Two-plane sub-bundles of nonorientable real vector-bundles

Let be a nonorientable m-plane bundle over a CW complex X of dimension m or less. Given a 2-plane bundle over X, we wish to know whether can be embedded as a sub-bundle of . The bundle need not be orientable. When is even-dimensional there is the added complication of twisted coefficients. In that case, we use Postnikov decomposition of certain nonsimple fibrations in order to describe the obstructions for the embedding problem. Emery Thomas [11] and [12] treated this problem for and both orientable. The results found here are applied to the tangent bundle of a closed, connected, nonorientable smooth manifold, as a special case.The writing of this paper was partially supported by CNPq grant     

Calculus of variations as a basic tool for modelling of reaction paths and localisation of stationary points on potential energy surfaces

ABSTRACT

The theory of calculus of variations is a mathematical tool which is widely used in different scientific areas in particular in physics and chemistry. This theory is strongly related with optimisation. In fact the former seeks to optimise an integral related with some physical magnitude over some space to an extremum by varying a function of the coordinates. On the other hand, reaction paths and potential energy surfaces, in particular their stationary points, are the basis of many chemical theories, in particular reactions rate theories. We present a review where it is gathered together the variational nature of many types of reaction paths: steepest descent, Newton trajectories, artificial force induced reaction (AFIR) paths, gradient extremals, and gentlest ascent dynamics (GAD) curves. The variational basis permits to select the best optimisation technique in order to locate important theoretical objects on a potential energy surface.     

On the kinetic theory of a dense gas of rough spheres

The revised Enskog equation for a dense gas of rough spheres is considered. TheH theorem and the conservation equations are discussed.     

Luminescence of Fe3+ in single crystals of LiAl5O8

We have measured the luminescent properties of single crystals of LiAl₅O₈:Fe³⁺. In addition to a zero-phonon line due to Fe³⁺ in A-sites, we have observed another sharp fluorescent line at 699.2 nm which we assign to Fe³⁺ occupying B-sites. The excitation spectrum of the B-site Fe³⁺ shows characteristics similar to those of the A-site Fe³⁺ but are also shifted towards longer wavelengths. The spectra of the single crystals are compared with those of ordered and disordered powder samples.     

Hydrodynamic equations for attractive particle systems on ℤ

Hydrodynamic properties for a class of nondiffusive particle systems are investigated. The method allows one to study local equilibria for a class of asymmetric zero-range processes, and applies as well to other models, such as asymmetric simple exclusion and misanthropes. Attractiveness is an essential ingredient. The hydrodynamic equations present shock wave phenomena. Preservation of local equilibrium is proven to hold away from the shocks. The problem of breakdown of local ergodicity at the shocks, which was investigated by D. Wick in a particular model, remains open in this more general setup.     

Laurdan in Fluid Bilayers: Position and Structural Sensitivity

Laurdan (2-dimethylamino-6-lauroylnaphthalene) is a hydrophobic fluorescent probe widely used in lipid systems. This probe was shown to be highly sensitive to lipid phases, and this sensitivity related to the probe microenvironment polarity and viscosity. In the present study, Laurdan was incorporated in 1,2-dipalmitoyl-sn-glycero-3-[phospho-rac-(1-glycerol)] (DPPG), which has a phase transition around 41°C, and DLPC (1,2-dilauroyl-sn-glycero-3-phosphocholine), which is in the fluid phase at all temperatures studied. The temperature dependence of Laurdan fluorescent emission was analyzed via the decomposition into two gaussian bands, a short- and a long-wavelength band, corresponding to a non-relaxed and a water-relaxed excited state, respectively. As expected, Laurdan fluorescence is highly sensitive to DPPG gel–fluid transition. However, it is shown that Laurdan fluorescence, in DLPC, is also dependent on the temperature, though the bilayer phase does not change. This is in contrast to the rather similar fluorescent emission obtained for the analogous hydrophilic probe, Prodan (2-dimethylamino-6-propionylnaphthalene), when free in aqueous solution, over the same range of temperature. Therefore, Laurdan fluorescence seems to be highly dependent on the lipid bilayer packing, even for fluid membranes. This is supported by Laurdan fluorescence anisotropy and spin labels incorporated at different positions in the fluid lipid bilayer of DLPC. The latter were used both as structural probes for bilayer packing, and as Laurdan fluorescence quenchers. The results confirm the high sensitivity of Laurdan fluorescence emission to membrane packing, and indicate a rather shallow position for Laurdan in the membrane.     

An independent component analysis-based approach on ballistocardiogram artifact removing

Interest about simultaneous electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) data acquisition has rapidly increased during the last years because of the possibility that the combined method offers to join temporal and spatial resolution, providing in this way a powerful tool to investigate spontaneous and evoked brain activities. However, several intrinsic features of MRI scanning become sources of artifacts on EEG data. Noise sources of a highly predictable nature such as those related to the pulse MRI sequence and those determined by magnetic gradient switching during scanning do not represent a major problem and can be easily removed. On the contrary, the ballistocardiogram (BCG) artifact, a large signal visible on all EEG traces and related to cardiac activity inside the magnetic field, is determined by sources that are not fully stereotyped and causing important limitations in the use of artifact-removing strategies. Recently, it has been proposed to use independent component analysis (ICA) to remove BCG artifact from EEG signals. ICA is a statistical algorithm that allows blind separation of statistically independent sources when the only available information is represented by their linear combination. An important drawback with most ICA algorithms is that they exhibit a stochastic behavior: each run yields slightly different results such that the reliability of the estimated sources is difficult to assess. In this preliminary report, we present a method based on running the FastICA algorithm many times with slightly different initial conditions. Clustering structure in the signal space of the obtained components provides us with a new way to assess the reliability of the estimated sources.