A Borsuk–Ulam Theorem for Maps from a Sphere to a Generalized Manifold

H. J. Munkholm obtained a generalization for topological manifolds of the famous Borsuk–Ulam type theorem proved by Conner and Floyd. The purpose of this paper is to prove a version of Conner and Floyd's theorem for generalized manifolds.     

Addition reactions of a phosphorus triamide to nitrosoarenes and acylpyridines

Abstract

Tricoordinate phosphorus compounds react with a wide variety of double bonds through addition reactions. The dipolar and cyclic products formed are important intermediates in organophosphorus chemistry. We investigated the reactivity between phosphorus triamide 1 and nitrosoarenes and 2-acylpyridines. For sterically congested substrates, the formation of σ⁵ Aroyan, C. E.; Dermenci, A.; Miller, S. J. The Rauhut–Currier Reaction: A History and Its Synthetic Application. Tetrahedron 2009, 65, 4069–4084. DOI: 10.1016/j.tet.2009.02.066.[Crossref], [Web of Science ®] , [Google Scholar],λ⁵-phosphorus products is observed. DFT calculations indicate this product is formed through a concerted [4?+?1] mechanism. For less sterically congested substrates, products are observed arising from cleavage of the N?=?O or C?=?O bond with formation of a terminal P?=?O bond and aryl nitrene or carbene migration into a P–N bond of the phosphorus triamide core. DFT calculations are consistent with an initial [2?+?1] addition to phosphorus followed by formal carbene/nitrene migration in these cases.     

(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.     

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.     

Bacterial cellulose/triethanolamine based ion-conducting membranes

New bacterial cellulose (BC)–triethanolamine (TEA) ion-conducting membranes have been prepared and characterized. The samples were obtained by soaking BC membranes in triethanolamine aqueous solutions and drying. The scanning electron microscopy pictures revealed that the incorporation of TEA in BC membranes covers the cellulose microfibrils. Raman spectra exhibited BC and TEA characteristic group frequencies and thermal analysis evidenced an influence of TEA content on the sample thermal stability. The ion-conductivity as a function of the temperature showed an Arrhenius behavior increasing from 1.8 × 10^?5 S/cm at room temperature to 7.0 × 10^?4 S/cm at 80 °C for the BC–TEA 1 M sample.     

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.