A New Approach to Equations with Memory

In this work, we present a novel approach to the mathematical analysis of equations with memory based on the notion of a state, namely, the initial configuration of the system which can be unambiguously determined by the knowledge of the future dynamics. As a model, we discuss the abstract version of an equation arising from linear viscoelasticity. It is worth mentioning that our approach goes back to the heuristic derivation of the state framework, devised by L.Deseri, M.Fabrizio and M.J.Golden in "The concept of minimal state in viscoelasticity: new free energies and applications to PDEs", Arch. Ration. Mech. Anal., vol. 181 (2006) pp.43-96. Starting from their physical motivations, we develop a suitable functional formulation which, as far as we know, is completely new.Comment: 39 pages, no figur

The old anticentre open cluster Berkeley 32: membership and fundamental parameters

We have obtained medium-low resolution spectroscopy and BVI CCD imaging of Berkeley 32, an old open cluster which lies in the anticentre direction. From the radial velocities of 48 stars in the cluster direction we found that 31 of them, in crucial evolutionary phases, are probable cluster members, with an average radial velocity of +106.7 (sigma = 8.5) km/s. From isochrone fitting to the colour magnitude diagrams of Berkeley 32 we have obtained an age of 6.3 Gyr, (m-M)0 = 12.48 and E(B-V) = 0.10. The best fit is obtained with Z=0.008. A consistent distance, (m-M)0 ~= 12.6 +/- 0.1, has been derived from the mean magnitude of red clump stars with confirmed membership; we may assume (m-M)0 ~= 12.55 +/- 0.1. The colour magnitude diagram of the nearby field observed to check for field stars contamination looks intriguingly similar to that of the Canis Major overdensity.Comment: MNRAS, in press. Degraded resolution for Fig.

Possible phases of two coupled n-component fermionic chains

A two-leg ladder with $n$-component fermionic fields in the chains has been considered using an analytic renormalization group method. The fixed points and possible phases have been determined for generic filling as well as for a half-filled system and for the case when one of the subbands is half filled. A weak-coupling Luttinger-liquid phase and several strong-coupling gapped phases have been found. In the Luttinger liquid phase, for the most general spin dependence of the couplings, all $2n$ modes have different velocities if the interband scattering processes are scaled out, while $n$ doubly degenerate modes appear if the interband scattering processes remain finite. The role of backward-scattering, charge-transfer and umklapp processes has been analysed using their bosonic form and the possible phases are characterized by the number of gapless modes. As a special case the SU($n$) symmetric Hubbard ladder has been investigated numerically. It was found that this model does not scale to the Luttinger liquid fixed point. Even for generic filling gaps open up in the spectrum of the spin or charge modes, and the system is always insulator in the presence of umklapp processes

Transport properties of single channel quantum wires with an impurity: Influence of finite length and temperature on average current and noise

The inhomogeneous Tomonaga Luttinger liquid model describing an interacting quantum wire adiabatically coupled to non-interacting leads is analyzed in the presence of a weak impurity within the wire. Due to strong electronic correlations in the wire, the effects of impurity backscattering, finite bias, finite temperature, and finite length lead to characteristic non-monotonic parameter dependencies of the average current. We discuss oscillations of the non-linear current voltage characteristics that arise due to reflections of plasmon modes at the impurity and quasi Andreev reflections at the contacts, and show how these oscillations are washed out by decoherence at finite temperature. Furthermore, the finite frequency current noise is investigated in detail. We find that the effective charge extracted in the shot noise regime in the weak backscattering limit decisively depends on the noise frequency $\omega$ relative to $v_F/gL$, where $v_F$ is the Fermi velocity, $g$ the Tomonaga Luttinger interaction parameter, and $L$ the length of the wire. The interplay of finite bias, finite temperature, and finite length yields rich structure in the noise spectrum which crucially depends on the electron-electron interaction. In particular, the excess noise, defined as the change of the noise due to the applied voltage, can become negative and is non-vanishing even for noise frequencies larger than the applied voltage, which are signatures of correlation effects.Comment: 28 pages, 19 figures, published version with minor change

LA PROTECCIÓN DE LOS DERECHOS INTELECTUALES COMO HERRAMIENTA DE ESTÍMULO PARA LOS SECTORES CIENTÍFICO-TECNOLÓGICOS, NDUSTRIAL Y PARA LA SOCIEDAD

En el presente trabajo, se pondrá de relieve la necesidad de aplicar una herramienta de estímulo poco utilizada por los países en desarrollo: la Protección de la Propiedad Intelectual. Ésta constituye un instrumento válido, que aún no se ha generalizado lo suficiente y que ha mostrado ser útil para incrementar sensiblemente el desarrollo tanto del Sector Científico-Tecnológico, como del Sector Industrial, así como para lograr integrar su actividad con las necesidades e intereses de la Sociedad. Se destaca también la importancia de realizar una búsqueda en bases documentales de patentes antes de emprender un proyecto Científico-Tecnológico, describiendo su mecanismo y los recursos disponibles, y se enfatiza la necesidad proteger el trabajo realizado, a su finalización. Así, la aplicación del derecho de Propiedad Industrial surge como un soporte adecuado para coadyuvar en el proceso de transformación de un logro científico o innovación tecnológica, en una aplicación industrial y en el de su propiedad intelectual que finalmente se tornará en capital intelectual para poder llegar eficazmente a la Sociedad en su conjunto

Assessment of a urban sustainability and life quality index for elderly

The research here presented originates from some of the ongoing challenges of our society: the demographic changes and the high share of population living in urban areas. The aim of the research is the definition of an index of sustainability and quality of life for elderly at suburban scale, not only able to outline aspects related to the local territorial context but also to represent the neighbourhood level. This would provide significant added value to existing indicators that represent the quality of life for much larger areas as cities, regions and nations. Indeed, it is universally recognised that the quality of life varies quite considerably depending on whether you live in different neighbourhoods or urban areas. The index proposed with the research is elaborated on the base of objective and subjective indicators integrated with the judgment of experts, in order to give an accurate and truthful weight to each indicator. Moreover, it has been elaborated for microscale analysis, dividing urban areas into cells, in order to highlight more in detail the real needs of each specific zone. As a result, the elaborated index would be an available tool to be provided to the local public administration to facilitate and optimise the urban planning and management, prioritizing interventions on the base of the sustainability principles and subjective needs of the population, in particular of elderly