Galois representations, embedding problems and modular forms

To an odd irreducible 2-dimensional complex linear representation of the absolute Galois group of the field Q of rational numbers, a modular form of weight 1 is associated (modulo Artin's conjecture on the L-series of the representation in the icosahedral case). In addition, linear liftings of 2-dimensional projective Galois representations are related to solutions of certain Galois embedding problems. In this paper we present some recent results on the existence of liftings of projective representations and on the explicit resolution of embedding problems associated to orthogonal Galois representations, and explain how these results can be used to construct modular forms.

Arithmetical problems in number fields, abelian varieties and modular forms

Number theory, a fascinating area in mathematics and one of the oldest, has experienced spectacular progress in recent years. The development of a deep theoretical background and the implementation of algorithms have led to new and interesting interrelations with mathematics in general which have paved the way for the emergence of major theorems in the area. This report summarizes the contribution to number theory made by the members of the Seminari de Teoria de Nombres (UB-UAB-UPC) in Barcelona. These results are presented in connection with the state of certain arithmetical problems, and so this monograph seeks to provide readers with a glimpse of some specific lines of current mathematical research.

Reduction of symmetry in grandite solid solution

The results of a crystal structure refinement of an anisotropic grandite garnet specimen with composition Gro36-4 And63-6 are given. The structure obtained has orthorrombic symmetry (space group Fddd) and is compared with similar results obtained by other authors. In all cases the reduction of symmetry is due to the ordering of Fe3+ and Al in octahedral sites. Non cubic structures of grandites are discussed in connection with optical, morphological an grou-th features of these minerals.

Factors influencing privatization of urban solid waste collection: some evidence from Spain

In this paper we analyse some of the organisational aspects of the urban solid waste collection and, in particular, the privatization modality of contracting out. We start by discussing some of the theoretical aspects of contracting out. We then specify and estimate an explanatory model on a sample of municipalities that we surveyed. Our purpose is twofold: on the one hand, we identify the economic factors at work when deciding to contract out the service and, on the other hand, we analyse the role of ideological factors in choosing between the public production of the service or contracting it out. The results show a significant effect of the demand for waste collection on contracting out. There also appears to be a neighbouring effect as the municipalities close to other cities that contract out are also more prone to do so. Finally, the decisions to contract seem to have been motivated by pragmatic rather than ideological reasons.

Semiclassical image potential at a solid surface

A surface dielectric function of a semi-infinite plane-bounded metal is defined in the spirit of the plasmon-pole dielectric function of the bulk. It is modeled in such a way that the surface-plasmon dispersion relation is recovered for small momentum transfer. This function is employed to compute the image potential at all distances outside the surface. Interaction with bulk modes is neglected for simplicity and clarity. The interaction of a massive point charge with a metal surface is also considered in the context of a boson model for surface-plasmon excitation. We present a new definition of the image potential for this case.

Freezing of 4He and its liquid-solid interface from density functional theory

We show that, at high densities, fully variational solutions of solidlike types can be obtained from a density functional formalism originally designed for liquid 4He . Motivated by this finding, we propose an extension of the method that accurately describes the solid phase and the freezing transition of liquid 4He at zero temperature. The density profile of the interface between liquid and the (0001) surface of the 4He crystal is also investigated, and its surface energy evaluated. The interfacial tension is found to be in semiquantitative agreement with experiments and with other microscopic calculations. This opens the possibility to use unbiased density functional (DF) methods to study highly nonhomogeneous systems, like 4He interacting with strongly attractive impurities and/or substrates, or the nucleation of the solid phase in the metastable liquid.

Diffusion on a solid surface: anomalous is normal

We present a numerical study of classical particles diffusing on a solid surface. The particles motion is modeled by an underdamped Langevin equation with ordinary thermal noise. The particle-surface interaction is described by a periodic or a random two-dimensional potential. The model leads to a rich variety of different transport regimes, some of which correspond to anomalous diffusion such as has recently been observed in experiments and Monte Carlo simulations. We show that this anomalous behavior is controlled by the friction coefficient and stress that it emerges naturally in a system described by ordinary canonical Maxwell-Boltzmann statistics.

From subdiffusion to superdiffusion of particles on solid surfaces

We present a numerical and partially analytical study of classical particles obeying a Langevin equation that describes diffusion on a surface modeled by a two-dimensional potential. The potential may be either periodic or random. Depending on the potential and the damping, we observe superdiffusion, large-step diffusion, diffusion, and subdiffusion. Superdiffusive behavior is associated with low damping and is in most cases transient, albeit often long. Subdiffusive behavior is associated with highly damped particles in random potentials. In some cases subdiffusive behavior persists over our entire simulation and may be characterized as metastable. In any case, we stress that this rich variety of behaviors emerges naturally from an ordinary Langevin equation for a system described by ordinary canonical Maxwell-Boltzmann statistics.

Coarsening of solid-liquid mixtures in a random acceleration field

The effects of flow induced by a random acceleration field (g-jitter) are considered in two related situations that are of interest for microgravity fluid experiments: the random motion of isolated buoyant particles, and diffusion driven coarsening of a solid-liquid mixture. We start by analyzing in detail actual accelerometer data gathered during a recent microgravity mission, and obtain the values of the parameters defining a previously introduced stochastic model of this acceleration field. The diffusive motion of a single solid particle suspended in an incompressible fluid that is subjected to such random accelerations is considered, and mean squared velocities and effective diffusion coefficients are explicitly given. We next study the flow induced by an ensemble of such particles, and show the existence of a hydrodynamically induced attraction between pairs of particles at distances large compared with their radii, and repulsion at short distances. Finally, a mean field analysis is used to estimate the effect of g-jitter on diffusion controlled coarsening of a solid-liquid mixture. Corrections to classical coarsening rates due to the induced fluid motion are calculated, and estimates are given for coarsening of Sn-rich particles in a Sn-Pb eutectic fluid, an experiment to be conducted in microgravity in the near future.

Proposed gravitational wave observatory based on solid elastic spheres

Spherical gravitational wave (GW) detectors offer a wealth of so far unexplored possibilities to detect gravitational radiation. We find that a sphere can be used as a powerful testbed for any metric theory of gravity, not only general relativity as considered so far, by making use of a deconvolution procedure for all the electric components of the Riemann tensor. We also find that the spheres cross section is large at two frequencies, and advantageous at higher frequencies in the sense that a single antenna constitutes a real xylophone in its own. Proposed GW networks will greatly benefit from this. The main features of a two large sphere observatory are reported.

Inhibition of glutathione efflux in the perfused rat liver and isolated hepatocytes by organic anions and bilirubin. Kinetics, sidedness, and molecular forms.

Using isolated, in situ, single-pass perfused rat livers, incubations of freshly isolated hepatocytes, and sinusoidal membrane-enriched vesicles, we and others have shown the saturability of transport (efflux) of hepatic glutathione (GSH). These observations have implicated a carrier mechanism. Our present studies were designed to provide further evidence in support of a carrier mechanism for hepatic GSH efflux by demonstrating competition by liver-specific ligands which are taken up by hepatocytes. Perfusing livers with different substances, we found that: (a) sulfobromophthalein-GSH (BSP-GSH) had a dose-dependent and fully reversible inhibitory effect on GSH efflux, while GSH alone did not have any effect; (b) taurocholate had no inhibitory effect; (c) all of the organic anions studied, i.e., BSP, rose bengal, indocyanine green, and unconjugated bilirubin (UCB), manifested potent, dose-dependent inhibitory effects, with absence of toxic effects and complete reversibility of inhibition in the case of UCB. The inhibitory effects of UCB could be overcome partially by raising (CoCl2-induced) hepatic GSH concentration. Because of the physiological importance of UCB, we conducted a detailed study of its inhibitory kinetics in the isolated hepatocyte model in the range of circulating concentrations of UCB. Studies with Cl- -free media, to inhibit the uptake of UCB by hepatocytes, showed that the inhibition of GSH efflux by UCB is apparently from inside the cell. This point was confirmed by showing that the inhibition is overcome only when bilirubin-loaded cells are cleared of bilirubin (incubation with 5% bovine serum albumin). Using Gunn rat hepatocytes and purified bilirubin mono- and diglucuronides, we found that both UCB and glucuronide forms of bilirubin inhibit GSH efflux in a dose-dependent manner. We conclude that the organic anions, although taken up by a mechanism independent of GSH, may competitively inhibit the carrier for GSH efflux from inside the hepatocyte.

Factors influencing privatization of urban solid waste collection: some evidence from Spain

In this paper we analyse some of the organisational aspects of the urban solid waste collection and, in particular, the privatization modality of contracting out. We start by discussing some of the theoretical aspects of contracting out. We then specify and estimate an explanatory model on a sample of municipalities that we surveyed. Our purpose is twofold: on the one hand, we identify the economic factors at work when deciding to contract out the service and, on the other hand, we analyse the role of ideological factors in choosing between the public production of the service or contracting it out. The results show a significant effect of the demand for waste collection on contracting out. There also appears to be a neighbouring effect as the municipalities close to other cities that contract out are also more prone to do so. Finally, the decisions to contract seem to have been motivated by pragmatic rather than ideological reasons.

Solid-phase synthesis and DNA binding studies of dichloroplatinum(II) conjugates of dicarba analogues of octreotide as a new anticancer drugs

The first dichloroplatinum(II) conjugates of dicarba analogues of octreotide , which is expected to act as a"tumour-targeting device", have been efficiently synthesized following a stepwise solid-phase approach; these compounds emulate the mechanism of cisplatin since they form a 1,2-intrastrand cross-link with two consecutive guanines of an oligonucleotide.

Structure and spatial variability of Pinus uncinata Ram. growth forms at two contrasting treeline ecotones in the Spanish Pyrenees.

Describimos la distribución espacial de individuos de Pinus uncinata clasificados según su forma de crecimiento y tamaño en dos ecotonos poco perturbados del límite altitudinal del árbol situados en los Pirineos Centrales españoles (Ordesa, O; Tessó, T). En cada sitio situamos una parcela rectangular (30 140 m), que incluía los límites del árbol y del bosque, y cuyo lado mayor seguía el gradiente altitudinal. En ambos sitios, los individuos vivos eran más grandes y tenían un mayor número de cohortes de acículas pendiente abajo. La distribución de las clases de individuos según su forma de crecimiento y tamaño en el sitio O seguía una secuencia de mayor tamaño pendiente abajo, desde abundantes individuos policórmicos arbustivos (krummholz) con pocas cohortes de acículas (1-3) hasta individuos arbóreos mayores unicórmicos con varias cohortes de acículas (4-12). Por el contrario, los cambios estructurales en el ecotono del sitio T fueron graduales y no siguieron de forma tan clara dicha secuencia