective varieties X_1 , X_2 with normal bundle N_{Y |X_1} ∼ X_{Y |X_2} ∼ (n − d)O_{P^d} (1) are formally equivalent .Moreover, we see that Y is G2 in both X_1 and X_2. As an immediate consequence of this result and if furthermore Y is G3 in both X_1 and X_2 then we deduce that the two embeddings are Zariski equivalent
Dirichlet problem with L^p-boundary data for real sub-Laplacians
Get PDFLet L be a real sub-Laplacian on a stratified Lie group G. In this note we present some results on the Dirichlet problem for L with L^p-boundary data, on domains which are contractible with respect to the natural dilations of G. One of the main difficulties we overcome is the presence of non-regular boundary points for the usual Dirichlet problem for L. A potential theoretical approach is followed
Boundary estimates for solutions to singular elliptic equations
Get PDFWe deal with the Dirichlet problem in a bounded smooth domain.[omissis
Application of formative processes to the decision problem in set theory
Get PDFAs part of a project aimed at the implementation of a proof-checker based on the set-theoretic formalism, the decision problem in set theory has been studied very intensively, starting in the late seventies.Several results have been produced in the first decade of research, giving rise to the novel field of computable set theory. At that point, it already was clear that to face the tremendous amount of technicalities involved in the combination of smaller decidable fragments into larger ones, new techniques were in order.Such techniques have recently emerged, by a careful analysis of the formation process of disjoint families of sets. This has led to the characterization of suitable decidable conditions for the satisfiability of set-theoretic formulae belonging to specific collections.In this paper we give an elementary introduction to the formative process technique and discuss some open problems
Combinatorial problems arising from pooling designs for dna library screening
Get PDFColbourn (1999) developed some strategy for nonadaptive group testing when the items are linearly ordered and the positive items form a consecutive subset of all items.Müller and Jimbo (2004) improved his strategy by introducing the concept of 2-consecutive positive detectable matrices (2CPD-matrix) requiring that all columns and bitwise OR-sum of each two consecutive columns are pairwise distinct. Such a matrix is called maximal if it has a maximal possible number of columns with respect to some obvious constraints. Using a recursive construction they proved the existence of maximal 2CPD-matrices for any column size m ∈ N except for the case m = 3. Moreover, maximal 2CPD-matrices such that each column is of some fixed constant weight areconstructed. This leads to pooling designs, where each item appears in the same number of pools and all pools are of the same size.Secondly, we investigate 2CPD-matrices of some constant column weight τ ∈ N. We give some recursive construction of such matrices having the maximal possible number of columns. Thirdly, error correction capability of group testing procedures is essential in view of applications such as DNA library screening. We consider a error correcting 2CPD-matrices
Coloring mixed hypergraphs: from combinatorics to philosophy
Get PDFWe survey recent results and open problems on the chromatic spectrum,planarity and colorability of mixed hypergraphs and their relations to suchcategories of philosophy as identity and difference
Risultati di esistenza per alcune classi di disequazioni variazionali-emivariazionali di tipo ellittico
Get PDFThe main purpose of this lecture is to present some basic notions on variational and variational-hemivariational inequalities as well as two recent existence results in the elliptic case. A wide bibliography is also provided
Some results on special binomial ideals
Get PDFThe main goal of this paper is to characterize a particular class of ideals whose structure can still be interpreted directly from their generators: binomial ideals having a finite number of binomials generators in a polynomial ring k[x] = k[x_1 , ..., x_n ]. More in details, we associate to every binomial ideal a homogeneous linear system constructed on its generators. We call it Toric System because it supplies us Toric Ideals given as elimination ideals. We observe that the constructed Toric Ideals depend only on the rank of a matrix that is solution of the Toric System. In addition, we define a binomial principal generator and then, we give some results for the case of a particular class of binomial ideals
Families of n-gonal curves with maximal variation of moduli
Get PDFThe aim of this paper is to generalize a lemma by Caporaso to families of n- gonal curves, namely curves that have a n to 1 map to P^1 . In order to explain the results we obtained and to give the ideas of our proofs, we first review the instructive proof of Caporaso’s lemma