Enzyme based amperometric biosensors

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Stereoselective synthesis of functionalized vinyl ethers from allyl bromides activated by triethylamine

An efficient coupling reaction of allyl bromides with various alcohols as nucleophiles activated by triethylamine, leading to functionalized vinyl ethers in good yields and with full stereoselectivity.     

Evidence for involvement of cationic intermediate in epoxidation of chiral allylic alcohols and unfunctionalised alkenes catalysed by MnIII(quinazolinone) complexes

A pair of Mn^III(quinazolinone) complexes was prepared and evaluated in the catalytic epoxidation of the chiral allylic alcohols and unfunctionalised alkenes with iodosylbenzene. Epoxidation of chiral allylic alcohols with 1,3-allylic strain proceeded chemo- and diastereoselectively to give threo-epoxy alcohol (up to 99% d.r). Epoxidation of unfunctionalised alkenes by the proposed catalyst system proceeded nonselectively, as evidenced by the formation of isomerization and rearrangement products in the epoxidation of (Z)-stilbene. A three-step pathway involving a cationic intermediate is proposed for the formation of isomerization and rearrangement products. The fact that only products resulting from the cationic intermediate were detected in the oxidation of a mechanistic probe, (2-methoxy-3-vinylcyclopropyl)benzene, with Mn^III(quinazolinone) and PhIO substantiated the cationic oxygen transfer mechanism.     

Rigorous computational shadowing of orbits of ordinary differential equations

Summary. The existence of a true orbit near a numerically computed approximate orbit -- shadowing -- of autonomous system of ordinary differential equations is investigated. A general shadowing theorem for finite time, which guarantees the existence of shadowing in ordinary differential equations and provides error bounds for the distance between the true and the approximate orbit in terms of computable quantities, is proved. The practical use and the effectiveness of this theorem is demonstrated in the numerical computations of chaotic orbits of the Lorenz equations. Received December 15, 1993     

Numerical solution of the scalar double-well problem allowing microstructure

The direct numerical solution of a non-convex variational problem () typically faces the difficulty of the finite element approximation of rapid oscillations. Although the oscillatory discrete minimisers are properly related to corresponding Young measures and describe real physical phenomena, they are costly and difficult to compute. In this work, we treat the scalar double-well problem by numerical solution of the relaxed problem () leading to a (degenerate) convex minimisation problem. The problem () has a minimiser and a related stress field which is known to coincide with the stress field obtained by solving () in a generalised sense involving Young measures. If is a finite element solution, is the related discrete stress field. We prove a priori and a posteriori estimates for in and weaker weighted estimates for . The a posteriori estimate indicates an adaptive scheme for automatic mesh refinements as illustrated in numerical experiments.