Quasiregular Mappings on Sub-Riemannian Manifolds

We study mappings on sub-Riemannian manifolds which are quasiregular with respect to the Carnot–Carathéodory distances and discuss several related notions. On H-type Carnot groups, quasiregular mappings have been introduced earlier using an analytic definition, but so far, a good working definition in the same spirit is not available in the setting of general sub-Riemannian manifolds. In the present paper we adopt therefore a metric rather than analytic viewpoint. As a first main result, we prove that the sub-Riemannian lens space admits nontrivial uniformly quasiregular (UQR) mappings, that is, quasiregular mappings with a uniform bound on the distortion of all the iterates. In doing so, we also obtain new examples of UQR maps on the standard sub-Riemannian spheres. The proof is based on a method for building conformal traps on sub-Riemannian spheres using quasiconformal flows, and an adaptation of this approach to quotients of spheres. One may then study the quasiregular semigroup generated by a UQR mapping. In the second part of the paper we follow Tukia to prove the existence of a measurable conformal structure which is invariant under such a semigroup. Here, the conformal structure is specified only on the horizontal distribution, and the pullback is defined using the Margulis–Mostow derivative (which generalizes the classical and Pansu derivatives).     

Quinomethides versus unsymmetric hybrids: two variations of non-radicaloid SEM-states in four-electron redox systems of bis-4<Emphasis Type="Italic">H</Emphasis>-imidazoles

A series of bis-4H-imidazoles 1a-h has been synthesized and characterized. Due to the integration of rigid substructures, the first fluorescent 4H-imidazole 1h which possesses the substructure of pyrrolo-pyrrol was obtained. Upon protonation of bis-4H-imidazoles, a bathochromic shift of 100 to almost 200 nm was observed originating from the transformation of merocyanine chromophores into cyanines. All 4H-imidazoles were reduced chemically yielding bridged 1H-imidazoles which immediately reoxidize when exposed to air. Stable quinomethide-like species 3a,b which represent the SEM form in this four-electron redox system are only observed during the reduction of bis-4H-imidazoles 1a,b. Influenced by larger bridging elements in derivatives 1c–1h, the electronic communication between terminal 4H-imidazoles is impaired. Therefore, detection and isolation of neither quinomethide-like nor biradikaloid SEM forms succeeded. Most likely a very fast electron-transfer-step leads to unsymmetric hybrids, consisting of one 1H- and one 4H-imidazole. The new synthesized derivative 1k is not only such a stable hybrid molecule, but also may be an indication for the existence of non-quinoid SEM-forms.     

Colchicin

Colchicin was extracted from grinded seeds of meadow saffron and purified by flash chromatography and preparative HPLC. All analytical spectra were recorded and are reproduced either in the main part or in the supporting information. The NMR‐ and mass‐spectra have been interpreted and compared with theoretical calculations of the ¹³C chemical shifts. The project is a follow up of the recent book “Classics in Spectroscopy” by S. Berger und D. Sicker (Wiley‐VCH 2009).     

P-stereogenic trifluoromethyl derivatives of Josiphos: synthesis, coordination properties, and applications in asymmetric catalysis

Intermolecular nucleophilic substitution of a CF(3) group of bis(trifluoromethyl)phosphanes by a lithiated Ugi's amine (4) affords both diastereoisomers of the corresponding P-stereogenic trifluoromethylphosphanes 6 and 7. Separation of the isomers by column chromatography on silica gel followed by substitution of the dimethylamino group with phosphanes or pyrazoles yields the bidentate P^P (9 and 10) or P^N ligands (12 and 13) without epimerization at the stereogenic phosphorus center. The coordination properties of these bidentate ligands were investigated on the basis of crystal structures of the corresponding palladium and rhodium complexes. IR spectroscopic measurements of rhodium-carbonyl complexes 16-23 indicated the strongly electronic-withdrawing character of these phosphanes. The catalytic potential of these ligands was demonstrated in the rhodium-catalyzed hydrogenation of olefins as well as in the palladium-catalyzed allylic alkylation reaction, where high activities and enantioselectivities were observed.     

Reaction of hydroxyl radicals with C4H5N (pyrrole): temperature and pressure dependent rate coefficients

Absolute (pulsed laser photolysis, 4-639 Torr N(2) or air, 240-357 K) and relative rate methods (50 and 760 Torr air, 296 K) were used to measure rate coefficients k(1) for the title reaction, OH + C(4)H(5)N → products (R1). Although the pressure and temperature dependent rate coefficient is adequately represented by a falloff parametrization, calculations of the potential energy surface indicate a complex reaction system with multiple reaction paths (addition only) in the falloff regime. At 298 K and 760 Torr (1 Torr = 1.33 mbar) the rate coefficient obtained from the parametrization is k(1) = (1.28 ± 0.1) × 10(-10) cm(3) molecule(-1) s(-1), in good agreement with the value of (1.10 ± 0.27) × 10(-10) cm(3) molecule(-1) s(-1) obtained in the relative rate study (relative to C(5)H(8), isoprene) at this temperature and pressure. The accuracy of the absolute rate coefficient determination was enhanced by online optical absorption measurements of the C(4)H(5)N concentration at 184.95 nm using a value σ(184.95nm) = (1.26 ± 0.02) × 10(-17) cm(2) molecule(-1), which was determined in this work.     

Dumbbells of five-connected Ge atoms and superconductivity in CaGe3

CaGe(3) has been synthesized at high-pressure, high-temperature conditions. The atomic pattern comprises intricate germanium layers of condensed moleculelike dimers. Below T(c) = 6.8 K, type II superconductivity with moderately strong electron-phonon coupling is observed.     

Strongly transitive multiple trees

We give an amalgamation construction of free multiple trees with a strongly transitive automorphism group. The construction shows that any partial codistance function on a tuple of finite trees can be extended to yield strongly transitive multiple trees.