Synthesis of the HCV protease inhibitor Vaniprevir (MK-7009) using ring-closing metathesis strategy

A highly efficient synthesis of Vaniprevir (MK-7009) has been accomplished in nine linear steps and 55% overall yield. The key features of this synthesis include a cost-effective synthesis of the isoindoline subunit and efficient construction of the 20-membered macrocyclic core of Vaniprevir (MK-7009) utilizing ring-closing metathesis technology. A high-performing ring-closing metathesis protocol has been achieved by simultaneous slow addition of the ruthenium catalyst (0.2 mol %) and the diene substrate at a concentration of 0.13 M.     

The multiple-partners assignment game with heterogeneous sales and multi-unit demands: competitive equilibria

A multiple-partners assignment game with heterogeneous sales and multi-unit demands consists of a set of sellers that own a given number of indivisible units of potentially many different goods and a set of buyers who value those units and want to buy at most an exogenously fixed number of units. We define a competitive equilibrium for this generalized assignment game and prove its existence by using only linear programming. In particular, we show how to compute equilibrium price vectors from the solutions of the dual linear program associated to the primal linear program defined to find optimal assignments. Using only linear programming tools, we also show (i) that the set of competitive equilibria (pairs of price vectors and assignments) has a Cartesian product structure: each equilibrium price vector is part of a competitive equilibrium with all optimal assignments, and vice versa; (ii) that the set of (restricted) equilibrium price vectors has a natural lattice structure; and (iii) how this structure is translated into the set of agents?? utilities that are attainable at equilibrium.     

Effects of CO<Subscript>2</Subscript> Compressibility on CO<Subscript>2</Subscript> Storage in Deep Saline Aquifers

The injection of supercritical CO₂ in deep saline aquifers leads to the formation of a CO₂ plume that tends to float above the formation brine. As pressure builds up, CO₂ properties, i.e. density and viscosity, can vary significantly. Current analytical solutions do not account for CO₂ compressibility. In this article, we investigate numerically and analytically the effect of this variability on the position of the interface between the CO₂-rich phase and the formation brine. We introduce a correction to account for CO₂ compressibility (density variations) and viscosity variations in current analytical solutions. We find that the error in the interface position caused by neglecting CO₂ compressibility is relatively small when viscous forces dominate. However, it can become significant when gravity forces dominate, which is likely to occur at late times of injection.     

A Phenyl α-Nitronyl Nitroxide with a Forced Chiral Conformation

Summary.  A new phenyl α-nitronyl nitroxide bearing a hydroxyl group at position 2 of the aromatic ring and a chiral methyl lactate substituent at position 5 has been synthesized with the aim of combining the magnetic properties of this kind of radical with the optical properties endowed by the chiral group. The optically active compound forms intramolecular hydrogen bonds between the OH group and one of the NO groups and shows a large torsion angle between the two rings when compared with similar radicals with no substituent in this position. Therefore, the optical properties are distinct. The optical and magnetic properties of the new radical in both solution and solid state are presented. Received June 23, 2000. Accepted (revised) September 18, 2000     

Two Limit Cycles in Liénard Piecewise Linear Differential Systems

Some techniques for studying the existence of limit cycles for smooth differential systems are extended to continuous piecewise linear differential systems. Rigorous new results are provided on the existence of two limit cycles surrounding the equilibrium point at the origin for systems with three zones separated by two parallel straight lines without symmetry. As a relevant application, it is shown the existence of bistable regimes in an asymmetric memristor-based electronic oscillator.

     

Numerical procedures in electrochemical simulation

The use of both the Laplace transformation technique and the finite element method has been analyzed in an electrochemical system. The diffusion-controlled adsorption process of a species onto an electrode surface is studied in detail. © 1994 John Wiley & Sons, Inc.     

A note on: “Relaxation oscillators with exact limit cycles”

In this note we give a family of planar polynomial differential systems with a prescribed hyperbolic limit cycle. This family constitutes a corrected and wider version of an example given in the work [M.A. Abdelkader, Relaxation oscillators with exact limit cycles, J. Math. Anal. Appl. 218 (1998) 308-312]. The result given in this note may be used to construct models of Liénard differential equations exhibiting a desired limit cycle.