Synthesis of the Chiral Pair of a Novel Thromboxane Antagonist, 3‐[2‐(3‐Benzenesulfonylamino‐7‐oxabicyclo[2.2.1]hept‐2‐yl‐methyl)phenyl] Propionic Acid

Preparation of the enantiomeric pair of 3‐[2‐(3‐benzenesulfonylamino‐7‐oxabicyclo[2.2.1]hept‐2‐yl‐methyl)phenyl] propionic acid, a novel thromboxane antagonist is reported. They are synthesized from either enantiomers of known (1R,2R,3R,4S)‐3‐[2‐(3‐carboxy‐7‐oxabicyclo[2,2,1]hept‐2‐yl‐methyl)phenyl]‐propionic acid methyl ester via epimerization, modified Curtius' rearrangement and sulfonylamino formation. Other derivatives may be prepared similarly.     

On variable discounting in dynamic programming: applications to resource extraction and other economic models

This paper generalizes the classical discounted utility model introduced in Samuelson (Rev. Econ. Stud. 4:155–161, 1937) by replacing a constant discount rate with a function. The existence of recursive utilities and their constructions are based on Matkowski’s extension of the Banach Contraction Principle. The derived utilities go beyond the class of recursive utilities studied in the literature and enable a discussion on subtle issues concerning time preferences in the theory of finance, economics or psychology. Moreover, our main results are applied to the theory of optimal economic growth related with resource extraction models with unbounded utility function of consumption.     

On the optimality equation for average cost Markov control processes with Feller transition probabilities

We consider Markov control processes with Borel state space and Feller transition probabilities, satisfying some generalized geometric ergodicity conditions. We provide a new theorem on the existence of a solution to the average cost optimality equation.     

Discounted dynamic programming with unbounded returns: Application to economic models

In this paper, we study discounted Markov decision processes on an uncountable state space. We allow a utility (reward) function to be unbounded both from above and below. A new feature in our approach is an easily verifiable rate of growth condition introduced for a positive part of the utility function. This assumption, in turn, enables us to prove the convergence of a value iteration algorithm to a solution to the Bellman equation. Moreover, by virtue of the optimality equation we show the existence of an optimal stationary policy.     

General reflexivity and pattern subspaces

This paper extends the theory of reflexivity triples by extending notions and results in the theory of dual operator algebras to this more general setting. In addition, a complete and simple characterization is given for the reflexivity of two-dimensional pattern spaces of finite matrices.     

Zero-Sum Ergodic Semi-Markov Games with Weakly Continuous Transition Probabilities

Zero-sum ergodic semi-Markov games with weakly continuous transition probabilities and lower semicontinuous, possibly unbounded, payoff functions are studied. Two payoff criteria are considered: the ratio average and the time average. The main result concerns the existence of a lower semicontinuous solution to the optimality equation and its proof is based on a fixed-point argument. Moreover, it is shown that the ratio average as well as the time average payoff stochastic games have the same value. In addition, one player possesses an ε-optimal stationary strategy (ε>0), whereas the other has an optimal stationary strategy. A. Jaśkiewicz is on leave from Institute of Mathematics and Computer Science, Wrocław University of Technology. This work is supported by MNiSW Grant 1 P03A 01030.     

On Strong Reality of Finite Simple Groups

In this paper we shall consider the following problem. Which finite simple groups have the property: any element is inverted by an involution?     

Logarithmic Sobolev trace inequality

A logarithmic Sobolev trace inequality is derived. Bounds on the best constant for this inequality from above and below are investigated using the sharp Sobolev inequality and the sharp logarithmic Sobolev inequality.