A property of the lattice of equational theories

It had been conjectured that any algebraic lattice having a compact one could be represented as the lattice of equational theories extending some theory. However, we show that each lattice having such a representation satisfies a nontrivial quasidistributivity condition. In particular,M ₃ has no such representation.To the memory of András HuhnPresented by Walter Taylor.     

The duality of option investment strategies for hedge funds

This paper explores the structure of optimal investment strategies using stochastic programming and duality theory in investment portfolios containing options for a hedge fund manager who attempts to beat a benchmark. Explicit optimal conditions for option investments are obtained for several models. This research was supported by Inquire, the Social Sciences and Humanities Research Council of Canada, the Natural Sciences and Engineering Research Council of Canada, the National Center of Competence in Research FINRISK, a research instrument of the Swiss National Science Foundation, and MIT’s Sloan School of Management. J. R. Rodríguez-Mancilla thanks Gabriel Casillas-Olvera, Deputy Manager of Risk Control at Banco de Mexico, who read several drafts of this paper and made many helpful comments. The opinions in this paper do not necessarily represent those of Banco de México.     

Novel ring-cleaving reaction of 4-nitro-1,1,2,2,9,9,10,10-octafluoro[2.2]paracyclophane with nucleophiles

When 4-nitro-AF4 is treated with nucleophiles such as alkoxides and cyanide, a novel ring opening, cyclophane destroying reaction is observed whereby, via an S_NAr mechanism, the nucleophile attacks the bridgehead aryl carbon vicinal to the nitro group with subsequent aryl-CF₂ bond cleavage.     

Numerical analysis and computational testing of a high accuracy Leray‐deconvolution model of turbulence

We study a computationally attractive algorithm (based on an extrapolated Crank‐Nicolson method) for a recently proposed family of high accuracy turbulence models, the Leray‐deconvolution family. First we prove convergence of the algorithm to the solution of the Navier‐Stokes equations and delineate its (optimal) accuracy. Numerical experiments are presented which confirm the convergence theory. Our 3d experiments also give a careful comparison of various related approaches. They show the combination of the Leray‐deconvolution regularization with the extrapolated Crank‐Nicolson method can be more accurate at higher Reynolds number that the classical extrapolated trapezoidal method of Baker (Report, Harvard University, 1976). We also show the higher order Leray‐deconvolution models (e.g. N = 1,2,3) have greater accuracy than the N = 0 case of the Leray‐α model. Numerical experiments for the 2d step problem are also successfully investigated. Around the critical Reynolds number, the low order models inhibit vortex shedding behind the step. The higher order models, correctly, do not. To estimate the complexity of using Leray‐deconvolution models for turbulent flow simulations we estimate the models' microscale.© 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008