Evidence for an indirect halogen exchange in the reaction of trans- 2,3-dibromo-2,3-dihydrobenzofuran with chloride ions

Treatment of the title compound with chloride ions in acetonitrile leads mainly to the formation of trans-2,3-dichloro-2,3-dihydrobenzofuran. Since a nucleophilic displacement of bromide anion by chloride anion can be excluded, a mechanism involving the equilibrium 2Cl^? + Br₂ ? 2Br^? + Cl₂ is suggested.     

Counting bitangents with stable maps

This paper is an elementary introduction to the theory of moduli spaces of curves and maps. As an application to enumerative geometry, we show how to count the number of bitangent lines to a projective plane curve of degree d by doing intersection theory on moduli spaces.     

Core-shell copper hydroxide-polysaccharide composites with hierarchical macroporosity

A new method of preparation of polymeric-inorganic porous nanocomposites with core-shell morphology allowed to stabilise copper hydroxide salts in water. A shell of inorganic salts was formed around microspheres of alginate gel by migration of the metal ions from the core of the particles. The formation of the copper hydroxide nitrate shell was controlled by the kind of mineralisation treatment. The natural polysaccharide was an effective agent of inorganic growth control. The mineral shell stabilised the hydrated polymer gel by considerably limiting the drying and induced the formation of a hierarchical macroporosity when drying the microspheres under supercritical CO₂ conditions.     

High-loop perturbative renormalization constants for lattice QCD (I): finite constants for Wilson quark currents

We present a high order perturbative computation of the renormalization constants Z_V, Z_A and of the ratio Z_P/Z_S for Wilson fermions. The computational setup is the one provided by the RI’-MOM scheme. Three- and four-loop expansions are made possible by numerical stochastic perturbation theory. Results are given for various numbers of flavors and/or (within a finite accuracy) for generic n_f up to three loops. For the case n_f=2 we also present four-loop results. Finite-size effects are well under control, and the continuum limit is taken by means of hypercubic symmetric Taylor expansions. The main indetermination comes from truncation errors, which should be assessed in connection with the convergence properties of the series. The latter is best discussed in the framework of boosted perturbation theory, whose impact we try to assess carefully. Final results and their uncertainties show that high-loop perturbative computations of lattice QCD renormalization constants (RCs) are feasible and should not be viewed as a second choice. As a by-product, we discuss the perturbative expansion for the critical mass, for which results are also for generic n_f up to three loops, while a four-loop result is obtained for n_f=2.     

Fluxional Behaviour of Isocyanide Derivatives of Dodecacarbonyltetrairidium

The fluxional behaviour of [Ir₄(CO)₁₁(t-BuNC)] ( 1 ) and [Ir₄(CO)₁₁(ArNC)] (Ar = 4-methoxyphenyl, 4-tolyl, phenyl, 4-chlorophenyl, 4-nitrophenyl; 2 – 5 ) has been investigated by 2D and variable-temperature ¹³C-NMR. These techniques give new evidence of the processes responsible for CO exchange, namely two successive merry-go-rounds causing Cotton-like scrambling and a CO rotation about one metal center.     

Asymmetric synthesis of cyclopropanes from lithiated aryloxiranes and alpha,beta-unsaturated Fischer carbene complexes

A diastereo- and enantiospecific formation of tetrasubstituted cyclopropane carbene complexes and cyclopropanecarboxylates from lithiated aryloxiranes and alpha,beta-unsaturated Fischer carbene complexes is described.