Preparative regioselective acylation of glycols by enzymatic transesterification in organic solvents

Porcine pancreatic lipase can catalyze transesterification reac tions in organic solvents in a highly regioselective manner. Lipase powder was suspended in solutions of various diols in ethyl carboxylates, and the mixtures were shaken at 30°C; as a result, pri mary monoesters of glycols were produced on a preparative scale.     

Protecting convex sets

A point-setS is protecting a collection F =T ₁,T ₂,..., _n ofn mutually disjoint compact sets if each one of the setsT _i is visible from at least one point inS; thus, for every setT _i ∈F there are points xS andy T _i such that the line segment joining x to y does not intersect any element inF other thanT _i . In this paper we prove that [2(n-2)/3] points are always sufficient and occasionally necessary to protect any family F ofn mutually disjoint compact convex sets. For an isothetic family F, consisting ofn mutually disjoint rectangles, [n/2] points are always sufficient and [n/2] points are sometimes necessary to protect it. IfF is a family of triangles, [4n/7] points are always sufficient. To protect families ofn homothetic triangles, [n/2] points are always sufficient and [n/2] points are sometimes necessary.     

Phase synchronization of chaotic oscillations in terms of periodic orbits

We consider phase synchronization of chaotic continuous-time oscillator by periodic external force. Phase-locking regions are defined for unstable periodic cycles embedded in chaos, and synchronization is described in terms of these regions. A special flow construction is used to derive a simple discrete-time model of the phenomenon. It allows to describe quantitatively the intermittency at the transition to phase synchronization. (c) 1997 American Institute of Physics.     

On convergence of random walks generated by compound Cox processes to Lévy processes

A functional limit theorem is proved establishing weak convergence of random walks generated by compound doubly stochastic Poisson processes to Lévy processes in the Skorokhod space. As corollaries, theorems are proved on convergence of random walks with jumps having finite variances to Lévy processes with mixed normal distributions, and in particular, to stable Lévy processes.     

Role of unstable periodic orbits in phase and lag synchronization between coupled chaotic oscillators

An increase of the coupling strength in the system of two coupled R?ssler oscillators leads from a nonsynchronized state through phase synchronization to the regime of lag synchronization. The role of unstable periodic orbits in these transitions is investigated. Changes in the structure of attracting sets are discussed. We demonstrate that the onset of phase synchronization is related to phase-lockings on the surfaces of unstable tori, whereas transition from phase to lag synchronization is preceded by a decrease in the number of unstable periodic orbits.     

Action of butyllithium on butadiene and isoprene sulfolenes

Conclusions The deprotonation of butadiene and isoprene sulfolenes with butyllithium gives the salts of the corresponding 1Z,3-butadiene-1-sulfinic acids.Deceased.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 3, pp. 641–643, March, 1979.