Le Matematiche (Dipartimento di Matematica e Informatica, Università degli Studi di Catania)
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Problemi lineari e non lineari di flusso intorno ad ostacoli
Get PDFWe discuss the problem of the steady two-dimensional flow past fixed disturbances in an open channel of finite depth. We consider different types of obstacles, like submerged or surface-piercing bodies, and localized perturbations of a horizontal bottom; recent results on unique solvability of the linear problem and rigorous proofs of solvability of the non linear, free boundary problem are reviewed
Maximal subgroups of finite classical groups and their geometry
Get PDFWe survey some recent results on maximal subgroups of finite classical groups
On Chern ratios for surfaces with ample cotangent bundle
Get PDFIn this paper we study the problem of density in (1, 3) for the Chern ratio of surfaces with ample cotangent bundle. In particular we prove density in (1, 2) by constructing a family of complete intersection surfaces in a product of varieties with big cotangent bundle. We also analyse the case of complete intersections in a product of curves of genus at least 2
Weak well posedness of the Dirichlet problem for equations of mixed ellptic-hyperbolic type
Get PDFEquations of mixed elliptic-hyperbolic type with a homogeneous Dirichlet condition imposed on the entire boundary will be discussed. Such closed problems are typically overdetermined in spaces of classical solutions in contrast to the well-posedness for classical solutions that can result from opening the boundary by prescribing the boundary condition only on a proper subset of the boundary. Closed problems arise, for example, in models of transonic fluid flow about a given profile, but very little is known on the well-posedness in spaces of weak solutions. We present recent progress, obtained in collaboration with D. Lupo and C.S. Morawetz, on the well-posedness in weighted Sobolev spaces as well as the beginnings of a regularity theory
Semiregular factorization of simple graphs
Get PDFA graph G is a (d, d + s)-graph if the degree of each vertex of G lies in the interval [d, d + s]. A (d, d + 1)-graph is said to be semiregular. An (r, r + 1) -factorization of a graph is a decomposition of the graph into edgedisjoint (r, r + 1)-factors.We discuss here the state of knowledge about (r, r + 1)-factorizations of d -regular graphs and of (d, d + 1)-graphs.For r, s ≥ 0, let φ(r, s) be the least integer such that, if d ≥ φ(r, s) and G is any simple [d, d + s]-graph, then G has an (r, r + 1)-factorization.Akiyama and Kano (when r is even) and Cai (when r is odd) showed that φ(r, s) exists for all r, s. We show that, for s ≥ 2, φ(r, s) = r(r + s + 1) + 1. Earlier φ(r, 0) was determined by Egawa and Era, and φ(r, 1) was determined by Hilton
Balanced generalized weighing matrices and their applications
Get PDFBalanced generalized weighing matrices include well-known classical combinatorial objects such as Hadamard matrices and conference matrices; moreover, particular classes of BGW -matrices are equivalent to certain relative difference sets. BGW -matrices admit an interesting geometrical interpretation, and in this context they generalize notions like projective planes admitting a full elation or homology group. After surveying these basic connections, we will focus attention on proper BGW -matrices; thus we will not give any systematic treatment of generalized Hadamard matrices, which are the subject of a large area of research in their own right. In particular, we will discuss what might be called the classical parameter series. Here the nicest examples are closely related to perfect codes and to some classical relative difference sets associated with affine geometries; moreover, the matrices in question can be characterized as the unique (up to equivalence) BGW -matrices for the given parameters with minimum q-rank.One can also obtain a wealth of monomially inequivalent examples and deter mine the q-ranks of all these matrices by exploiting a connection with linear shift register sequences
Maximal set of factors
No full textIn this paper, a survey is presented of results concerning maximal sets of factors in graphs. These factors at times satisfy additional structural constraints, such as being connected, or such as requiring each component of each factor to be isomorphic. Each set of factors occurs in some natural family of graphs, including complete graphs and complete multipartite graphs
Combinatorial aspects of covering arrays
Get PDFCovering arrays generalize orthogonal arrays by requiring that t -tuples be covered, but not requiring that the appearance of t -tuples be balanced.Their uses in screening experiments has found application in software testing, hardware testing, and a variety of fields in which interactions among factors are to be identified. Here a combinatorial view of covering arrays is adopted, encompassing basic bounds, direct constructions, recursive constructions, algorithmic methods, and applications
Isomorphism of modular group algebras of finite torsion-free rank coproducts of p-mixed countable abelian groups
Get PDFSuppose G is with finite torsion-free rank a coproduct of p-mixed countable abelian groups and F is a field with characteristic p such that the group algebras FG and FH are F -isomorphic for another group H . Then G and H are isomorphic
Infinitely many solutions to the Dirichlet problem for quasilinear elliptic systems
Get PDFIn this paper we deal with the existence of weak solutions for some Dirichlet problem.The existence of solutions is proved by applying a critical point variational principle obtained by B. Ricceri as consequence of a more general variational principle