Showing papers in "Le Matematiche in 1991"

Neutral surfaces in neutral four-spaces

Abstract: Properties of the Gauss map of neutral surfaces are studied. Special attention is given to surfaces of parallel, or zero, mean curvature. Bilagrangian structures are defined and used in ways analogous to the use of complex structures in the Riemannian case. The nonsimplicity of the structure group SO(2,2) is used to factor the Gauss map and to construct analogs of the twistor space, called in this context reflector space.

On two conjectures to generalize Vizing's Theorem

Abstract: Visizing's Theorem states that for a single graph G , the chromatic index q(G) is equal to the maximum degree Δ(G) or to Δ(G)+1 . To extend this theorem to some classes of hypergraphs, we suggest two conjectures, non-comparable, but, in some sense, dual, which are discussed in the present paper.

Mathematical characterization of functions underlying the principle of relativity

Abstract: In a Minkowsky space V , complete representation formulae are derived for scalar-valued, vector valued and tensor-valued sunctions subjected to the principle of relativity with an arbitrary number of scalars, vectors and tensors (of the second order symmetric and skewsymmetric) as variables.

Controllability of partial differential inclusions depending on a parameter and distributed parameter control processes

Abstract: Let Λ be a topological space and let F be a multifunction from [0,a]x[0,b]x( R n ) 4 xΛ into R n . In this paper we prove that, under suitable assumptions, the set of all λ in Λ such that the partial differential inclusion is locally controllable around the origin of R n at the point (a,b) (resp. R n -completely controllable) is open in Λ . Next, we present an application to the study of two kinds of controllability for the distribuited parameter control process.

Oscillatory behaviour of difference equations with positive and negative coefficients

Abstract: We obtain sufficient conditions for the oscillation of all solutions of linear difference equations with positive and negative coefficients of a particular form.

Applications of the monotone-iterative techniques of V. Lakshmikantham to the solutions of the initial value problem for functional differential equations

Abstract: In the paper a technique of approximate finding of extremal quasisolutions of an inirial value problem for systems of functional differential equations is justified.

On the use of pairwise balanced designs and closure spaces in the construction of structures of degree at least 3

Abstract: We prove that a set of v-2 symmetric idempotent latin squares of order v , such that no two of them agree in a off-diagonal position, exists for all odd v>>0 . We describe how the techniques used in the proof relate to techniques used in [17] to construct generalised idempotent ternary quasigroups whose conjugate invariant group contains some specific subgroup. We also showhow these techniques fit into the more general context of trying to extend group divisible design methods to combinatorial structures, using closure spaces.

Linear spaces: history and theory

Abstract: Linear spaces belong to the most fundamental geometric and combinatorial structures. In this paper I would like to give an onerview about the theory of embedding finite linear spaces in finite projective planes.

Stabilizability of oscillatory systems: a classical approach supported by symbolic computation

Abstract: In this paper we study the stabilization of planar single-input non-linear systems, whose linearization at the origin has purely immaginary eigenvalues A classical recursive procedure based on polar coordinates transformation is applied to obtain some sufficient conditions Then we focus on bilinear systems; a complete solution of the problem is given in this case Explicit statements of the conditions are possible thanks to the use of symbolic computation packages

On the existence of weak solutions of the stationary semiconductor equations with velocity saturation

Abstract: In the present paper we prove the existence and differentiability of weak solutions to the stationary semiconductor equations where the mobility coefficients model the effect of saturation of drift velocity The proof of existence relies on approximation by uniformly bounded mobility coefficients

Supports of (ν,4,2) designs

Abstract: The spectrum of possible numbers of repeated blocks in (ν,4,2) designs is determined for all ν⩾121.

A mathematical model for radiation hydrodynamics

Abstract: We adopt here the idea of describing a radiation field by means of the radiation energy density E and the radiative flux vector F which must satisfy a set of evolution equations; in these equations an unknown tensorial function P(E, F ) appears that is determined by the methods of extended thermodynamics.

Remars on K-midconvex set-valued functions with closed epigraph

Abstract: In this note we present some continuity results on K -midconvex set-valued functions. In particular, we give conditions under which K -midconvex and set valued functions with closed epigraph are K -continuous.

On projective manifolds admitting 3-gonal or 4-gonal curve sections

Abstract: Let X be a projective manifold, of dimension n≥3 , and L a very ample line bundle on X In this paper we investigate the pairs (X,L) with the following property: there exists a transversal intersection of n-1 members of |L| which is a smooth d -gonal curve ( d=3,4 ) We prove, under suitable assumptions, that n≤4 or 5 (resp if d=3 or 4 ) and (X,L) is a fibration over P 1 with genera; fibre a rational cubic (resp quartic) scroll

On the point linear arboricity of a graph

Abstract: In a linear forest, every component is a path. The linear arboricity of a graph G is the smallest number of edge disjoint linear forests whose union is G ; this concept has been much studied. We now introduce the point linear arboricity of G , defined as the smallest number of parts in a partition of V=V(G) such that each part induces a linear forest. We prove an analogue to the classical theorem of Brooks for the invariant.

Barbier type theorems for plane curves

Abstract: A C 1 class of simple closed and convex plane curves which contains all ovals is considered. This class is divided into subclasses for which greatest lower bound of number of Barbier sets are determined.