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.     

Some remarks on variable range hopping—in particular in the quantum Hall regime

An expression for the heat conductivity _xx is derived in the effective medium approximation. Mott type formulas are obtained for _xx and the Peltier coefficient _xx . Using percolation theory in a three-dimensional system the Wiedemann-Franz ratio was found to depend on the temperature like . The Mott type formulas were evaluated in a similar way for a two-dimensional system in the quantum Hall regime within the high-field percolation model. In contrast to previous calculations of the high field hopping conductivity _xx , the results are fully consistent with the experimental data on _xx and the density of states at the Fermi level. Finally, _xx is estimated which together with _xx and _xy =ie ²/h(i=0,1,2,...), determines both thermopower coefficients _xx and _xy .Dedicated to Professor W. Brenig on the occasion of his 60th birthday     

Fourier transform ion cyclotron resonance study of ion-molecule reactions of [M – OCH3]+ ions of methyl 2,3,4,6-tetra-O-methyl-d-hexopyranosides with ammonia

Glycosidic oxocarbenium ions A₁⁺ were formed by isobutane chemical ionization from methyl 2,3,4,6-tetra-O-methyl-β-D -mannopyranoside, methyl 2,3,4,6-tetra-0-methyl-β-D -galactopyranoside and methyl 2,3,4,6-tetra-O-methyl-β-D -glucopyranoside (the ring - O-being converted into ? O ? ), and then- reaction with ammonia was studied by Fourier transform ion cyclotron resonance Spectrometry. Very slow formation (reaction efficiency 0.6-1.4%) of the adduct ion [A₁ + NH₃]⁴ was observed as the main process for carefully thermalized ions A₁⁺. Interestingly, the efficiency of the adduct ion formation depends on the sterochemistry of ions A₁⁺.     

Synthesis of enzyme-inhibitory phospholipid analogs II. Preparation of chiral 1-acyl-2-acylamido-2-deoxyglycerophosphorycholines from serine

A facile and efficient stereospecific route to the enzyme-inhibitory 2-amide analogs of phosphatidycholine is reported.     

Nanosensors based on responsive polymer brushes and gold nanoparticle enhanced transmission surface plasmon resonance spectroscopy

Swelling (and shrinking) of poly(2-vinylpyridine), P2VP, polymer brushes, caused by pH changes, could be readily monitored by transmission surface plasmon resonance, T-SPR, spectroscopy. Gold nanoparticles attached to the P2VP polymer brushes dramatically enhanced the pH-induced shift in the T-SPR absorption spectra. (A 50 nm shift of the absorption maximum of the T-SPR spectrum of the supporting gold nanoislands was observed upon changing the pH from 5.0 to 2.0, corresponding to a swelling of the polymer brushes from 8.1 +/- 0.7 to 24.0 +/- 2.0 nm. Same shift in the opposite direction was observed upon changing the pH from 2.0 to 5.0.)     

Umwandlung von 6-Methylen-tricyclo[3.2.1.02,7]oct-3-en-8-onen in Polymethyltropyliumsalze

When dissolved in trifluoroacetic or fluorosulfonic acid, 6-methylene-tricyclo[3.2.1.0^2,7]oct-3-ene-8-one derivatives of type 2 (;scheme 1); give polymethyltropylium salts in moderate to good yields by CO-extrusion. These tropylium salts can be isolated pure as hexachloroplatinates. Thus the tricyclic compound 6 gives 1,2,4-trimethyltropylium trifluoroacetate 19 in trifluoroacetic acid (;scheme 3);. This salt in CDCl₃ is in equilibrium with its covalent cycloheptatriene (;tropilidene); form 20 , the ratio of the two forms being 1.5–2.1/1. The tropylium salt 19 is reduced by lithium aluminium hydride to a mixture of 1,2,4-trimethylcycloheptatrienes, isomeric with respect to the double bonds, which on hydride abstraction with trityl-tetrafluoroborate gives again the 1,2,4-trimethyltropylium salt 19 (;scheme 3);. From the trimethyl-substituted tricyclic compounds 7 and 8 , in trifluoroacetic acid, are obtained respectively the 1,2,4,6- and 1,2,3,4-tetramethyltropylium ions (; 22 and 24 ); (;schemes 4 and 5);. In this way the 1,2,3,5,6-pentamethyl-tropylium ion (; 26 ); was obtained from 9 (;scheme 6);. With the higher substituted tropylium trifluoroacetates in CDCl₃ the equilibrium tropylium trifluoroacetate ? trifluoroacetoxycycloheptatrienes lies well to the left. The hexamethylated tricyclic compound 10 gives a small quantity of heptamethyltropylium trifluoroacetate (; 27 ); and as the main product the C(;3);-protonated species 28 (;scheme 7);, which when treated with aqueous sodium hydrogencarbonate yielded unchanged educt 10 . - The heptamethyltropylium ion (; 27 ); was, apart from polymeric species, the only product from the treatment of starting material 10 with fluorosulfonic acid (;50%);; its salts have as yet not been isolated in their pure form, however. The mechanism for the rearrangement of the tricyclic compounds of type 2 into tropylium salts is presented for compound 6 in scheme 8: The first step is the protonation at C(;9);. Ring opening of the cyclopropane of the tertiary carbenium ion 29 gives the allylic ion 30 , which then yields the aromatic tropylium salt 19 by carbon monoxide extrusion in a linear cheletropic reaction. The smooth conversion with strong acids of the easily accessible tricyclic compounds of type 2 to the corresponding polymethylated tropylium salts, presents a new and useful method for the synthesis of the latter compounds.