Instantons and vacuum expectation values in the Schwinger model

Vacuum expectation values for the Schwinger model are computed within the path integral formalism for an instanton vacuum. The calculations are done in flat Euclidean space and use the wellknown anomaly result. It can be demonstrated that the instanton vacuum is absolutely necessary to obtain a consistent quantization. At last the results are compared to a similar treatment on the sphere and to the operator solution of the Schwinger model.Supported by Fonds zur Förderung der wissenschaftlichen Forschung in Österreich, Projekt Nr. P8444-TEC     

A precision measurement of the average lifetime ofB hadrons

The average lifetime ofB hadrons was measured using data collected with the DELPHI detector at the LEP collider during 1991 and 1992. The measurement was performed using two different anayses. The first method was an improvement on a previous technique, which used charged particle impact parameter distributions. This analysis measured an average lifetime forB hadrons of

Production rate and decay lifetime measurements ofBs0 mesons at LEP usingDs and? mesons

The study of the properties of inclusive production ofD _s mesons and of events in which a and a muon are present in the same jet provides two independent measurements of the probability,f _s ^w , for a heavy quark to hadronize into a strangeB orD meson. The data sample analysed corresponds to 243,000 hadronicZ ⁰ decays. The combined value of these measurements isf _s ^w =0.19±0.06±0.08. From the flight distance distributions ofD _s and of (-lepton) secondary vertices, with the lepton emitted at high transverse momentum relative to the jet axis, two values are obtained for theB _s ⁰ meson lifetime. Combining these measurements with a previous result based on the study ofD _s- events, theB _s ⁰ meson lifetime is measured to be: 0.96±0.37 ps.     

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.