Serendipitous synthesis of a ditwistane: a one-step access!

4-tert-Butyl-2-cyclohexen-1-one dimerizes in THF solution via its kinetic enolate, leading to di-tert-butylditwistane 8 in up to 36% yield (−78 °C → room temp., protonolysis, flash chromatography). X-ray crystallography shows that 8 incorporates one R and one S enantiomer of the starting ketone; none of the diastereomeric ditwistanes epi-8, epi’-8 or iso-8 was isolated. This means that the formation of 8 proceeds with mutual kinetic resolution and 100% induced diastereoselectivity.     

Zur Natur der Aluminiumsilicatniederschläge aus Na2H2SiO4-und AlCl3-Lösungen bei neutraler Reaktion

On addition, at neutral reaction, of increasing amounts of AlCl₃ solutions to 0.005 m Na-silicate solutions, in which the silicate anions are monomeric, amorphous, almost Na⁺-free precipitates are formed being at first characterised by a higher atomic Al:Si ratio than the total Al:Si mixing ratio. With increasing Al:Si addition, the Al:Si ratio of the precipitates increases until — at a 3:1 ratio in both the liquid and the solid phase — a definite, “saturated” compound, {[(OH)₂AlO]₃SiOH · aq}, is formed. In this compound the silicate anions are monomeric and not condensable at room temperature. This is valid, too, for precipitates from Al:Si > 3 which contain, besides the “saturated” compound, free Al hydroxide. The first-mentioned precipitates with Al:Si < 3, however, contain polymeric Si units which easily condense to more high-polymeric silicate anions.     

Correction to: Fatou closedness under model uncertainty

Positivity - There is an error in Proposition&nbsp;3.10. In fact, the stated proof only shows     

The Bounded Axiom A Forcing Axiom

We introduce the Bounded Axiom A Forcing Axiom (BAAFA). It turns out that it is equiconsistent with the existence of a regular ∑₂‐correct cardinal and hence also equiconsistent with BPFA. Furthermore we show that, if consistent, it does not imply the Bounded Proper Forcing Axiom (BPFA) (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Fermionic atoms in a three dimensional optical lattice: observing Fermi surfaces, dynamics, and interactions

We have studied interacting and noninteracting quantum degenerate Fermi gases in a three-dimensional optical lattice. We directly image the Fermi surface of the atoms in the lattice by turning off the optical lattice adiabatically. Because of the confining potential, gradual filling of the lattice transforms the system from a normal state into a band insulator. The dynamics of the transition from a band insulator to a normal state is studied, and the time scale is measured to be an order of magnitude larger than the tunneling time in the lattice. Using a Feshbach resonance, we increase the interaction between atoms in two different spin states and dynamically induce a coupling between the lowest energy bands. We observe a shift of this coupling with respect to the Feshbach resonance in free space which is anticipated for strongly confined atoms.     

Explicit Solution of a Non-Linear Filtering Problem for Lévy Processes with Application to Finance

In this paper we explicitly solve a non-linear filtering problem with mixed observations, modelled by a Brownian motion and a generalized Cox process, whose jump intensity is given in terms of a Lévy measure. Motivated by empirical observations of R. Cont and P. Tankov we propose a model for financial assets, which captures the phenomenon of time inhomogeneity of the jump size density. We apply the explicit formula to obtain the optimal filter for the corresponding filtering problem.     

Schemata, Distributions and Graphical Models in Evolutionary Optimization

In this paper the optimization of additively decomposed discrete functions is investigated. For these functions genetic algorithms have exhibited a poor performance. First the schema theory of genetic algorithms is reformulated in probability theory terms. A schema defines the structure of a marginal distribution. Then the conceptual algorithm BEDA is introduced. BEDA uses a Boltzmann distribution to generate search points. From BEDA a new algorithm, FDA, is derived. FDA uses a factorization of the distribution. The factorization captures the structure of the given function. The factorization problem is closely connected to the theory of conditional independence graphs. For the test functions considered, the performance of FDA—in number of generations till convergence—is similar to that of a genetic algorithm for the OneMax function. This result is theoretically explained.