Über den Weierstraßschen Vorbereitungssatz

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Aerobic oxidation of benzylic alcohols with solid alkaline metal hydroxides

Solid alkaline metal hydroxides displayed high catalytic activity and full selectivity in the aerobic oxidation of benzylic alcohols in a non-polar medium. The activity of the solid bases, in decreasing order of reactivity, was KOH > NaOH ≫ LiOH. Water, which is the only by-product of the reaction, plays a crucial role in KOH deactivation by converting the crystal phase of KOH to KOH · H₂O, as confirmed by XRD measurements.     

Solvent density effects on the solvation behavior and configurational structure of bare and passivated 38-atom gold nanoparticle in supercritical ethane

In exploring the effects of solvent density on the mode and the degree of solvation of the bare and passivated 38-atom gold particle in supercritical ethane, we have extended the molecular dynamics simulations of the system, reported previously,(34) to cover a range of isotherms in the T > T(c) regime, where T(c) is the critical temperature of the solvent. Consonant with our previous observations, the modes of solvation of the bare and the passivated particle, deduced from the radial distribution of the solvent about the metal core center of mass, are found to be vastly different from each other at all solvent densities: while the molecules solvating the bare particle form a well-defined, two-region layer around it, those solvating the passivated particle are loosely dispersed in the passivating layer. For the bare particle, the degree of solvation (vartheta) as a function of solvent density passes through a maximum occurring in the close vicinity of the critical point, consistent with our previous results and in agreement with Debenedetti's theoretical analysis,(22,23) which predicts a solvation enhancement effect in the critical region for systems where the unlike solvent/solute interaction is much stronger than the solvent/solvent interaction. Taking the degree of solvation (vartheta) as a measure of solvent quality, we have investigated how the solvent quality would vary along the solvent-density isotherms. In the solvent-density regime rho > rho(c), the solvent quality is found to be a decreasing function of the density as a result of progressive dominance of the excluded volume effect over the attractive particle/solvent interactions. The particle/solvent affinity is greatly reduced in the presence of the passivating layer, resulting in considerable shrinkage of the good-solvent-quality domain in the supercritical regime. The solvent environment and the presence of the passivating chains produce significant disorder in the equilibrium structure assumed by the nanoparticle core.     

On almost precipitous ideals

With less than 0^# two generic extensions ofL are identified: one in which ${\aleph_1}With less than 0^# two generic extensions ofL are identified: one in which à₁{\aleph_1}, and the other à₂{\aleph_2}, is almost precipitous. This improves the consistency strength upper bound of almost precipitousness obtained in Gitik M, Magidor M (On partialy wellfounded generic ultrapowers, in Pillars of Computer Science, 2010), and answers some questions raised there. Also, main results of Gitik (On normal precipitous ideals, 2010), are generalized—assumptions on precipitousness are replaced by those on ∞-semi precipitousness. As an application it is shown that if δ is a Woodin cardinal and there is an f:w₁ ? w₁{f:\omega_1 \to \omega_1} with ||f||=w₂{\|f\|=\omega_2}, then after Col(à₂,d){Col(\aleph_2,\delta)} there is a normal precipitous ideal over à₁{\aleph_1}. The existence of a pseudo-precipitous ideal over a successor cardinal is shown to give an inner model with a strong cardinal.     

Note über die Gleichung der auf einer Ebene abbildbaren Flächen

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Bemerkung über pseudosphärische Mannigfaltigkeiten von drei Dimensionen

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Ueber binäre Formen und die Gleichung sechsten Grades

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