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.     

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⁺.     

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.)     

Direct analysis of thin-layer chromatographic spots of narcotics by means of diffuse reflectance Fourier transform infrared spectroscopy

The technique of diffuse reflectance Fourier transform infrared spectrometry (DRIFT) as an in situ detection method was used for the qualitative and quantitative analysis of drugs (heroin, cocaine and codeine) separated by thin layer chromatography.It was found that at a given interferometer throughput and detector sensitivity the quality of the spectrum depends strongly in the type of the chromatographic thin layer used. A detection limit of approx. 2 g was attained on a microcrystalline cellulose thin layer with a dynamically aligned Bio-Rad Digilab FTS 60A/896 type interferometer and room temperature DTGS detector. A reliable qualitative analysis can be made with as little as 10 to 15 g drug per spot.     

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.     

A new boundary treatment: HF surface potential model applied to solid-state cluster calculations

A new boundary treatment, a Hartree–Fock (HF ) surface potential model, is proposed to deal with the surface effect in the solid-state cluster calculations using the LCAO –MO –SCF ab initio method. The surface potential arises from one or more atoms, which have no basis function and are added to the calculated cluster system. These atoms are placed in such sites so that the HF potential field of the calculated system should possess a point-group symmetry. The surface potential could be found by the corresponding HF potential using a symmetry operator. The fact that a rather symmetric electronic structure of the asymmetric cluster YBa₂CuZn₂O₇ is obtained using the HF surface potential shows that the surface effect in the cluster calculations could be neutralized to a great extent. © 1995 John Wiley & Sons, Inc.