On embeddings of full amalgamated free product C-algebras

We examine the question of when the -homomorphism of full amalgamated free product C-algebras, arising from compatible inclusions of C-algebras , and , is an embedding. Results giving sufficient conditions for to be injective, as well as classes of examples where fails to be injective, are obtained. As an application, we give necessary and sufficient conditions for the full amalgamated free product of finite-dimensional C-algebras to be residually finite dimensional.

     

Partial Dynamical Systems and the KMS Condition

 Given a countably infinite 0–1 matrix A without identically zero rows, let 𝒪 _A be the Cuntz–Krieger algebra recently introduced by the authors and 𝒯 _A be the Toeplitz extension of 𝒪 _A , once the latter is seen as a Cuntz–Pimsner algebra, as recently shown by Szymański. We study the KMS equilibrium states of C ^* -dynamical systems based on 𝒪 _A and 𝒯 _A , with dynamics satisfying for the canonical generating partial isometries s _x and arbitrary real numbers N _x > 1. The KMS_β states on both 𝒪 _A and 𝒯 _A are completely characterized for certain values of the inverse temperature β, according to the position of β relative to three critical values, defined to be the abscissa of convergence of certain Dirichlet series associated to A and the N(x). Our results for 𝒪 _A are derived from those for 𝒯 _A by virtue of the former being a covariant quotient of the latter. When the matrix A is finite, these results give theorems of Olesen and Pedersen for 𝒪 _n and of Enomoto, Fujii and Watatani for 𝒪 _A as particular cases. Received: 21 November 2000 / Accepted: 31 May 2002 Published online: 22 November 2002 RID="*" ID="*" Partially supported by CNP_q RID="**, ***"     

Affinity driven social networks

In this work we present a model for evolving networks, where the driven force is related to the social affinity between individuals of a population. In the model, a set of individuals initially arranged on a regular ordered network and thus linked with their closest neighbors are allowed to rearrange their connections according to a dynamics closely related to that of the stable marriage problem. We show that the behavior of some topological properties of the resulting networks follows a non trivial pattern.     

Non-crossing matchings of points with geometric objects

Given an ordered set of points and an ordered set of geometric objects in the plane, we are interested in finding a non-crossing matching between point–object pairs. In this paper, we address the algorithmic problem of determining whether a non-crossing matching exists between a given point–object pair. We show that when the objects we match the points to are finite point sets, the problem is NP-complete in general, and polynomial when the objects are on a line or when their size is at most 2. When the objects are line segments, we show that the problem is NP-complete in general, and polynomial when the segments form a convex polygon or are all on a line. Finally, for objects that are straight lines, we show that the problem of finding a min-max non-crossing matching is NP-complete.     

Euclidean hypersurfaces with genuine deformations in codimension two

We classify hypersurfaces of rank two of Euclidean space ${\mathbb{R}^{n+1}}$ that admit genuine isometric deformations in ${\mathbb{R}^{n+2}}$ . That an isometric immersion ${\hat{f}\colon M^n \to \mathbb{R}^{n+2}}$ is a genuine isometric deformation of a hypersurface ${f\colon M^n\to\mathbb{R}^{n+1}}$ means that ${\hat f}$ is nowhere a composition ${\hat f=\hat F\circ f}$ , where ${\hat{F} \colon V\subset \mathbb{R}^{n+1} \to\mathbb{R}^{n+2}}$ is an isometric immersion of an open subset V containing the hypersurface.     

An analysis of X-ray absorption spectra in the XANES region of platinum-based electrocatalysts for low-temperature fuel cells

The knowledge of the electronic state of Pt-based electrocatalysts used in low temperature fuel cells is very important for the understanding of the activity of the material. Near-edge X-ray absorption spectroscopy (XANES), a particular region of the X-ray absorption spectra (XAS), can provide the desired information, but the analysis is not straightforward, particularly for the non-specialist. Mansour et al. (J. Phys. Chem., 88:2330, 1984) and Shukla et al. (J. Electroanal. Chem., 563:181, 2004) presented methods to obtain information on electronic states from XANES spectra. In this work, procedures to implement the two methods are presented in detail and applied to XANES results for Pt₂Sn₁/C and Pt/C electrocatalysts prepared in this laboratory. The scope and limitations of the two methods are also discussed. The results show that the presence of Sn in the Pt₂Sn₁/C material promotes a partial filling of the Pt 5d band, in comparison to Pt/C, which contributes to explain the better activity of the bimetallic material. This paper is dedicated to Prof. Francisco Nart, in memoriam.