Mesh independent superlinear convergence estimates of the conjugate gradient method for some equivalent self-adjoint operators

A mesh independent bound is given for the superlinear convergence of the CGM for preconditioned self-adjoint linear elliptic problems using suitable equivalent operators. The results rely on K-condition numbers and related estimates for compact Hilbert-Schmidt operators in Hilbert space.This research was supported by the Hungarian National Research Fund OTKA under grant No. T043765.     

Comparative docking studies on ligand binding to the multispecific antibodies IgE-La2 and IgE-Lb4

Summary A large comparative study is presented in which the binding of approximately 30 different ligands to two IgE antibodies (La2 and Lb4) is analyzed by means of an automated-docking procedure based on simulated annealing. The method is able to reproduce experimentally verified binding orientations, as shown by application to the Ig-AN02-hapten complex. The main address of the study is to investigate the concept of antibody multispecificity. Problems and usefulness of docking in this context are discussed. The results indicate reasons for multispecific binding properties and how they can be understood from the topology of the binding site. Though similar in general behaviour, the two antibodies show interesting differences in their binding characteristics. The binding sites of both antibodies are described and the main interacting residues revealed.     

Basenkatalysierte Cyclisierungen von 2-(2-Propinyl)oxybenzamiden

Base Catalysed Cyclizations of 2-(2-Propynyl)oxy-benzamide Systems 2-(2-Propynyl)oxy-benzamides were cyclized under base catalysis to 6- or 7-membered ring compounds, depending on the reaction conditions. Treatment of 2-(2-propynyl)oxy-benzamide ( 10 ) with sodium methylsulfinylmethanide (NaMSM) in DMSO gave two isomeric oxazepinons 11 (34%) and 12 (7%), while the transformation with sodium-2-propanolate in 2-propanol afforded the oxazinone 13 (34%) and with lithium cyclohexyl-isopropylamide (Li-CHIP) in N-methylpyrrolidone 11 (48%) exclusively (Scheme 4). N-Methyl-2-(2-propynyl)-oxy-benzamide ( 14 ) behaved similarly. In the reaction of 14 with sodium 2-propanolate in 2-propanol yielding the benzoxazinone 16 , the allenyloxy-benzamide 17 could be isolated as an intermediate (Scheme 5). The N-phenyl-compounds 18 and 22 treated with NaMSM/DMSO were converted to 3-anilino-2-methyl-benzo- and naphtho-pyran-4-ones, respectively (Schemes 6 and 7). The mechanisms for these reactions are discussed (Schemes 8, 9 and 10).     

Synthese und thermisches Verhalten von 6,8-Dimethylentricyclo[3.2.1.02,7]oct-3-enen; [3s 3s]-sigmatropische Umlagerungen von 6-Allenyl- und 6-Propargly-1- Methylen-cyclohexa-2,4-dienen in aromatische Kohlenwasserstoffe als Beispiele für konzertierte Semibenzol → Benzol-Umlagerungen

The tricyclic dimethylene hydrocarbons 5 , 6 , 7 , 8 and d₂- 5 , (Scheme 2), which are prepared by Wittig-reaction from the corresponding ketones, are rearranged, by heating, to 4-aryl-but-1-yne derivatives via the unstable 6-allenyl-1-methylene-cyclohexa-2, 4-diene intermediates (e.g. Scheme 14). Using the deuterium-labelled compound d₂- 5 , it was shown that the allenyl moiety, formed by a retro-Diels-Alder reaction (cycloreversion) of the tricyclic dimethylene compound, migrates with complete inversion in the final o-semibenzene-benzene rearrangement (Schemes 11 and 14). Reaction of 6-propargyl-cyclohexa-2, 4-dien-1-ones with triphenylphosphonium methylide gives 6-propargyl-1-methylene-cyclohexa-2 4-dienes, which immediately undergo a [3s, 3s]-rearrangement to form 4-aryl-buta-1, 2-dienes (Scheme 9). In contrast, the rearrangement of the corresponding 4-propargyl-1-methylene-cyclohexa-2, 5- dienes proceeds by a radical mechanism (Schemes 10 and 13).     

Rh(I)-katalysierte Umlagerungen von 3,4-Diacycloxy-1,5-hexadiinen; synthese von (E)-4-acyloxymethyliden-2-cyclopenten-1-onen

Rh(I)-Catalysed Rearrangements of 3,4-Diacyloxy-1,5-hexadiynes; Synthesis of (E)-4-Acyloxymethyliden-2-cyclopenten-1-ones The 3,4-diacyloxy-1,5-hexadiynes 3, 6 and 8 which were synthesized according to a known, slightly modified procedure react with [Rh(CO)₂Cl]₂ at 100° in chloroform with formation of the (E)-4-acyloxymethyliden-2-cyclopenten-1-ones 4, 7 and 9 (Schemes 2, 3 and 4), respectively. DL - and meso- 3 as well as trans- and cis- 8 , give the same (E)-isomers 4 and 9 , respectively. 3,4-Diacetoxy-3, 4-dimethyl-1, 6-diphenyl-1,5-hexadiyne ( 10 ) produces with the same catalyst 2,6-diacetoxy-3, 4-dimethyl-1,6-diphenylfulvene ( 11 ) (Scheme 5). A mechanism for the formation of the cyclopentenones is proposed in Scheme 6.