Le Matematiche (Dipartimento di Matematica e Informatica, Università degli Studi di Catania)
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Geometric k-normality of curves and applications
Get PDFThe notion of geometric k-normality for curves is introduced in complete generality and is investigated in the case of nodal and cuspidal curves living on several types of surfaces. We discuss and suggest some applications of this notion to the study of Severi varieties of nodal curves on surfaces of general type and on P^2
Algèbre de Sobolev et structure m-convexe
No full textWe examine the structure of a class of Sobolev spaces. We also show that the unitization of a locally uniformly A-convex algebra is not, in general, of the same type
Schur\u27s lemma and best constants in weighted norm inequalities
Get PDFStrong forms of Schur\u27s Lemma and its converse are proved for maps taking non-negative functions to non-negative functions and having formal adjoints. These results are applied to give best constants in a large class of weighted Lebesgue norm inequalities for non-negative integral operators. Since general measures are used, norms of non-negative matrix operators may be calculated by the same method
Current problems in mathematical phisics: the original contribution of David Hilbert
No full textThe significance of Hilbert\u27s seminal work in kinetic theory of gases for modern research in mathematical phisics is investigated
The origins and the further development of Hilbert\u27s "Grundlagen der Geometrie"
No full textThe year 1999 stimulates to look back at the expiring century, ..
A two-phase variational problem with curvature
Get PDFIn this paper we consider a two phases variational problem related to a functional F. In particular we obtain results about the smoothness of the free boundary {u = 0}
The Foucault\u27s current problem with temperature dependent resistivity
Get PDFA result of existence and uniqueness of solutions is presented for the system of P.D.E. modelling the eddy currents and the heating in a cylindrical conductor
A singular cubic fourfold containing a plane
No full textIn this paper we consider cubic 4-folds containing a plane whose discriminant curve is a reduced nodal plane sextic. In particular, we describe the singular points of such cubic 4-folds and we give conditions on the geometry of the plane sextics so that all the associated cubic 4-folds are singular. Moreover, we construct a family of smooth rational cubic 4-folds whose discriminant curve is reduced but reducible
Hilbert e il calcolo delle variazioni
No full textI fondamentali contributi di Hilbert al Calcolo Delle Variazioni ..
Hilbert e i fondamenti della matematica: il metodo assiomatico
No full textIl ruolo esercitato da David Hilbert nel campo dei fondamenti della matematica è insigne