Holographic formula for Q-curvature. II

We extend the holographic formula for the critical Q-curvature in Graham and Juhl (2007) [9] to all Q-curvatures. Moreover, we confirm a conjecture of Juhl (2009) [11].     

Modular optimization of enantiopure epoxide-derived P,S-ligands for rhodium-catalyzed hydrogenation of dehydroamino acids

The optimization of P,S-ligands derived from enantiopure (2S,3S)-phenylglycidol for asymmetric rhodium-catalyzed hydrogenation of dehydroamino esters is described. The exceptionally high modular character of the (2S,3S)-phenylglycidol platform is demonstrated by systematic modification of the ether and thioether moieties, the skeletal aryl substituent and the stereo and regiochemistry of the ligands. An experimentally useful method for the monitoring of hydrogenation reactions is also described and used for obtaining relevant data of the catalytic systems studied.     

Dicompleteness and real dicompactness of ditopological texture spaces

The authors consider interrelations between the completeness of certain initial di-uniformities and the real dicompactness of completely biregular bi-T₂ nearly plain ditopological spaces. Completions and real dicompactifications of almost plain spaces are also considered.     

The higher derived functors of the primitive element functor of quasitoric manifolds

Let P be an n-dimensional, q?1 neighborly simple convex polytope and let M2n(λ) be the corresponding quasitoric manifold. The manifold depends on a particular map of lattices λ:Zm→Zn where m is the number of facets of P. In this note we use ESP-sequences in the sense of Larry Smith to show that the higher derived functors of the primitive element functor are independent of λ. Coupling this with results that appear in Bousfield (1970) [3] we are able to enrich the library of nice homology coalgebras by showing that certain families of quasitoric manifolds are nice, at least rationally, from Bousfield?s perspective.     

Efficient Synthesis of 2-Arylamino-2-imidazolines and 2-Ami-nobenzimidazoles with Aminoiminomethanesulfonic Acid Derivatives

A highly efficient synthesis of 2‐arylamino‐2‐imidazolines and 2‐aminobenzimidazoles from aminoimino‐methanesulfonic acid derivatives is described. The method is simple and practical, generating imidazoline and benzimidazoline derivatives in excellent isolated yields.     

Amino-acid-mediated epoxidation of α,β-unsaturated ketones by hydrogen peroxide in aqueous media

Amino acids, such as arginine and lysine, can be used as an efficient catalyst in the epoxidation of α,β-unsaturated ketones with aqueous hydrogen peroxide. Up to >99% conversion was obtained in the reaction toward 11 α,β-unsaturated ketones.     

Palladium(II) complexes of Y,C,Y‐chelated phosphines: synthesis,structure, and catalytic activity in Suzuki–Miyaura reaction

The phosphines L¹PPh₂ (1) and L²PPh₂ (2) containing different Y,C,Y‐chelating ligands, L¹ = 2,6‐(^tBuOCH₂)₂C₆H₃^? and L² = 2,6‐(Me₂NCH₂)₂C₆H₃^?, were treated with PdCl₂ and di‐µ‐chloro‐bis[2‐[(N,N‐dimethylamino)methyl]phenyl‐C,N]‐dipalladium(II) and yielded complexes trans‐{[2,6‐(^tBuOCH₂)₂C₆H₃]PPh₂}₂PdCl₂ (3), {[2,6‐(Me₂NCH₂)₂C₆H₃]PPh₂} PdCl₂ (4), {[2,6‐(^tBuOCH₂)₂C₆H₃]PPh₂}Pd(Cl)[2‐(Me₂NCH₂)C₆H₄] (5) and {[2,6‐(Me₂NCH₂)₂C₆H₃]PPh₂}Pd(Cl)[2‐(Me₂NCH₂)C₆H₄] (6) as the result of different ability of starting phosphines 1 and 2 to complex PdCl₂. Compounds 3–6 were characterized by ¹H, ¹³C, ³¹P NMR spectroscopy and ESI‐MS. The molecular structures of 3,4 and 6 were also determined by X‐ray diffraction analysis. The catalytic activity of complexes 3–6 was evaluated in the Suzuki‐Miyaura cross‐coupling reaction. Copyright © 2010 John Wiley & Sons, Ltd.