Synthesis of 2,6-disubstituted dihydropyrans via an efficient BiBr3-initiated three component, one-pot cascade

The rapid synthesis of cis-2,6-disubstituted dihydropyrans is achieved in a three-component, one-pot cascade reaction. BiBr₃-mediated addition of ketene silyl acetals or silyl enol ethers to β,γ-unsaturated cis-4-trimethylsilyl-3-butenal provides a Mukaiyama aldol adduct containing a vinylsilane moiety tethered to a silyl ether. Addition of a second aldehyde initiates a domino sequence involving intermolecular addition followed by an intramolecular silyl-modified Sakurai (ISMS) reaction. Isolated yields of this one-pot reaction vary from 44 to 80% and all compounds were isolated as the cis-diastereomers (10 examples).     

Stereochemistry of nucleophilic additions to hexafluoro-2-butyne

Base-catalysed additions of alcohols to F-2-butyne (1) give mainly products of $\text{trans}$-addition while $\text{cis}$-addition predominates in uncatalysed additions of alcohols carried out in a diluent. The stereochemistry of addition of diethylamine is very dependent on the solvent used and $\text{cis}$- or $\text{trans}$-addition may predominate. Stepwise and concerted mechanisms are advanced to account for these observations. Nucleophilic addition of sulphur to (1) gives F-tetramethylthiophene (68%) and hydration gives CF₃CH₂COCF₃ (91%).     

Fermionic Quantization and Configuration Spaces for the Skyrme and Faddeev-Hopf Models

The fundamental group and rational cohomology of the configuration spaces of the Skyrme and Faddeev-Hopf models are computed. Physical space is taken to be a compact oriented 3-manifold, either with or without a marked point representing an end at infinity. For the Skyrme model, the codomain is any Lie group, while for the Faddeev-Hopf model it is S². It is determined when the topology of configuration space permits fermionic and isospinorial quantization of the solitons of the model within generalizations of the frameworks of Finkelstein-Rubinstein and Sorkin. Fermionic quantization of Skyrmions is possible only if the target group contains a symplectic or special unitary factor, while fermionic quantization of Hopfions is always possible. Geometric interpretations of the results are given. The first author was partially supported by NSF grant DMS-0204651 The second author was partially supported by EPSRC grant GR/R66982/01     

Solitons on Tori and Soliton Crystals

Necessary conditions for a soliton on a torus \({M = \mathbb{R}^m/\Lambda}\) to be a soliton crystal, that is, a spatially periodic array of topological solitons in stable equilibrium, are derived. The stress tensor of the soliton must be L ² orthogonal to \({\mathbb{E}}\) , the space of parallel symmetric bilinear forms on TM, and, further, a certain symmetric bilinear form on \({\mathbb{E}}\) , called the hessian, must be positive. It is shown that, for baby Skyrme models, the first condition actually implies the second. It is also shown that, for any choice of period lattice Λ, there is a baby Skyrme model which supports a soliton crystal of periodicity Λ. For the three-dimensional Skyrme model, it is shown that any soliton solution on a cubic lattice which satisfies a virial constraint and is equivariant with respect to (a subgroup of) the lattice symmetries automatically satisfies both tests. This verifies, in particular, that the celebrated Skyrme crystal of Castillejo et  al., and Kugler and Shtrikman, passes both tests.     

Stahl und Eisen

Ohne Zusammenfassung     

Effect of substrate temperature on electrical and magnetic properties of epitaxial La1−x Pb x MnO3 films

Epitaxial La_1−x Pb _x MnO₃ (LPMO) thin films, grown on (100) SrTiO₃ substrates by laser ablation technique at different temperatures between 600 and 850°C, have been characterized for electrical and magnetic properties. The temperature dependence of resistivity showed that the metal-insulator transition temperature (T _MI) decreases with increasing substrate temperature, which has been attributed to decrease in Pb content in the filsm. The YBa₂Cu₃O _x /La_1−x MnO₃ heterostructures, exhibiting both superconductivity and ferromagnetism, have been fabricated.     

Porosity,Differentiability and Pansu’s Theorem

We use porosity to study differentiability of Lipschitz maps on Carnot groups. Our first result states that directional derivatives of a Lipschitz function act linearly outside a \(\sigma \)-porous set. The second result states that irregular points of a Lipschitz function form a \(\sigma \)-porous set. We use these observations to give a new proof of Pansu’s theorem for Lipschitz maps from a general Carnot group to a Euclidean space.