Universal deformation rings need not be complete intersections

We answer a question of M. Flach by showing that there is a linear representation of a profinite group whose universal deformation ring is not a complete intersection. We show that such examples arise in arithmetic in the following way. There are infinitely many real quadratic fields F for which there is a mod 2 representation of the Galois group of the maximal unramified extension of F whose universal deformation ring is not a complete intersection. To cite this article: F.M. Bleher, T. Chinburg, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Universal Deformation Rings of Modules for Algebras of Dihedral Type of Polynomial Growth

Let k be an algebraically closed field, and let Λ be an algebra of dihedral type of polynomial growth as classified by Erdmann and Skowroński. We describe all finitely generated Λ-modules V whose stable endomorphism rings are isomorphic to k and determine their universal deformation rings R(Λ, V). We prove that only three isomorphism types occur for R(Λ, V): k, k[[t]]/(t ²) and k[[t]].     

Effects of dietary Na+ deprivation on epithelial Na+ channel (ENaC), BDNF, and TrkB mRNA expression in the rat tongue

Background  

In rodents, dietary Na⁺ deprivation reduces gustatory responses of primary taste fibers and central taste neurons to lingual Na⁺ stimulation. However, in the rat taste bud cells Na⁺ deprivation increases the number of amiloride sensitive epithelial Na⁺ channels (ENaC), which are considered as the "receptor" of the Na⁺ component of salt taste. To explore the mechanisms, the expression of the three ENaC subunits (α, β and γ) in taste buds were observed from rats fed with diets containing either 0.03% (Na⁺ deprivation) or 1% (control) NaCl for 15 days, by using in situ hybridization and real-time quantitative RT-PCR (qRT-PCR). Since BDNF/TrkB signaling is involved in the neural innervation of taste buds, the effects of Na⁺ deprivation on BDNF and its receptor TrkB expression in the rat taste buds were also examined.     

Utilising Metal Melts of Low‐Melting Metals as a Novel Approach for MOF Synthesis: The 3D‐Imidazolate 3∞[Ga2(Im)6ImH] from Gallium and Imidazole

Metals with low melting points like gallium (mp. 30 °C) prove a new approach for the synthesis of MOFs. As the melting point of gallium is even lower than of the linker ligand imidazole, formation of the MOF , Im^– = imidazolate anion, ImH = imidazole, can be achieved by reaction of a melt of the referring metal with a melt of the ligand. Gallium is oxidised in the reaction, and hydrogen gas and the imidazolate amide as colourless single crystalline product are formed. At the melting point of imidazole (mp. 88–90 °C) two liquid phases are observed. Phase separation lasts until the reaction, starting at 120 °C, consumes the liquid reagents. We consider this a reaction on the phase border between the liquid phases as no mixing is observed. constitutes of a three‐dimensional framework structure with a 3,6 topology that is built of two Kagome nets sharing common connectivity points. Each Ga³⁺ ion is octahedrally coordinated by six nitrogen atoms of imidazolate and imidazole ligands. The framework exhibits a limited porosity of 8.5 % of accessible space and a diameter of 376–509 pm for the pore windows.     

Enantioselective Catalysis. Part 156 [1]. Ruthenium Procatalysts and 2-Pyridinealdehyde/( S)- NOBIN-Derived Cocatalysts in the Transfer Hydrogenation of Acetophenone with 2-Propanol

Several ruthenium procatalysts were tested in the transfer hydrogenation of acetophenone with 2-propanol using the chiral imine ligand (S)-2-(2-pyridinylmethyleneamino)-2-hydroxy-1,1-binaphthyl and the corresponding amine (S)-2-(2-pyridinylmethylamino)-2-hydroxy-1,1-binaphthyl. Ru(PPh ₃)₃Cl₂ was the best procatalyst. Its triphenylphosphane ligands were crucial for the catalytic activity and take part in the chirality transfer. Triphenylphosphane removing reagents such as copper(I) chloride, TEMPO, or TMAO improved the catalytic performance to enantioselectivities up to 99% ee. The findings led to a mechanistic proposal including dissociation equilibria of triphenylphosphane and chelate ring opening of the tridentate chiral binaphthyl ligand. New ligands with an additional chiral center were synthesized and tested as cocatalysts. The nature of catalytically active intermediates was examined by MS and NMR spectroscopy.