Le Matematiche (Dipartimento di Matematica e Informatica, Università degli Studi di Catania)
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Decomposition of the Bessel functions with respect to the cyclic group of order n
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Betti numbers of space curves bounded by Hilbert functions
Get PDFWe study relationships between Hilbert functions and graded Betti numbers of two space curves C and C_0 bilinked by a sequence of basic double linkages; precisely we obtain bounds for the graded Betti numbers of C by means of the Hilbert functions of the two curves and the graded Betti numbers of C_0 . On the other hand for every set of integers satisfying these bounds we can construct a curve with these integers as its graded Betti numbers. As a consequence we get a Dubreil-type theorem for a curve C which strongly dominates C_0 at height h which is exactly the Amasaki bound for Buchsbaum curves. Moreover we deduce for biliaison classes of Buchsbaum curves that a strong Lazarsfeld-Rao property holds
The upper chromatic number of quasi-interval co-hypergraphs
Get PDF We investigate the structural and colouring properties of clique hyper-graphs of interval graphs called the quasi-interval hypergraphs. We find the conditions when they are interval hypergraphs. The upper chromatic number for the clique co-hypergraphs of interval graphs is found
New solutions of the confluent Heun equation
Get PDFNew compact triple series solutions of the confluent Heun equation (CHE) are obtained by the appropriate applications of the Laplace transform and its inverse to a suitably constructed system of soluble differential equations. The computer-algebra package MAPLE V is used to tackle an auxiliary system of non-linear algebraic equations. This study is partly motivated by the relationship between the CHE and certain Schrödininger equations
A generalization of Lax-Milgram\u27s theorem
Get PDFIn this paper we generalize a theorem of Lax-Milgram
Esistenza di soluzioni per una disequazione ellittica quasilineare derivante da un problema di frontiera libera
Get PDFIn this work we prove the existence of (at least) one solution of theinequality: a(u, v − u) + l(u, v − u) ≥ 0 for any v ∈ M(u^◦ ) u ∈ M(u^◦ ) ∩ L^∞ (Omega)where M(u^◦) = {v ∈ H^{1,2}(Omega) : v = u^◦ on Gamma^+ and v ≤ u^◦ on Gamma^◦}, a and l are non linear forms, whose coefficients satisfy Caratheodory\u27s conditions and suitable growth\u27s assumptions, Gamma^+ and Gamma^◦ are parts of ∂Omega.The above introduced inequality represents a mathematical generalization of a free boundary problem studied in [1], where, in the same space M(u^◦), the author looks for solutions of : Integral_Omega k(u)∇(v − u)a(·)(∇u + e(·, u)) dx ≥ 0 for any v ∈ M(u^◦),where e is bounded and satisfying Caratheodory\u27s conditions, k piecewise continuous, bounded and not negative, a bounded and uniformly elliptic
Blocking sets of small size and colouring in finite affine planes
Get PDFLet (S, L) be an either linear or semilinear space and X ⊂ S. Starting from X we define three types of colourings of the points of S. We characterize the Steiner systems S(2, k, ν) which have a colouring of the first type with X = {P}. By means of such colourings we construct blocking sets of small size in affine planes of order q. In particular, from the second and third type of colourings we get blocking sets B with |B| ≤ 2q − 2
A unifying minimax theorem
Get PDFIn the present note, a minimax theorem is given which combines the most general topological and quantitative conditions employed in the literature. This result encompasses a large part of the classes of topological, quantitative, and mixed minimax theorems, and includes several new variants
The Picard and the Gauss-Weierstrass singular integrals of functions in two variables
Get PDFWe study some approximation properties of the Picard and the Gauss-Weierstrass singular integrals of functions of two variables belonging to some exponential weighted spaces. In Sec. 3.1 and 3.2 we give two theorems on the degree of approximation and two theorems of the Voronovskaya type. In Sec. 3.3 the Bernstein inequalities for these singular integrals are proved.Some similar results for the Picard and the Gauss-Weierstrass singular integral of functions of one variable were given in [1] - [3]
Oscillatory and asymptotic behaviour of higher order difference equations
Get PDFThis paper is concerned with the oscillation and asymptotic behaviour of nonoscillatory solutions of nonlinear difference equation of a particular form