α-Arylation and Ring Expansion of Annulated Cyclobutanones: Stereoselective Synthesis of Functionalized Tetralones

α-Arylcyclobutanones display unique reactivity that makes them valuable synthetic intermediates and target molecules. We describe the preparation of α-aryl- and α-heteroarylcyclobutanones through a direct α-arylation reaction. Problematic fragmentations are avoided by the use of LiO^tBu, which promotes a rapid but reversible self-aldol reaction that slowly releases the enolate required for α-arylation. We also demonstrate the ring expansion of α-arylcyclobutanones, a process that is highlighted in the stereoselective synthesis of 1-methoxy coniothyrinone D.     

Solving stochastic convex feasibility problems in hilbert spaces

In a stochastic convex feasibility problem connected with a complete probability space (Ω,A,μ) and a family of closed convex sets (C_ω)_ωεΩ in a real Hilbert space H, one wants to find a point that belongs to C_ω for μ almost all ω ε Ω. We present a projection based method where the variable relaxation parameter is defined by a geometrical condition, leading to an iteration sequence that is always weakly convergent to a μ almost common point. We then give a general condition assuring norm convergence of this equation to that μ almost common point     

Predicting Low-Pressure O2 Adsorption in Nanoporous Framework Materials for Sensing Applications

A set of 98 nanoporous framework material (NFM) structures was investigated by classical Grand canonical Monte Carlo simulations for low-pressure O₂ adsorption properties (Henry’s constant and isosteric heat of adsorption). The set of materials includes those that have shown high O₂ uptake experimentally as well as a subset of more than 2000 structures previously screened for noble-gas uptake. While use of the general force field UFF is fruitful for noble-gas adsorption studies, its use is shown to be limited for the case of O₂ adsorption—one distinct limitation is a lack of sufficient O₂–metal interactions to be able to describe O₂ interaction with open metal sites. Nonetheless, those structures without open metal sites that have very small pores (<2.5 Å) show increased O₂/N₂ selectivity. Additionally, O₂/N₂ mixture simulations show that in some cases, H₂O or N₂ can hinder O₂ uptake for NFMs with small pores due to competitive adsorption.     

Variational Analysis of Toda Systems

The author surveys some recent progress on the Toda system on a two-dimensional surface Σ,arising in models from self-dual non-abelian Chern-Simons vortices,as well as in differential geometry.In particular,its variational structure is analysed,and the role of the topological join of the barycentric sets of Σ is shown.     

Comparison of phantom materials for use in quality assurance of microbeam radiation therapy

Microbeam radiation therapy (MRT) is a promising radiotherapy modality that uses arrays of spatially fractionated micrometre‐sized beams of synchrotron radiation to irradiate tumours. Routine dosimetry quality assurance (QA) prior to treatment is necessary to identify any changes in beam condition from the treatment plan, and is undertaken using solid homogeneous phantoms. Solid phantoms are designed for, and routinely used in, megavoltage X‐ray beam radiation therapy. These solid phantoms are not necessarily designed to be water‐equivalent at low X‐ray energies, and therefore may not be suitable for MRT QA. This work quantitatively determines the most appropriate solid phantom to use in dosimetric MRT QA. Simulated dose profiles of various phantom materials were compared with those calculated in water under the same conditions. The phantoms under consideration were RMI457 Solid Water (Gammex‐RMI, Middleton, WI, USA), Plastic Water (CIRS, Norfolk, VA, USA), Plastic Water DT (CIRS, Norfolk, VA, USA), PAGAT (CIRS, Norfolk, VA, USA), RW3 Solid Phantom (PTW Freiburg, Freiburg, Germany), PMMA, Virtual Water (Med‐Cal, Verona, WI, USA) and Perspex. RMI457 Solid Water and Virtual Water were found to be the best approximations for water in MRT dosimetry (within ±3% deviation in peak and 6% in valley). RW3 and Plastic Water DT approximate the relative dose distribution in water (within ±3% deviation in the peak and 5% in the valley). PAGAT, PMMA, Perspex and Plastic Water are not recommended to be used as phantoms for MRT QA, due to dosimetric discrepancies greater than 5%.     

One‐pot carboxylative cyclization of propargylic alcohols and CO2 catalysed by N‐heterocyclic carbene/Ag systems

A series of N ‐heterocyclic carbene (NHC)/Ag systems were developed for the carboxylative assembly of propargylic alcohols and carbon dioxide (CO₂). With the catalysis of these catalytic systems, a variety of target α‐alkylidene cyclic carbonates could be obtained smoothly under atmospheric CO₂ pressure in straightforward one‐pot processes. Particularly, these reactions could be performed without any stoichiometric addition of bases or additives. Further mechanistic investigation reveals that the excellent activities are attributed to the effective activations of CO₂ accomplished by the NHCs via the formation of the NHC‐CO₂ adducts.     

A note on simultaneous preconditioning and symmetrization of non‐symmetric linear systems

Motivated by the theory of self‐duality that provides a variational formulation and resolution for non‐self‐adjoint partial differential equations (Ann. Inst. Henri Poincaré (C) Anal Non Linéaire 2007; 24 :171–205; Selfdual Partial Differential Systems and Their Variational Principles. Springer: New York, 2008), we propose new templates for solving large non‐symmetric linear systems. The method consists of combining a new scheme that simultaneously preconditions and symmetrizes the problem, with various well‐known iterative methods for solving linear and symmetric problems. The approach seems to be efficient when dealing with certain ill‐conditioned, and highly non‐symmetric systems. The numerical and theoretical results are provided to show the efficiency of our approach. Copyright © 2010 John Wiley & Sons, Ltd.