DSpace Collection:

Some Remarks on Homogeneous Minimal Reductions

Mon, 01 Jan 2007 00:00:00 GMT

Title: Some Remarks on Homogeneous Minimal Reductions Authors: Spangher, Walter Abstract: Let I be a homogeneous ideal of a graded affine k–algebra R such that there exists some homogeneous minimal reduction. We prove that the degrees (of a basis) of every homogeneous minimal reduction J of I are uniquely determined by I; moreover if the fiber cone F(I) is reduced, then the last degree of J is equal to the last degree of I. Moreover, if R is Cohen– Macaulay and I is of analytic deviation one, with 0 < ht(I) := g, it is shown that the first g degrees of J are equals to the first g degrees of I. These results are applied to the ideals I of $k[x_0, . . . , x_{d−1}]$, which have scheme–th. generations of length \leq ht(I) + 2. Some examples are given. Type: Articolo

An Algorithm for Reconstructing a Convex Polygon from its Covariogram

Mon, 01 Jan 2007 00:00:00 GMT

Title: An Algorithm for Reconstructing a Convex Polygon from its Covariogram Authors: Benassi, Carlo; D'Ercole, Giuliana Abstract: The covariogram of a compact convex set $K \subset \mathbb R^n$ is the function that at each point $x \in \mathbb R^n$ associates the volume of $K \cap (K + x)$. The covariogram determines, among all convex bodies, any planar convex polygon. In this paper we present an algorithm for reconstructing an arbitrary convex polygon from its covariogram. Type: Articolo

On the Limit Behavior in a Free Boundary Model for the Diffusion in a Polymer

Mon, 01 Jan 2007 00:00:00 GMT

Title: On the Limit Behavior in a Free Boundary Model for the Diffusion in a Polymer Authors: Gaudiano, Marcos; Godoy, Tomas; Turner, Cristina Abstract: Free boundary problems arise modelling the sorption of solvents into glassy polymers. There are physical reasons to expect that a convective condition with coefficient h, behaves asymptotically as a Dirichlet condition. In this work we prove, analyzing the uniform convergence the equivalence of these problems. A condition is also derived that allows one to decide whether a specific application lies within the asymptotic regime. Type: Articolo

Countability Properties of the Pseudocompact-Open Topology on C (X ): A Comparative Study

Mon, 01 Jan 2007 00:00:00 GMT

Title: Countability Properties of the Pseudocompact-Open Topology on C (X ): A Comparative Study Authors: Kundu, S.; Garg, Pratibha Abstract: The main goal of this paper is to study the countability properties, such as the countable chain condition, Lindeöf property and second countability of the pseudocompact-open topology on C(X), the set of all continuous real-valued functions on a Tychonoff space X. But in order to make this study fruitful, these countability properties of the pseudocompact-open topology are compared with those of the point-open and compact-open topologies on C(X). Type: Articolo