Classification of generic 3-dimensional Lagrangian singularities with (Z2) l -symmetries

The paper provides the complete list of local models forZ ₂ ^l -invariant generic germs of Lagrangian submanifolds of dimension ≦3. Classification is done directly for genrating functions of Lagrangian submanifolds and contains both elementary singularities and non-elementary ones with continuous moduli. The results demonstrate, in particular, that in contrast to the non-equivariant case the classification of equivariant Lagrangian singularities is not subordinated to the classification of symmetric functions up to the right equivariant equivalences.     

Chiral hydroperoxides as oxygen source in the catalytic stereoselective epoxidation of allylic alcohols by sandwich-type polyoxometalates: control of enantioselectivity through a metal-coordinated template

The epoxidation of allylic alcohols is shown to be efficiently and selectively catalyzed by the oxidatively resistant sandwich-type polyoxometalates, POMs, namely [WZnM(2)(ZnW(9)O(34))(2)](q)(-) [M = OV(IV), Mn(II), Ru(III), Fe(III), Pd(II), Pt(II), Zn(II); q = 10-12], with organic hydroperoxides as oxygen source. Conspicuous is the fact that the nature of the transition metal M in the central ring of polyoxometalate affects significantly the reactivity, chemoselectivity, regioselectivity, and stereoselectivity of the allylic alcohol epoxidation. For the first time, it is demonstrated that the oxovanadium(IV)-substituted POM, namely [ZnW(VO)(2)(ZnW(9)O(34))(2)](12-), is a highly chemoselective, regioselective, and also stereoselective catalyst for the clean epoxidation of allylic alcohols. A high enantioselectivity (er values up to 95:5) has been achieved with [ZnW(VO)(2)(ZnW(9)O(34))(2)](12)(-) and the sterically demanding TADOOL-derived hydroperoxide TADOOH as regenerative chiral oxygen source. Thus, a POM-catalyzed asymmetric epoxidation of excellent catalytic efficiency (up to 42 000 TON) has been made available for the development of sustainable oxidation processes. The high reactivity and selectivity of this unprecedented oxygen-transfer process are mechanistically rationalized in terms of a peroxy-type vanadium(V) template.     

Lewis Acid-Promoted Reduction of Bis(triorganotin) Oxides to Hexaorganoditins

Hexalkylditin is prepared by a Lewis acid-promoted (MgCl₂) reductive reaction of bis(trialkyltin) oxide using magnesium metal as reducing agent. Hexabutyl- and hexaphenylditin are synthesized with 95% and 80% yield separately and a radical mechanism is proposed for the reaction condition. Unsymmetric ditin, Bu₃Sn-SnPh₃, was first synthesized by this reductive method.     

Preparation of optically active allylic hydroperoxy alcohols and 1, 3-diols by enzyme-catalyzed kinetic resolution and photooxygenation of chiral homoallylic alcohols

All four possible enantiomers of the 3-hydroperoxy-4-penten-1-ols 2a, b and their corresponding 4-pentene-1,3-diols 4a,b have been prepared for the first time in high enantiomeric purity (up to 98% ee) and in preparative amounts according to two distinct ways: First the photooxygenation of the racemic homoallylic alcohols 1 gave the racemic hydroperoxy alcohols 2, which have subsequently been kinetically resolved by horseradish peroxidase (HRP); alternatively, first the lipase-catalyzed resolution afforded the optically active homoallylic alcohols 1 and subsequent photooxygenation led to the enantiomerically enriched hydroperoxy alcohols 2.     

Analytical possibilities of square-wave amperometry

The application of improved electronic equipment for square-wave amperometry (SWA) is described. This equipment has better resolution between waiting and sampling times and a simple, low-noise logic part. Titrations with electrogenerated bromine, iodine, iron(II) and silver ions were investigated as examples to compare SWA with d.c. amperometry (DCA). The sensitivity of SWA in titrations of < 10^?5 moll^?1 concentrations with iodine or silver(I) is more than 100 times greater than that of DCA. For measurements of higher concentations, DCA is preferred because of its better linear response. The change in current near the end-point of titrations with silver ions is sharper with SWA than with DCA.