Existence of optimal stationary policies in average reward Markov decision processes with a recurrent state

We consider discrete-timeaverage reward Markov decision processes with denumerable state space andbounded reward function. Under structural restrictions on the model the existence of an optimal stationary policy is proved; both the lim inf and lim sup average criteria are considered. In contrast to the usual approach our results donot rely on the average regard optimality equation. Rather, the arguments are based on well-known facts fromRenewal Theory.This research was supported in part by the Consejo Nacional de Ciencia y Tecnologia (CONACYT) under Grants PCEXCNA 040640 and 050156, and by SEMAC under Grant 89-1/00ifn$.     

Stationary critical points of the heat flow in the plane

In previous papers [MS 1, 2], we considered stationary critical points of solutions of the initial-boundary value problems for the heat equation on bounded domains in ℝ^N,N ≧ 2. In [MS 1], we showed that a solutionu has a stationary critical pointO if and only ifu satisfies a certain balance law with respect toO for any time. Furthermore, we proved necessary and sufficient conditions relating the symmetry of the domain to the initial datau ₀; in this way, we gave a characterization of the ball in ℝ^N([MS 1]) and of centrosymmetric domains ([MS 2]). In the present paper, we consider a rotationA _dby an angle 2π/d,d ≧ 2 for planar domains and give some necessary and some sufficient conditions onu ₀ which relate to domains invariant underA _d. We also establish some conjectures. This research was partially supported by a Grant-in-Aid for Scientific Research (C) (# 10640175) and (B) (# 12440042) of the Japan Society for the Promotion of Science. The first author was supported also by the Italian MURST.     

Electrostatic effect of specifically adsorbed electroinactive ions upon electrode processes: Part III. Further considerations on perbromate electroreduction in the presence of halide and pseudohalide ions

The effect of specifically adsorbed halides and pseudohalides upon the kinetics of BrO₄^? electroreduction, already investigated by the authors and Cozzi [7] and, more recently, by de Levie and Nemes [8], is further examined. The inadequacy of a simple diffuse-layer correction for the kinetics of BrO₄^? electroreduction and the “direct” effect of the charge density q_i at the inner Helmholtz plane (q_i-effect) upon such kinetics are stressed. An alternative method for estimating the q_i-effect, based on the use of corrected Tafel plots at constant q_i, is proposed.     

Necessary conditions for the optimality equation in average-reward Markov decision processes

An average-reward Markov decision process (MDP) with discretetime parameter, denumerable state space, and bounded reward function is considered. With such a model, we associate a family of MDPs. Then, we determinenecessary conditions for the existence of a bounded solution to the optimality equation for each one of the models in the family. Moreover,necessary andsufficient conditions are given so that the optimality equations have a bounded solution with an additional property.This research was supported in part by the Consejo Nacional de Ciencia y Tecnología (CONACYT) under Grant No. PCEXCNA-040640.Dedicated to Professor Eutimio Alberto Cuéllar-Goríbar on the occasion of his eightieth birthday     

An efficient access to (Z)-β-fluoroallyl alcohols based on the two carbon homologation of aromatic aldehydes by Horner–Wadsworth–Emmons reaction with 2-(diethoxyphosphinyl)-2-fluoro-ethanethioic acid,S-ethyl ester followed by reduction with sodium borohydride

We describe a biomimetic approach to (Z)-β-fluoroallyl alcohols based on the two carbon homologation of aromatic aldehydes to α-fluorocinnamic thioesters by Horner–Wadsworth–Emmons reaction with 2-(diethoxyphosphinyl)-2-fluoro-ethanethioic acid, S-ethyl ester, followed by reduction with sodium borohydride in mild conditions. The α-fluorothioesters were obtained in a good yield by condensing the aldehydes with the lithium anion of 2-(diethoxyphosphinyl)-2-fluoro-ethanethioic acid, S-ethyl ester in THF at ?78 °C. The (E,Z)-α-fluorocinnamic thioester mixtures were then cleanly reduced with double bond isomerisation to the corresponding (Z)-β-fluoroallyl alcohols by NaBH₄ at room temperature. This methodology may be applied to highly functionalized aldehydes as exemplified by the straightforward access to (Z)-β-fluoroconiferin, a strong inhibitor of lignin polymerization from O-glucosylated vanillin.     

Nuclear spin conversion to probe the methyl rotation effect on hydrogen-bond and vibrational dynamics

A noteworthy example of a molecule with coupled large-amplitude motions is provided by acetylacetone (methyl group torsions and intramolecular hydrogen bonds). The molecule was trapped in solid parahydrogen to investigate the complex proton tunneling processes. Nuclear spin conversion in methyl groups is observed and, combined with IR spectra, documents the coupling between high frequency modes and large amplitude motions.     

A Fully Nonlinear Boundary value Problem for the Laplace Equation in Dimension Two

We study the regularity up to the boundary of solutions to the boundary value problem:[math001] in D, ∣?u∣= g on &;pardD, where D is the unit disc. This problem finds its application in the study of geophysical and geomagnetic surveys. If g?C^,[math001](D) and is strictly positive, we prove that uis in the Holder class C1,α(D). An example shows that this is no longer true if g has some zeroes on ?D. In this case u isproved to be of class C¹(D)     

Structure and conformational motion of seven-coordinate diorganotin(IV) complexes derived from salen and salan type ligands

Reaction of R₂SnCl₂ (R = Me, nBu, Ph) and the potassium salts of salenN₃H₃ (N,N′-bis(salicylidene)diethylenetriamine) and saleanN₃H₅ (N,N′-bis(o-hydroxybenzyl)diethylenetriamine) provided diorganotin(IV) complexes of the composition [Me₂Sn(salenN₃H)]·solvate (solvate = 2.5H₂O, MeOH or DMSO), [nBu₂Sn(salenN₃H)]·H₂O, [Ph₂Sn(salenN₃H)]·2EtOH and [Me₂Sn(saleanN₃H₃)]·2.5H₂O. In all compounds the tin atoms are seven-coordinate and have pentagonal-bipyramidal coordination environments, in which the organic substituents attached to the tin atoms occupy the axial positions. This occurs both in solution and the solid state; however, in solution the molecules are involved in conformational equilibria that require the presence of intermediates, in which the N → Sn bonds are dissociated. Although the [saleanN₃H₃]²⁻ ligand is more flexible and basic, a very similar complexing behavior to that of [salenN₃H]²⁻ has been found, and there is evidence that it is even a weaker ligand. Both ligands show the tendency to adopt a curved conformation within the complex, thus indicating that the dynamic process resembles the flapping of butterfly wings. However, the folding is reduced with increasing steric bulk of the organic substitutents attached to the tin atoms. The six-membered heterocyclic rings in the [R₂Sn(salenN₃H)] derivatives have envelope conformation, while those in [Me₂Sn(saleanN₃H₃)] have distorted boat-conformation. Thus, small changes in the hybridization and basicity of the nitrogen atoms cause significant differences of the stability and the dynamic behavior of the resulting molecules.     

Author index

Kinetic measurements of diethylfumarate (DEF) electroreduction to diethylsuccinate in aqueous solutions of pH ranging from 1 to 10 were carried out by the polarographic technique under different experimental conditions, and DEF adsorption was measured by the chronocoulometric technique. The rate changes produced by changes in pH, in buffer concentration, in the potential _d at the outer Helmholtz plane or in the charge density σ_i at the inner Helmholtz plane due to specifically adsorbed iodide ions, were thoroughly examined. The effects of these changes are amenable to a straightforward interpretation if the overall electrode process is assumed to be controlled by an enol-keto transformation of the enol form of diethylsuccinate for 1$R^{?}\stackrel{+H^{+}}{\to }RH$