Non-negative scalar curvature

We study topological obstructions to the existence of Riemannian metrics of non-negative scalar curvature on almost spin manifolds using the Dirac operator, the Bochner technique, C ^* algebras and von Neumann algebras. We also derive some obstructions in terms of the eta invariants of Atiyah, Patodi and Singer. Next, we prove vanishing theorems for the Atiyah-Milnor genus. Finally, we derive obstructions to the existence of metrics of non-negative scalar curvature along the leaves of a leafwise non-amenable foliation on a spin manifold.     

(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.     

Flocculation of silver iodide sols by hydrolysed cations in the presence of a non-ionic surface active agent

Summary Previous studies have indicated that non-ionic surface active agents, such as n-dodecylhexaoxyethylene glycol monoether, confer considerable protection on silver iodide sols to flocculation by inorganic cations. In the present study the effects of hydrolysis of the flocculating cations, lanthanum, aluminium and thorium have been examined. It was found that with the hydrolysed cations the protective action of the non-ionic surface active agent was considerably diminished. It was deduced that the hydrolysed species are more strongly adsorbed than the nonionic surface active agent and either displace the latter from the surface or form species which are large enough to cause flocculation by interparticle bridging.

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Zusammenfassung Vorausgehende Untersuchungen haben gezeigt, daß nichtionische oberflächenaktive Substanzen wie n-Dodecylhexaoxyäthylen-glykol-monoäther beträchtliche Schutzwirkung Silberjodidsolen gegenüber Flokkung durch anorganische Kationen verleihen. In der vorliegenden Untersuchung wird die Wirkung der Hydrolyse flockender Kationen, Lanthan, Aluminium und Thorium, geprüft. Es wurde gefunden, daß durch die hydrolisierten Kationen die Schutzwirkung der nichtionischen oberflächenaktiven Substanz beträchtlich vermindert wird. Daraus ist zu schließen, daß die hydrolisierte Ionenart stärker als das nichtoberflächenaktive Agens adsorbiert wird und deshalb das letztere von der Oberfläche entfernt wird oder genügend große interpartikuläre Brücken, bildet, um Flockung zu verursachen.

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With 6 figures and 1 table     

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.     

Spherical T-Duality

We introduce spherical T-duality, which relates pairs of the form (P, H) consisting of a principal SU(2)-bundle \({P \rightarrow M}\) and a 7-cocycle H on P. Intuitively spherical T-duality exchanges H with the second Chern class c ₂(P). Unless \({dim(M) \leq 4}\), not all pairs admit spherical T-duals and the spherical T-duals are not always unique. Nonetheless, we prove that all spherical T-dualities induce a degree-shifting isomorphism on the 7-twisted cohomologies of the bundles and, when \({dim(M) \leq 7}\), also their integral twisted cohomologies and, when \({dim(M) \leq 4}\), even their 7-twisted K-theories. While spherical T-duality does not appear to relate equivalent string theories, it does provide an identification between conserved charges in certain distinct IIB supergravity and string compactifications.     

The Role of Methoxy Group in the Nazarov Cyclization of 1,5-bis-(2-Methoxyphenyl)-1,4-Pentadien-3-one in the Gas Phase and Condensed Phase

ESI-protonated 1,5-bis-(2-methoxyphenyl)-1,4-pentadien-3-one (1) undergoes a gas-phase Nazarov cyclization and dissociates via expulsions of ketene and anisole. The dissociations of the [M + D]⁺ ions are accompanied by limited HD scrambling that supports the proposed cyclization. Solution cyclization of 1 was effected to yield the cyclic ketone, 2,3-bis-(2-methoxyphenyl)-cyclopent-2-ene-1-one, (2) on a time scale that is significantly shorter than the time for cyclization of dibenzalacetone. The dissociation characteristics of the ESI-generated [M + H]⁺ ion of the synthetic cyclic ketone closely resemble those of 1, suggesting that gas-phase and solution cyclization products are the same. Additional mechanistic studies by density functional theory (DFT) methods of the gas-phase reaction reveals that the initial cyclization is followed by two sequential 1,2-aryl migrations that account for the observed structure of the cyclic product in the gas phase and solution. Furthermore, the DFT calculations show that the methoxy group serves as a catalyst for the proton migrations necessary for both cyclization and fragmentation after aryl migration. An isomer formed by moving the 2-methoxy to the 4-position requires relatively higher collision energy for the elimination of anisole, as is consistent with DFT calculations. Replacement of the 2-methoxy group with an OH shows that the cyclization followed by aryl migration and elimination of phenol occurs from the [M + H]⁺ ion at low energy similar to that for 1.

Growth and Morphology of Hollow Bi2Te3 Whiskers by Physical Vapour Deposition Method

Hollow crystals of bismuth telluride have been grown by the physical vapour deposition (PVD) method. Whisker crystals as long as 10 mm have been grown and were identified by X-ray analysis. The possible mechanism for the growth of hollow whiskers has also been suggested.     

Semiclassical Asymptotics and Gaps in the Spectra of Magnetic Schrödinger Operators

In this paper, we study an L ² version of the semiclassical approximation of magnetic Schrödinger operators with invariant Morse type potentials on covering spaces of compact manifolds. In particular, we are able to establish the existence of an arbitrary large number of gaps in the spectrum of these operators, in the semiclassical limit as the coupling constant goes to zero.