Torsors and Stacks

It is shown that the groupoid of G-torsors, suitably defined, can be used to construct a model for the stack associated to G, for arbitrary sheaves of groupoids G. This research was supported by the Natural Sciences and Engineering Research Council of Canada.     

A short and efficient enantioselective route to a key intermediate for the total synthesis of forskolin

A simple route for the enantioselective synthesis of key intermediates (11 and 12) for the total synthesis of forskolin has been developed starting from acid 6 and (S)-alcohol 5. The latter is prepared by enantioselective catalytic CBS reduction of dienone 3, and is converted by an intramolecular Diels-Alder reaction to tricyclic lactone 9.     

Physisorption of molecular oxygen on C60 thin films

The interaction of oxygen molecules with a fullerene surface has been studied using high resolution electron energy loss spectroscopy and temperature programmed desorption. Vibrational excitation of the adsorbed oxygen is observed at 190 meV, an energy value comparable with that for molecular oxygen in the gas phase. We take this to indicate physisorption of molecular oxygen on the C(60) surface. Thermal desorption results also show that the bonding of oxygen molecules to the C(60) overlayer is comparable to that on a graphite surface. A detailed study of the energy dependence of the vibrational excitation reveals an inelastic electron resonance scattering process. The angular dependence of the resonant vibrational excitation exhibits features distinctively different from those for molecular oxygen physisorbed on the related graphite surface, at a comparable coverage. One possible reason is that the corrugated surface potential, due to the curvature of the C(60) molecules, promotes the preferential ordering of the physisorbed oxygen molecules perpendicular to the surface plane of the C(60) overlayer.     

(Z)-3-p-tolylsulfinylacrylonitrile as a chiral dienophile: diels-alder reactions with furan and acyclic dienes

The behavior of (Z)-3-p-tolylsulfinylacrylonitrile (1) as a chiral dienophile has been evaluated from its reactions with furan and acyclic dienes. Electrostatic interactions of the cyano group with the sulfinyl one restrict the conformational mobility around the C-S bond, thus controlling the pi-facial selectivity, which is almost complete in all cases, the approach of the diene from the less-hindered face of the dienophile (that bearing the lone electron pair) in the predominant rotamer being the favored one. The regioselectivity is also completely controlled by the cyano group. Additionally, the reactivity of compound 1 as well as its endo-selectivity are both higher than those observed for the corresponding (Z)-3-sulfinylacrylates, thus proving the potential of sulfinylnitriles as chiral dienophiles.     

High resolution on a quadrupole ion trap mass spectrometer

By using a modified ion trap mass spectrometer, resolution in excess of 30,000 (FWHM) at m I z 502 is demonstrated. The method of increasing resolution in the ion trap mass spectrometer operated in the mass-selective instability mode depends on decreasing the rate of scanning the primary radio frequency amplitude as well as using resonance ejection at the appropriate frequency and amplitude. A theoretical basis for the method is introduced.     

Narrow band quantitative and multivariate electroencephalogram analysis of peri-adolescent period

ABSTRACT: BACKGROUND: The peri-adolescent period is a crucial developmental moment of transition from childhood to emergent adulthood. The present report analyses the differences in Power Spectrum (PS) of the Electroencephalogram (EEG) between late childhood (24 children between 8 and 13 years old) and young adulthood (24 young adults between 18 and 23 years old). RESULTS: The narrow band analysis of the Electroencephalogram was computed in the frequency range of 0--20 Hz. The analysis of mean and variance suggested that six frequency ranges presented a different rate of maturation at these ages, namely: low delta, delta-theta, low alpha, high alpha, low beta and high beta. For most of these bands the maturation seems to occur later in anterior sites than posterior sites. Correlational analysis showed a lower pattern of correlation between different frequencies in children than in young adults, suggesting a certain asynchrony in the maturation of different rhythms. The topographical analysis revealed similar topographies of the different rhythms in children and young adults. Principal Component Analysis (PCA) demonstrated the same internal structure for the Electroencephalogram of both age groups. Principal Component Analysis allowed to separate four subcomponents in the alpha range. All these subcomponents peaked at a lower frequency in children than in young adults. CONCLUSIONS: The present approaches complement and solve some of the incertitudes when the classical brain broad rhythm analysis is applied. Children have a higher absolute power than young adults for frequency ranges between 0-20 Hz, the correlation of Power Spectrum (PS) with age and the variance age comparison showed that there are six ranges of frequencies that can distinguish the level of EEG maturation in children and adults. The establishment of maturational order of different frequencies and its possible maturational interdependence would require a complete series including all the different ages.     

Scars of the Wigner Function

We propose a picture of Wigner function scars as a sequence of concentric rings along a two-dimensional surface inside a periodic orbit. This is verified for a two-dimensional plane that contains a classical hyperbolic orbit of a Hamiltonian system with 2 degrees of freedom. The stationary wave functions are the familiar mixture of scarred and random waves, but the spectral average of the Wigner functions in part of the plane is nearly that of a harmonic oscillator and individual states are also remarkably regular. These results are interpreted in terms of the semiclassical picture of chords and centers.