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.)     

On input/output stabilization of singular integrodifferential systems

In this paper we consider a class of systems described by singular integrodifferential equations. This type of systems appear, for example, in the modeling of certain aeroelastic control problems. We study these systems in frequency domain framework and show the existence of finite-dimensional stabilizing controllers. An algorithmic procedure is outlined for the construction of such controllers. In order to illustrate the numerical aspects of this algorithm, we present an example involving the classical Theodorsen model of an airfoil, which fits in the class of systems considered here.This work was supported in part by the National Science Foundation under Grants DMS-8907019 and MSS-9203418.     

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.