Cyclic Markov equilibria in stochastic games

We examine a three-person stochastic game where the only existing equilibria consist of cyclic Markov strategies. Unlike in two-person games of a similar type, stationary ε-equilibria (ε > 0) do not exist for this game. Besides we characterize the set of feasible equilibrium rewards.     

Cumulated double bond systems as ligands : X. N-sulfinylaniline complexes of rhodium(I) and iridium(I) of the type [MCl(PR3)2L] in which L is coordinated via the π-NS and via the sulfur atom respectively; crystal and molecular structure of [RhCl(P-i-Pr3)2(4-MeC6H4NSO)]; determination of the 1J(103Rh15N) by 15N NMR spectroscopy

Each of the compounds [MCl(Pr₃)₂(ArylNSO)] (M = Rh^I, Ir^I; R = i-Pr, Cy: Aryl = C₆H₅, 4-MeC₆H₄, 4-ClC₆H₄, 2,4,6-Me₃C₆H₂ appears to exist as two isomers both in the solid state and in solution. The molecular and single crystal structure of one of the isomers of [RhCl(P-i-Pr)₃)₂(4-Me₆H₄NSO)] shows that the N-sulfinylaniline ligand is in the cis-configuration and coordinated to the rhodium atom via the sulfur-atom. The ligand lies in a plane which includes the rhodium atom and is in agreement with the Rh-S distance of 2.10 Å. IR results of the compounds (solid and solutions), ²¹P NMR data and ¹⁵N NMR of a ¹⁵N labelled compound, which yielded a ¹⁰³Rh¹⁵N coupling constant of 15.5 Hz, show that in the second isomer the N-sulfinylaniline ligand is probably bonded to the metal atom via the π-NS bond.The ratio of the metal-π-NS bonded isomer and the metal-S bonded isomer decreases in the order Aryl = 4-ClC₆H₄ > C₆H₅ > 4-MeC₆H₄; R = i-Pr > Cy and M = Rh > Ir. The interconversion of the two isomers is intramolecular and becomes observable on the ³¹P NMR time scale at about 40° C for M = Rh.In the case of [Ir(P-i-Pr₃)₂(4-MeC₆H₄NSO)], cyclometallation of the sul- finylaniline is observed via the ortho-carbon atom, whereas cyclometallation via P-i-Pr₃ is observed when the ortho-positions are blocked by methyl groups, e.g. when L = 2,4,6-Me₃C₆H₂NSO.     

Reference-free NOE NMR analysis

Nuclear Overhauser Effect (NOE) methods in NMR are an important tool for 3D structural analysis of small molecules. Quantitative NOE methods conventionally rely on reference distances, known distances that have to be spectrally separated and are not always available. Here we present a new method for evaluation and 3D structure selection that does not require a reference distance, instead utilizing structures optimized by molecular mechanics, enabling NOE evaluation even on molecules without suitable reference groups.

A quantitative Nuclear Overhauser Effect (NOE) analysis approach that avoids the use of and internal reference distance to perform molecular configuration selection.     

Diazabutadienes as σ,π-bridging ligands in binuclear molybdenum carbonyl complexes containing molybdenummolybdenum double bonds

Reduction of Mo(CO)₄ DAB (DAB = diazabutadiene) followed by oxidation with Mn(CO)₃BrDAB or HCl gives a small yield (15 to 25%) of complexes of the type Mo₂(CO)₆(DAB)₂, in which the two DAB ligands bridge a molybdenummolybdenum double bond and act as σ,π-donors.     

α-Diimines as monodentate or bridging ligands; synthesis and characterization of palladium(II) and rhodium(I) di(t-butyl)diimine complexes

Complexes of di(t-butyl)diimine with PdCl₂(PhCN)₂ and with (CO)₂RhCl dimer have been synthesized and characterized. The diimine ligand is monodentate bonded in PdCl₂(t-butyldiimine)₂, while in (t-butyldiimine)-[Rh(CO)₂Cl]₂ it bridges two Cl(CO)₂Rh units.     

Cumulated double bond systems as ligands : V. Dialkylsulfurdiimine compounds M(CO)4(RNSNR) (M = Cr,Mo, W) and M(CO)5(RNSNR) (M = Cr,W); structural,spectroscopic and fluxional properties.

The preparation and properties are reported of M(CO)₄(RNSNR) (M = Cr, Mo, W; R = i-Pr, t-Bu), in which the ligand is bidentate and in the trans,trans configuration, and of M(CO)₅(RNSNR) (M = CR, W; R = Et, i-Pr) in which the sulfurdiimine is monodentate and in the cis,trans configuration. In both cases the ligand is linked to the metal atom via the N-atom(s). With M(CO)₅(MeNSNMe) a second isomer is found in which the sulfurdiimine is probably bonded via the S-atom to the metal. All the pentacarbonyl compounds are fluxional; this is attributed to a gliding movement of the metal atom along the NSN system.Both W(CO)₄(t-BuNSN-tBu) and W(CO)₅(MeNSNMe) show vibronic coupling of metal to ligand charge transfer transitions with sulfurdiimine vibrations, as shown with Resonance Raman, but only for W(CO)₅(MeNSNMe) also with the symmetric mode of the equatorial carbonyl groups. The metalsulfurdiimine bond appears to be weak for M(CO)₅(RNSNR), but strong for M(CO)₄(RNSNR).     

Perfect equilibria in stochastic games

We examine stochastic games with finite state and action spaces. For the -discounted case, as well as for the irreducible limiting average case, we show the existence of trembling-hand perfect equilibria and give characterizations of those equilibria. In the final section, we give an example which illustrates that the existence of stationary limiting average equilibria in a nonirreducible stochastic game does not imply the existence of a perfect limiting average equilibrium.Support was provided by the Netherlands Organization for Scientific Research NWO via the Netherlands Foundation for Mathematics SMC, Project 10-64-10.     

Evaluation of sphingomyelin,cholester, and phosphatidylcholine-based immobilized artificial membrane liquid chromatography to predict drug penetration across the blood-brain barrier

Over the past decades, several in vitro methods have been tested for their ability to predict drug penetration across the blood-brain barrier. So far, in high-performance liquid chromatography, most attention has been paid to micellar liquid chromatography and immobilized artificial membrane (IAM) LC. IAMLC has been described as a viable approach, since the stationary phase emulates the lipid environment of a cell membrane. However, research in IAMLC has almost exclusively been limited to phosphatidylcholine (PC)-based stationary phases, even though PC is only one of the lipids present in cell membranes. In this article, sphingomyelin and cholester stationary phases have been tested for the first time towards their ability to predict drug penetration across the blood-brain barrier. Upon comparison with the PC stationary phase, the sphingomyelin- and cholester-based columns depict similar predictive performance. Combining data from the different stationary phases did not lead to improvements of the models. Figure

Schematic representation of how IAM-LC is used to predict drug penetration across the blood-brain barrier.