Stationary policies and Markov policies in Borel dynamic programming

Summary The question of the existence of good Markov [good stationary] policies is studied for a general class of Borel [stationary] dynamic programming models. It is shown, for example, that Markov [stationary] policies are uniformly adequate if every transition law is absolutely continuous with respect to a fixed measure [and the reward function is positive or the model satisfies certain compactness and continuity conditions].Research supported by Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 72Research supported by National Science Foundation Grant MCS 8100789     

Fast proton conductivity of polycrystalline titanoniobates

The proton conductivity of three layer-type compounds was studied: H₃OTi₂NbO₇. H₂O, HTiNbO₅ and HTiTaO₅. Measurements were made between 20 °C and 90°C on pellets pressed from crystalline powders and soaked with pure water. The hydrated compound had the highest conductivity, (20°C)-6.3–6.9·10^–4 (cm)^–1. Acid ions from the exchange process were quite firmly retained in its layer structure and contributed significantly to the measured conductivity. Consistent results were obtained after prolonged washing with water.Dedicated to Professor Harry Thomas on the occasion of his 60th birthday     

A formula for the determinant of a sum of matrices

We give a formula, involving circular words and symmetric functions of the eigenvalues, for the determinant of a sum of matrices. Theorem of Hamilton-Cayley is deduced from this formula.UQAM and LITPUniversité Paris 7 and LITP.     

Synthesis of functionalized 2-alkylidenetetrahydrofurans by cyclization of 1,3-bis(trimethylsilyloxy)-1,3-butadienes with epoxides

The Lewis acid mediated cyclization of epoxides with 1,3-bis(trimethylsilyloxy)-1,3-butadienes, electroneutral equivalents of 1,3-dicarbonyl dianions, results in the formation of 2-alkylidenetetrahydrofurans with a great variety of substitution patterns and functional groups. This includes the synthesis of 2,3'-bifuranylidenes and 7-oxabicyclo[4.3.0]nonanes. The cyclization of dienes with functionalized epoxides containing base-labile groups proceeds with good chemoselectivity. In all reactions, good regio- and E diastereoselectivities are observed. Based on the stereoselectivities observed for reactions of 1,2-disubstituted epoxides, a working hypothesis for the mechanism of the reaction is suggested.     

Mass spectrometry of steroid glucuronide conjugates. II-Electron impact fragmentation of 3-keto-4-en- and 3-keto-5alpha-steroid-17-O-beta glucuronides and 5alpha-steroid-3alpha,17beta-diol 3- and 17-glucuronides

The steroid glucuronide conjugates of 16,16,17-d(3)-testosterone, epitestosterone, nandrolone (19-nortestosterone), 16,16,17-d(3)-nortestosterone, methyltestosterone, metenolone, mesterolone, 5alpha-androstane-3alpha,17beta-diol, 2,2,3,4,4-d(5)-5alpha-androstane-3alpha,17beta-diol, 19-nor-5alpha-androstane-3alpha,17beta-diol, 2,2,4,4-d(4)-19-nor-5alpha-androstane-3alpha,17beta-diol and 1alpha-methyl-5alpha-androstane-3alpha/beta,17beta-diol were synthesized by means of the Koenigs-Knorr reaction. Selective 3- or 17-O-conjugation of bis-hydroxylated steroids was performed either by glucuronidation of the corresponding steroid ketole and subsequent reduction of the keto group or via a four-step synthesis starting from a mono-hydroxylated steroid including (a) protection of the hydroxy group, (b) reduction of the keto group, (c) conjugation reaction and (d) removal of protecting groups. The mass spectra and fragmentation patterns of all glucuronide conjugates were compared with those of the commercially available testosterone glucuronide and their characterization was performed by gas chromatography/mass spectrometry and nuclear magnetic resonance spectroscopy. For mass spectrometry the substances were derivatized to methyl esters followed by trimethylsilylation of hydroxy groups and to pertrimethylsilylated products using labelled and unlabelled trimethylsilylating agents. The resulting electron ionization mass spectra obtained by GC/MS quadrupole and ion trap instruments, full scan and selected reaction monitoring experiments are discussed, common and individual fragment ions are described and their origins are proposed.