Thinking Transport as a Twist

The determination of the conductivity of a deterministic or stochastic classical system coupled to reservoirs at its ends can in general be mapped onto the problem of computing the stiffness (the ‘energy’ cost of twisting the boundaries) of a quantum-like system. The nature of the coupling to the reservoirs determines the details of the mechanical coupling of the torque at the ends.     

Duality and Hidden Symmetries in Interacting Particle Systems

In the context of Markov processes, both in discrete and continuous setting, we show a general relation between duality functions and symmetries of the generator. If the generator can be written in the form of a Hamiltonian of a quantum spin system, then the “hidden” symmetries are easily derived. We illustrate our approach in processes of symmetric exclusion type, in which the symmetry is of SU(2) type, as well as for the Kipnis-Marchioro-Presutti (KMP) model for which we unveil its SU(1,1) symmetry. The KMP model is in turn an instantaneous thermalization limit of the energy process associated to a large family of models of interacting diffusions, which we call Brownian energy process (BEP) and which all possess the SU(1,1) symmetry. We treat in details the case where the system is in contact with reservoirs and the dual process becomes absorbing.     

Solution conformational preferences of glutaric, 3‐hydroxyglutaric, 3‐methylglutaric acid,and their mono‐ and dianions

Conformational preferences of glutaric, 3‐hydroxyglutaric and 3‐methylglutaric acid, and their mono‐ and dianions have been investigated with the aid of NMR spectroscopy. In contrast to succinic acid, glutaric acid displays essentially statistical conformational equilibria in polar and non‐polar solutions of high and low hydrogen‐bonding ability with no clear evidence for intramolecular hydrogen‐bonding interactions. The acid ionization constant ratios, K ₁/K₂, in D₂O and DMSO of glutaric, 3‐hydroxyglutaric, and 3‐methylglutaric acids also indicate that intramolecular interactions are much less important than, or indeed insignificant, for shorter‐chain acids. FTIR studies on 3‐methylglutaric acid indicate some preference for either association with solvent or dimerization, depending on the solvent, rather than intramolecular hydrogen bonding. Copyright © 2008 John Wiley & Sons, Ltd.     

On the Characterization of Linear Uniquely Decodable Codes

A Uniquely Decodable (UD) Code is a code such that any vector of the ambient space has a unique closest codeword. In this paper we begin a study of the structure of UD codes and identify perfect subcodes. In particular we determine all linear UD codes of covering radius 2.     

Immersions of cohomogeneity one Riemannian manifolds

This work deals with positively curved compact Riemannian manifolds which are acted on by a closed Lie group of isometries whose principal orbits have codimension one and are isotropy irreducible homogeneous spaces. For such manifolds we can show that their universal covering manifold may be isometrically immersed as a hypersurface of revolution in an euclidean space.     

Involutionn-aire et ses applications a l'étud des hyperquadriques dans les espaces euclidiens et non-euclidiens an dimensions

Sans résumé Présenté par G. Hajós     

Aggregati di cerchi di Minkowski

Sunto Uno teorema diFejes Tóth [2] che si riferisce algi aggregati di cerchi diMinkowski nel piano euclideo sarà esteso alle superficie a curvatura costante. Alla memoria di Guido Castelnuovo, nel primo centenario della nascita.     

Microchemical and microstructural characterisation of medieval and post-medieval ceramic glaze coatings

A large number of ceramic samples (from the 10th to the 19th century), found during the excavation of Sicilian archaeological sites (Syracuse, Caltagirone, Sciacca and Piazza Armerina), have been studied by combining scanning electron microscopy, energy-dispersive X-ray spectrometry and optical microscopy. Attention has been focused on the microchemical and microstructural properties of the painted surfaces to investigate the nature of the enamels and pigments in the decorative layers. The general perspective has been the identification of consistent archeometric criteria, other than the standard stylistic considerations, which can be used for a reliable recognition of the production sites. The results collected for each ceramic typology were used to cluster the different ceramic reference groups in a wide database suitable for a reliable discrimination of the provenance of artefacts. Moreover, the same compositional and microstructural data allow the identification of the raw materials used for pigments. There is evidence of some differences with existing information found in the literature concerning the formulas used in ancient times. Finally, attention has also been devoted to identify the technological aspects of the manufacturing techniques and firing conditions adopted for each typology of glaze coating depending on different ceramic materials .PACS 81.05.Je; 82.80.-d; 68.37.Hk; 68.55.-a     

Convergence of Sobolev spaces on varying manifolds

We deal with variational problems on varying manifolds in ℝⁿ. We represent each manifold by a positive measure μ, to which we associate a suitable notion of tangent space Tμ, of mean curvature H(μ), and of Sobolev spaces with respect to μ on an open subset Ω ⊆ ℝⁿ. We introduce the notions of weak and strong convergence for functions defined on varying manifolds, that is defined μ_h -a.e., being {μ_h} a weakly convergent sequence of measures. In this setting, we prove a strong-weak type compactness theorem for the pairs (P_{μ h} H(μ_h)), where P_{μ h} are the projectors onto the tangent spaces T_{μ h}. When μ_h belong to a suitable class of k-dimensional measures, having in particular a prescribed (k−1)-manifold as a boundary, we enforce this result to study the convergence of energy functionals, possibly with a Dirichlet condition on ∂Ω. We also address a perspective for optimization problems where the control variable is represented by a manifold with a prescribed boundary.