Le Matematiche (Dipartimento di Matematica e Informatica, Università degli Studi di Catania)
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Classification of general absolute geometries with Lambert-Saccheri quadrangles
Get PDFWithout claiming any kind of continuity we show that an absolute geometry has either a singular, a hyperbolic or an elliptic congruence
Geometric Goppa codes on Fermat curves
Get PDFWe consider a class of codes defined by Goppa’s algebraic-geometric construction on Fermat curves. Automorphisms and decoding of such codes are investigated
Mixed type of Fredholm-Volterra integral equation
Get PDFIn this paper, under certain conditions, the solution of mixed type of Fredholm-Volterra integral equation is discussed and obtained in the space L_2 (−1, 1) × C[0, T ], T < ∞. Here, the singular part of kernel of Fredholm-Volterra integral term is established in a logarithmic form, while the kernel of Fredholm-Volterra integral term is a positive continuous function in time and belongs to the class C[0, T ], T < ∞. The solution, when the mixed type integral, takes a system form of Fredholm integral equation of the first or second kind are discussed
Spaces of dimension three with congruence
Get PDFIt is well known that every Euclidean plane (E, L, α, ≡) is isomorphic to an affine plane AG(2,K) over a Pythagorean ordered commutative field K .There is a corrisponding theorem for hyperbolic panes (cf. [2]). For both proofs one first considers the group of motions, in particular the line reflections
Flag-transitive L_h.L*-geometries
Get PDFThe classification of finite flag-transitive linear spaces, obtained by Buekenhout, Delandtsheer, Doyen, Kleidman, Liebeck and Saxl [20] at the end of the eighties, gave new impulse to the program of classifying various classes of locally finite flag-transitive geometries belonging to diagrams obtained from a Coxeter diagram by putting a label L or L ∗ on some (possibly, all) of the singlebond strokes for projective planes
Steiner systems and large non-Hamiltonian hypergraphs
Get PDFFrom Steiner systems S(k − 2, 2k − 3, v), we construct k-uniform hyper- graphs of large size without Hamiltonian cycles. This improves previous estimates due to G. Y. Katona and H. Kierstead [J. Graph Theory 30 (1999), pp. 205–212]
Manifolds with integrable affine shape operator
Get PDFThis work establishes the conditions for the existence of vector fields with the property that theirs covariant derivative, with respect to the affine normal connection, be the affine shape operatorS in hypersurfaces. Some results are obtained from this property and, in particular, for some kind of affine decomposable hypersurfaces we explicitely get the actual vector fields
Characterization of the absolutely summing operators in a Banach space using μ-approximate l_1 sequences
Get PDFIn this paper we will give a characterization of 1-absolutely summing operators using μ-approximate l_1 sequences. Exactly if (x_n )_1^∞ is μ-approximate l_1 , basic and normalized sequence in Banach space X then every bounded linear operator T from X into Banach space Y is 1-absolutely summing if and only if Y is isomorphic to Hilbert space
Linear codes meeting the Griesmer bound, minihypers and geometric applications
Get PDFCoding theory and Galois geometries are two research areas which greatly influence each other. In this talk, we focus on the link between linear codes meeting the Griesmer bound and minihypers in finite projective spaces. Minihypers are particular (multiple) blocking sets. We present characterization results on minihypers, leading to equivalent characterization results on linear codes meeting the Griesmer bound. Next to being interesting from a coding-theoretical point of view, minihypers also are interesting for geometrical applications. We present results on maximal partial μ-spreads in PG(N, q), (μ + 1)|(N + 1), on minimal μ-covers in PG(N, q), (μ + 1)|(N + 1), on (N − 1)-covers of Q + (2N + 1, q), on partial ovoids and on partial spreads of finite classical polar spaces, and on partial ovoids of generalized hexagons, following from results on minihypers
Cycle decomposition with a sharply vertex transitive automorphism group
Get PDFIn some recent papers the method of partial differences introduced by the author in [4] was very helpful in the construction of cyclic cycle systems. Here we use and describe in all details this method for the purpose of constructing, more generally, cycle decompositions with a sharply vertex transitive automorphism group not necessarily cyclic