1,721,031 research outputs found
On the computation of the heigth of an ideal in a polynomial ring
No full textL. Chiantini, F. Orecchia Editors, pubblicato da W. de Gruyter, Berli
On the computation of Weierstrass Gap Sequences
No full textapparso nel 2001 perché la rivista era in arretrato con le pubblicazion
The Poicaré series of a local Gorenstein ring of multiplicity up to 10 is rational
No full textWe prove the rationality of the Poincaré series for a certain class of local Gorenstein rings
Structure Indicators for Transportation Graph Analysis I: Planar Connected Simple Graphs
Full text linkThe paper deals with the representation of a transportation infrastructure by a planar connected simple graph and aims at studying its features through the analysis of graph properties. All planar and connected graphs with 4 up to 7 edges are analysed and compared to extract the most suitable parameters to investigate some network features. Then, a set of 41 graphs representing some actual underground networks are also analysed. Besides, as a third scenario, the underground network of Milan, along its development in years, is proposed in order to apply the proposed methodology. Many parameters are taken into consideration. Some of them are already discussed in literature, such as the eigenvalues and gaps of adjacency matrix or such as the Bclassical^ parameters α, β, γ. Others, such as the first two Betti numbers, are new for these applications.In order to overcome the problem of comparing features of graphs with different size, the normalisation of these parameters is considered. Some relationships between Betti numbers, eigenvalues, and classical parameters are also investigated. Results show that the eigenvalues and gaps of the adjacency matrix well represent some features of the graphs while combining them with the Betti numbers, a more significant interpretation can be achieved. Particularly, their normalised values are able to describe the increasing complexity of a graph
TDOA–based Localization in Two Dimensions: the Bifurcation Curve
No full textIn this paper, we complete the study of the geometry of the TDOA map that encodes the
noiseless model for the localization of a source from the range differences between three receivers
in a plane, by computing the Cartesian equation of the bifurcation curve in terms of the positions of
the receivers. From that equation, we can compute its real asymptotic lines. The present manuscript
completes the analysis of [12]. Our result is useful to check if a source belongs or is closed to the
bifurcation curve, where the localization in a noisy scenario is ambiguous
A comparative analysis of underground and bus transit networks through graph theory
No full textThe aim of this paper is to study the topographical features of a transportation infrastructure
through graph theory. First, we construct a planar, connected, and simple graph for each considered infrastructure; then, we compute some normalized indices associated to the graph, namely largest eigenvalue, gap, a Betti number, and codimension. The set of indices proposed in this paper is new for this application. These indices are computed from either the adjacency matrix or the edge ideal of the graph, and so they depend on the overall topology of the graph itself; furthermore, since the normalized indices are scale-free, they allow us a more effective comparison between different transportation infrastructures. Two scenarios are considered in order to understand advantages and limits of the proposed approach: the first scenario concerns a set of underground networks of certain large cities in the world, whereas the second one concerns a set of bus transit networks of several medium-sized cities in Italy. Indices calculated for both scenarios show two types of results. First, they show that the proposed indices are able to estimate the different topologies of the considered networks: networks with the same number of vertices and of edges but not with the same graph have different indices. Second, they show that the values of the indices in the two scenarios not only belong to the same curve separately but fit well also into the same curve: the transportation networks, no matter whether underground or bus transit, seem to be controlled by similar mechanisms
Irreducibility of the Gorenstein loci of Hilbert schemes via ray families
Full text linkWe analyze the Gorenstein locus of the Hilbert scheme of d points on P^n i.e., the
open subscheme parameterizing zero-dimensional Gorenstein subschemes of P^n
of degree d. We give new sufficient criteria for smoothability and smoothness of
points of the Gorenstein locus. In particular we prove that this locus is irreducible
when d <= 13 and find its components when d = 14.
The proof is relatively self-contained and it does not rely on a computer algebra
system. As a by-product, we give equations of the fourth secant variety to the
d-th Veronese reembedding of P^n for d >= 4
A structure theorem for 2-stretched Gorenstein algebras
No full textIn this paper, we study isomorphism classes of local, Artinian, Gorenstein k-algebras A whose maximal ideal M satisfies dimk(M3/M4)=1 by means of Macaulay's inverse system generalizing a recent result by Elias and Rossi. Then we use such results in order to complete the description of the singular locus of the Gorenstein locus of Hilb11(pn)
Postulation of adjoint ideals and geometry of projective curves
No full textPapers from Shreeram S. Abhyankar' s 70th Birthday Conference, Christensen, Sundaram, Sathaye, Bajaj Editors, Springer Verla
- …
