The reactions of 3-Butyl-1,2-diphenylphosphindole with dimethyl acetylenedicarboxylate

Unlike 1,2,5-triphenylphosphole, 3-butyl-1,2-diphenylphosphindole reacts smoothly with two molecules of dimethyl acetylenedicarboxylate to give the phosphindole oxide, a yellow adduct and a colourless adduct. The case of the reaction is taken to indicate less lone pair interaction with the π-system in phosphindoles than in phospholes. The yellow adduct is shown to be a phosphindolium cyclopentadienylide, i.e. an adduct of the phosphindole and two molecules of the ester less one oxygen atom. The colourless adduct is shown to be a 1:2:1 adduct of the phosphindole, the ester and water and has a benzodihydrophosphonin structure. Mechanisms for the formation of both adducts are proposed. Adducts of this general type were previously unknown in organophosphorus chemistry.     

An adjustment scheme for nonlinear pricing problem with two buyers

We examine a contracting problem with asymmetric information in a monopoly pricing setting. Traditionally, the problem is modeled as a one-period Bayesian game, where the incomplete information about the buyers’ preferences is handled with some subjective probability distribution. Here we suggest an iterative online method to solve the problem. We show that, when the buyers behave myopically, the seller can learn the optimal tariff by selling the product repeatedly. In a practical modification of the method, the seller offers linear tariffs and adjusts them until optimality is reached. The adjustment can be seen as gradient adjustment, and it can be done with limited information and so that it benefits both the seller and the buyers. Our method uses special features of the problem and it is easily implementable.     

Synthesis and biological activities of conformationally restricted cyclopentenyl-glutamate analogues.

An efficient method for preparing conformationally restricted cyclopentenyl-glutamate analogues in a regioselective and diastereoselective manner has been developed using a formal [3 + 2] cycloaddition reaction of dehydroamino acids. Methods for preparing optically active versions of these compounds have also been devised. Of these compounds, (S)-2 is an agonist at the mGlu5 (EC(50) 18 microM) and mGlu2 (EC(50) 45 microM) receptors.     

Some ring expansion and related reactions of the phosphindole system

3-Butyl-1,2-diphenylphosphindole reacts smoothly with ethyl propiolate and water and with benzoyl chloride and water to give ring expanded products. The second of these products is further expanded to a seven-membered system by treatment with sodium hydride. With diiodo-methane followed by hydroxide ion, cleavage of the phosphorus-containing ring occurs. The nmr and mass spectral data are analyzed in detail and the results are discussed in the context of related studies with simple phospholes and dibenzophospholes. Some of the results further illustrate that predictions regarding the types of reaction entered into by phosphorus heterocycles must be made with caution.     

Conditional Markov equilibria in discounted dynamic games

This paper introduces conditional Markov strategies in discrete-time discounted dynamic games with perfect monitoring. These are strategies in which players follow Markov policies after all histories. Policies induced by conditional Markov equilibria can be supported with the threat of reverting to the policy that yields the smallest expected equilibrium payoff for the deviator. This leads to a set-valued fixed-point characterization of equilibrium payoff functions. The result can be used for the computation of equilibria and for showing the existence in behavior strategies.     

Basin Hopping Networks of continuous global optimization problems

Characterization of optimization problems with respect to their solvability is one of the focal points of many research projects in the field of global optimization. Our study contributes to these efforts with the usage of the computational and mathematical tools of network science. Given an optimization problem, a network formed by all the minima found by an optimization method can be constructed. In this paper we use the Basin Hopping method on well-known benchmarking problems and investigate the resulting networks using several measures.     

Properties of minimally t-tough graphs

A graph $G$ is minimally $t$-tough if the toughness of $G$ is $t$ and the deletion of any edge from $G$ decreases the toughness. Kriesell conjectured that for every minimally $1$-tough graph the minimum degree $\delta \left(G\right)=2$. We show that in every minimally $1$-tough graph $\delta \left(G\right)\le \frac{n}{3}+1$. We also prove that every minimally $1$-tough, claw-free graph is a cycle. On the other hand, we show that for every positive rational number $t$ any graph can be embedded as an induced subgraph into a minimally $t$-tough graph.