(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.     

Influence of catalyst depletion or deactivation on polymerization kinetics. III. Solution polymerization of acrylonitrile in N,N-dimethylformamide at −30°C.

The experimental results on homogeneous polymerization of acrylonitrile initiated with the sodium triethylthioisopropoxyaluminate, NaAlEt₃S(i-Pr), catalyst in DMF at ?30°C. are compared with the prediction of equations based on a postulated mechanism. The agreement between the calculated and observed number-average molecular weight combined with the kinetic data and the relationship between the conversion and the initial catalyst concentration provides a rigorous test concerning the validity of the equations and the mechanism of the polymerization. A plausible mechanism is postulated as follows: The initiation must be relatively fast in accordance with the rate equations and the growing polymer undergoes propagation, transfer (to monomer), and deactivation simultaneously. The infrared spectrum of the low molecular weight polymer prepared at a high catalyst concentration showed strong absorption at 2337, 2205, and 1620 cm.^?1 but no absorption at 900 cm.^?1, indicating that there are two nitriles in the polymer, one of which is conjugated. The possibility of having ? CH?CH₂ groups in the polymer is ruled out by the absence of the band at 900 cm.^?1. In view of these facts, it is concluded that the polymer has a ? CH?CHCN endgroup resulting from the transfer reaction.     

Instability criteria for steady flows of a perfect fluid

An instability criterion based on the positivity of a Lyapunov-type exponent is used to study the stability of the Euler equations governing the motion of an inviscid incompressible fluid. It is proved that any flow with exponential stretching of the fluid particles is unstable. In the case of an arbitrary axisymmetric steady integrable flow, a sufficient condition for instability is exhibited in terms of the curvature and the geodesic torsion of a stream line and the helicity of the flow.     

Generic eigenvalue multiplicities for two-parameter families of operators

A theorem about two-parameter families of Schrödinger operators in proved; the potential is parameter dependent.     

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.