Addition of cyclopropyl alkynes to a Brook silene: definitive evidence for a biradical intermediate

The addition of three newly developed mechanistic probes, (trans-2-phenylcyclopropyl)ethyne, (trans,trans-2-methoxy-3-phenylcyclopropyl)ethyne, and (trans,trans-2-methoxy-1-methyl-3-phenylcyclopropyl)ethyne, 1a-c, to a Brook silene, 2-tert-butyl-2-trimethylsiloxy-1,1-bis(trimethylsilyl)-1-silene, 10, was examined. When alkyne 1a was added to silene 10 products derived from a formal ene reaction were obtained. When alkynes 1b-c were added to silene 10, in addition to the typical silacyclobutenes, a variety of silacycloheptenes were obtained in which the cyclopropyl ring had clearly opened. Formal ene-addition products were also produced from the addition of 1b to 10. Based on the relative positions of the phenyl and methoxy substituents within the seven-membered ring of the silacycloheptenes and the known behavior of the alkyne probes under both radical and ionic conditions, it was concluded that a biradical intermediate was formed during the addition of alkynes 1b-c to silene 10. In the addition of alkynes 1a-b to silene 10, the ene products are most likely formed by a competitive pericyclic reaction. We also present a straightforward method for the unambiguous determination of the regiochemistry of silacyclobutenes derived from the cycloaddition of terminal alkynes to silenes.     

Effects of chemical lipid extraction and arithmetic lipid correction on stable isotope ratios of fish tissues

For accurate interpretation of fish trophodynamics from carbon stable isotope data it is necessary to extract tissue lipids. This is because lipid content varies within and among tissues in both space and time, and because lipids are 13C-depleted relative to proteins. However, lipid extraction may affect delta15N, thus requiring costly and time-consuming separation of delta13C and delta15N analyses. These problems have prompted the development of arithmetic correction techniques for delta13C, but the techniques and their underlying assumptions have not been systematically tested. This study compared the effects of lipid extraction and arithmetic correction techniques on delta13C and delta15N of European sea bass (Dicentrarchus labrax) tissues. Following Folch lipid extraction from muscle and liver, there was a mean increase in delta15N of 0.77 per thousand, but enrichment varied with lipid content such that effects on delta15N were hard to predict. Changes in delta13C and C:N between untreated and lipid-extracted samples reflected the quantity of lipid removed. The arithmetic correction techniques of mass balance and lipid correction were sensitive to the C:N of the lipid-extracted tissue and to the assumed depletion of lipid delta13C relative to protein delta13C. However, the mass balance approach was appropriate for the mathematical correction of bulk tissue data in most circumstances, provided that the C:N of lipid-extracted tissue could be determined for a small proportion of samples. Application of mass balance arithmetic correction can lead to significant time and cost savings in trophodynamic studies, because the majority of delta13C and delta15N analyses would not need to be run separately.     

Asymmetric ruthenium‐catalysed [2+2] cycloadditions between bicyclic alkenes and chiral aryl‐substituted acetylenic acyl camphorsultam alkynes

The regio‐ and absolute stereochemistry of (7S)‐N‐[4‐(3‐thienyl)tricyclo[4.2.1.0^2,5]non‐3‐en‐3‐ylcarbonyl]‐2,10‐camphorsultam tetrahydrofuran hemisolvate, C₂₄H₂₉NO₃S₂·0.5C₄H₈O, and (7S)‐N‐[4‐(4‐tolyl)tricyclo[4.2.1.0^2,5]non‐3‐en‐3‐ylcarbonyl]‐2,10‐camphorsultam, C₂₇H₃₃NO₃S, have been established. One contains a half‐occupancy tetrahydrofuran solvent molecule located on a twofold axis and the other contains two crystallographically unique molecules which are nearly identical. The extended structures of both complexes can be explained via weak C—H...O interactions, which link the molecules together into two‐dimensional sheets in the ab plane for the thienyl complex and ultimately into a three‐dimensional structure for the tolyl derivative. The stereochemistry of both structures confirms that [2+2] cycloadditions of bicyclic alkenes and alkynes catalysed by ruthenium are exclusively exo.     

An adaptive least-squares collocation radial basis function method for the HJB equation

We present a novel numerical method for the Hamilton–Jacobi–Bellman equation governing a class of optimal feedback control problems. The spatial discretization is based on a least-squares collocation Radial Basis Function method and the time discretization is the backward Euler finite difference. A stability analysis is performed for the discretization method. An adaptive algorithm is proposed so that at each time step, the approximate solution can be constructed recursively and optimally. Numerical results are presented to demonstrate the efficiency and accuracy of the method.