Tensor products and preservation of limits, for acts over monoids

In 1971, Stenström published one of the first papers devoted to the problem of when, for a monoid S and a right S -act A _S , the functor A? (from the category of left acts over S into the category of sets) has certain limit preservation properties. Attention at first focused on when this functor preserves pullbacks and equalizers but, since that time, a large number of related articles have appeared, most having to do with when this functor preserves monomorphisms of various kinds. All of these properties are often referred to as flatness properties of acts . Surprisingly, little attention has so far been paid to the obvious questions of when A _S ? preserves all limits, all finite limits, all products, or all finite products. The present article addresses these matters.     

Ozonolytic cleavage of cycloalkenes to terminally differentiated products

A method is described by which alkoxy hydroperoxides, obtained by ozonising cycloalkenes in alcohol solution, can be converted into terminally differentiated products by the action of metal salts. Cyclohexene and cycloheptene were converted to 1,1-dimethoxy-5-chloropentane and 1,1-dimethoxy-6-chlorohexane respectively in 47% yield, using ferric chloride. With ferrous sulphate as reactant salt, cyclooctene was converted into 1,1-dimethoxy-6-heptene. A synthesis of (Z)-4-heptenal from (Z,Z)-1,5-cyclooctadiene is also described. Fragmentation, causing the loss of one carbon atom, is a characteristic of these transformations. Other variations employed the salts as oxidants and reductants simultaneously.     

Molecular tagging velocimetry in the wake of an object in supersonic flow

Molecular tagging velocimetry using air photolysis and recombination tracking (APART) was applied to the wake flow of a 30^° wedge in a small Mach 3 wind tunnel. Average velocities could be determined with a standard deviation down to 0.4% (free stream) and 7% (expansion fan behind wedge). Instantaneous velocities (measurement time 7 µs) could be recorded with a standard deviation down to 2%, limited by the available laser power. The measured velocity profile behind the wedge is compared to a simulation.     

Stationary points and equilibria

Almost all existence results in mathematical economics and game theory rely on some type of fixed point theorem. However, in many cases it is much easier to apply an equivalent stationary point theorem. In this survey paper we show for various general equilibrium and game-theoretical models the usefulness of the stationary point approach to prove existence of equilibrium. We also consider path following methods to find a stationary point and illustrate such methods by an example. Finally, we discuss some refinements of stationary points and their application to solve the problem of equilibrium selection.     

Polarized X-ray absorption study of Bi2Sr2CuO6 and Bi2Sr2CaCu2O8

Polarization dependent X-ray absorption measurements on single crystal Bi₂Sr₂CuO₆ (T _c =9 K) and Bi₂Sr₂CaCu₂O₈ (T _c =80 K) with one and two CuO₂ layers, respectively, show no energy shift of the Cu 2p main peak, and no relation between the amount of 3d(m=0, ±1) character and the critical temperatureT _c . At grazing incidence a structure in Bi₂Sr₂CaCu₂O₈ is found at 937 eV, which can be ascribed to a composite state of Cu 3d(z ²), Cu 4s ando–2p(z).     

Unraveling orbital ordering in La0.5Sr1.5MnO4

Orbital ordering (OO) in the layered perovskite La0.5Sr1.5MnO4 has been investigated using the enhanced sensitivity of soft x-ray resonant diffraction at the Mn L edges. The energy dependence of an OO diffraction peak over the L(2,3) edges is compared to ligand-field calculations allowing a distinction between the influences of Jahn-Teller distortions and spin correlations. The energy dependence of the diffraction peak at the Mn L1 edge is remarkably different from that observed at the Mn K edge.     

Sum rules in x-ray resonant Raman scattering: recovering the Co ground state information in CoFe2O4 as a test case

We present an approach to x-ray resonant Raman scattering suitable for sum-rule analysis. In magnetic systems it gives ground state information as represented by an expansion in coupled multipoles of orbital and spin moments. The experiment is based on the angular dependence of the integrated peak intensities. In 3d transition elements one obtains information up to order 4 from the channel 2p(6)3d(n)-->2p(5)3d(n+1)-->2p(6)3s(1)3d(n+1). By combining these results with L(2,3) absorption dichroism, we show quantitatively the atomiclike properties of cobalt in CoFe2O4 up to high-order multipoles.     

Electron correlation effects in the valence band photoemission spectra of cooper dichloride

He I, He II and Al Kα photoemission measurements of the valence band of CuCl₂ are reported. The presence of the 3d⁸-like satellite indicates the strong correlation effects in the final state and the breakdown of the one-particle model. It is shown that the reduction of the satellite intensity in the valence band compared with the core hole emission is caused by the delocalization of the photo-hole. The satellite intensity in resonance with the super-Coster-Kronig decay is calculated.