“Big match” with lack of information on one side (Part II)

This is the second paper on a class of stochastic games with incomplete information. As inSorin [1984] we prove the existence of the asymptotic value (limv _n ) of the maxim and of the minmax although the infinite value may not exist. Nevertheless the results and the tools used are rather different from the previous case.     

Reflection measurements in CO2 laser solid deuterium target interaction

Using a 60 nsec, 300 MW CO₂ TEA laser reflection measurements from solid deuterium targets have been investigated. Energy, reflected and scattered pulse shape are recorded at various angles: 0°, 45°, 90°, 135°. Reflection, X-ray measurements and ion mean kinetic energy are correlated at the focussing lens position with respect to the target position. The maximum plasma temperature varies from 20 to 35 eV for incident laser fluxes ranging from 5 × 10¹⁰ up to 5 × 10¹¹ W/cm². The cut-off density inside the deuterium ice has been observed and located. In each case reflection has been found to be weak less than 5% for each direction. For the maximum fluxes X-ray energies greater than 0.5 keV have been observed.     

A novel phosphorus-carbon bond formation by ring opening with diethyl phosphite of oxazolines derived from serine

A new reaction of oxazolines derived from serine with diethyl phosphite leading to ring opening products with P-C bond formation is reported. This reaction, which proceeds under neutral conditions and without the use of any halogenated intermediate, results in a mixture of racemic α- and β-phosphono alanines in an approximate 1:2 ratio, with isolated yields up to 77%. The mechanism involves the rearrangement of the oxazoline into the corresponding α-benzamido acrylate, followed by addition of the diethyl phosphite to the double bond. Since no significant transesterification is observed, this method constitutes a simple route for α- and β-phosphono amino acids bearing suitable protecting groups.     

Synthesis of novel benzo[h] [1,6]naphthyridines via a rearrangement of hexahydro‐5H‐pyrrolo [2,1 ‐c] [1,4]benzodiazepines

Heating of hexahydro‐5H‐pyrrolo[2,1‐c][1,4]benzodiazepine‐2,5,11‐trione in boiling phosphoryl chloride led to a rearranged product like 3,5‐dichlorobenzo[h][1,6]naphthyridine. This structure was established from X‐ray diffraction analysis.     

Thiazolo[4,3-c][1,4]benzodiazepines. I. Synthesis of amidine derivatives

Reactivity of 1,2,3,10,11,11a-hexahydro-5H-thiazolo[4,3-c][1,4]benzodiazepin-5-one-11-thione and 1,2,3,10,11,11a-hexahydro-5H-thiazolo[4,3-c][1,4]benzodiazepine-5,11-dithione was evaluated against various amines. The synthetic pathways involved in these reactions which led to new thiazolo[4,3-c]-[1,4]benzodiazepine amidines are described.     

Ring-closing metathesis: a powerful tool for the synthesis of simplified salicylihalamide-based V-ATPase inhibitors

Based on our synthetic strategy developed for the total synthesis of the macrocyclic salicylate natural product salicylihalamide, we describe herein the synthesis of a series of simplified salicylihalamide-based analogs. Alterations in the aromatic fragment, the macrolactone scaffold and side-chain were evaluated for in vitro inhibition of V-ATPase activity and human tumor cell growth.     

Carbinol derivatives via rhodium-catalyzed addition of potassium trifluoro(organo)borates to aldehydes

Reaction of potassium aryltrifluoroborates with aldehydes, in the presence of a rhodium catalyst, afforded carbinol derivatives in high yields under mild aqueous conditions; this efficient reaction proved to be general, allowing the production of highly hindered diarylmethanols and aliphatic aldehydes were also reactive under these conditions.     

Direct access to ketones from aldehydes via rhodium-catalyzed cross-coupling reaction with potassium trifluoro(organo)borates

A direct cross-coupling reaction of aromatic aldehydes with potassium trifluoro(organo)borates afforded ketones in high yields and under mild conditions in the presence of a rhodium catalyst and acetone. This new reaction, involving a formal aldehyde C-H bond activation, is believed to proceed via a Heck-type mechanism followed by hydride transfer to acetone.     

Diastereomeric excess upon cleavage and reformation of diastereomeric alkoxyamines

The thermal reactions of several TEMPO and DEPN (N-(2-methylpropan-2-yl)-N-(1-diethylphosphono-2,2-dimethylpropyl)-aminoxyl) based alkoxyamines were studied by means of (1)H and (31)P NMR spectroscopy aiming to distinguish the contributions of diastereoselective homolysis and coupling to the total equilibrium diastereomeric distribution. The TEMPO-based compounds reveal no diastereomeric excess while DEPN based compounds show a moderate excess both upon homolysis and coupling. The diastereomeric preference of homolysis for DEPN-(propionate-like) adducts does not depend on the ester group and it is mainly affected by the size of beta-substituents. The diastereoselective coupling is sensitive to the total recombination rate constant k(c) and diastereoselectivity increases with the decrease of k(c). Small diastereoselective coupling is found in the recombination of DEPN with sec-butyl isobutyrate radical, where no prochiral centers are formed upon cleavage of corresponding alkoxyamine.