Aromatization of cyclohexadienes by TEMPO electro-mediated oxidation: Kinetic and structural aspects

Cyclohexadienes are easily converted into the corresponding aromatics in excellent yield (>90%) in the presence of 2,2,6,6-tetramethyl-1-oxopiperidinium ion (TEMPO⁺). The TEMPO radical was used in catalytic amount and was electrochemically regenerated in the presence of 2,6-lutidine as a base in hydro-organic medium (AcCN/H₂O 95/5). This work has been focused on the kinetic aspects. We have demonstrated that the reactivity of different cyclohexadienes is strongly dependent on the configuration of the double bonds and on the nature of the substituents. Competition between allylic functionalization and aromatization has been observed during the oxidation of 1,2-dihydro-4-phenylnaphthalene.     

Children’s use of realistic considerations in problem solving: some English evidence

This is the second of two papers exploring children’s responses to an extended version of a division-with-remainder problem intended to elicit general rather than particular realistic considerations during mathematical problem solving. Responses to two problems are analyzed. The first is a ‘realistically’ contextualised item drawn from national tests in England whose ambiguities have been previously discussed (Cooper, 1992); the second is a version of this problem revised to encourage a wider range of realistic responses. In Cooper and Harries (2002), the responses of children at the end of their first year of secondary schooling were analyzed. Here the responses of children at the end of their primary schooling are analyzed and compared with the previous results. It is shown that many children, given suitable encouragement, are willing and able to enter into an extended form of realistic thinking during problem solving, although the original test item renders this invisible.     

Catalytic enantioselective epoxidation with arabinose-derived uloses containing tunable steric sensors

Readily available arabinose-derived 4-uloses, containing a tunable butane-2,3-diacetal as the steric sensor, displayed increasing enantioselectivity (up to 93% ee) with the size of the acetal alkyl group in catalytic asymmetric epoxidation of trans-disubstituted and trisubstituted alkenes.     

A choice probability characterization of generalized extreme value models

A set of necessary and sufficient conditions is established for the representability of choice probabilities by additive random utility models with generalized extreme value (GEV) distributions of utilities. These conditions yield an operational testing procedure for GEV-representability which does not require explicit construction of the underlying distribution of utilities. In addition, this characterization of GEV models reveals a number of their underlying behavioral features.     

o-quinodimethanes from 3,6-dihydrobenzo[b]-1,2-oxathiin-2-oxides

A two step synthesis of 3,6-dihydrobenzo[b]-1,2-oxathiin-2-oxide 5a from o-tolual-dehyde via the photochemically produced 1-hydroxy-1,3-dihydrobenzo[b]thiophene-2,2-dioxide is described. Analogous syntheses of 3 and 6 substituted derivatives of the benzosultines 5 have also been carried out. The feasibility of using these benzosultines as o-quinodimethane precursors has been tested by thermalizing the phenyl sultine 5c in refluxing cyclohexane in the presence of dimethyl fumarate, dimethyl maleate and methyl crotonate to form cycloadducts, stereospecifically and in good yield. The stereochemistry of addition of maleate appears to be exclusively “exo” in conflict with earlier studies on Diels-Alder reactions of α-aryl-o-quino-dimethanes.     

Overlapping Schwarz methods on unstructured meshes using non-matching coarse grids

Summary. We consider two level overlapping Schwarz domain decomposition methods for solving the finite element problems that arise from discretizations of elliptic problems on general unstructured meshes in two and three dimensions. Standard finite element interpolation from the coarse to the fine grid may be used. Our theory requires no assumption on the substructures that constitute the whole domain, so the substructures can be of arbitrary shape and of different size. The global coarse mesh is allowed to be non-nested to the fine grid on which the discrete problem is to be solved, and neither the coarse mesh nor the fine mesh need be quasi-uniform. In addition, the domains defined by the fine and coarse grid need not be identical. The one important constraint is that the closure of the coarse grid must cover any portion of the fine grid boundary for which Neumann boundary conditions are given. In this general setting, our algorithms have the same optimal convergence rate as the usual two level overlapping domain decomposition methods on structured meshes. The condition number of the preconditioned system depends only on the (possibly small) overlap of the substructures and the size of the coarse grid, but is independent of the sizes of the subdomains. Received March 23, 1994 / Revised version received June 2, 1995     

Transpose-free formulations of Lanczos-type methods for nonsymmetric linear systems

We present a transpose-free version of the nonsymmetric scaled Lanczos procedure. It generates the same tridiagonal matrix as the classical algorithm, using two matrix–vector products per iteration without accessing A^T. We apply this algorithm to obtain a transpose-free version of the Quasi-minimal residual method of Freund and Nachtigal [15] (without look-ahead), which requires three matrix–vector products per iteration. We also present a related transpose-free version of the bi-conjugate gradients algorithm. This revised version was published online in June 2006 with corrections to the Cover Date.     

Photochemical free radical formation from aliphatic dicarboxylic acids in solution as studied by electron spin resonance spectroscopy

Various free radicals formed during UV.-irradiation of aliphatic dicarboxylic acids in aqueous and methanolic solution are identified by ESR.-spectroscopy. Their structures point to α-cleavage and photoreduction as the dominant primary photochemical decay processes. The relative contributions of these reactions to the overall photodecomposition depend on solvent and degree of α-alkylation of the acid. Emission ESR.-spectra are found for radicals formed by C, CO-bond cleavage of α-dimethyl substituted acids. The polarization is referred to the triplet mechanism of CIDEP. and indicates this cleavage reaction occurs from a triplet molecular state.