Statevector reduction in discrete time: A random walk in Hilbert space

A simple model is presented in which the statevector evolves every seconds in one of two ways, according to a particular probability rule. It is shown that this random walk in Hilbert space results in reduction of the statevector. It is also shown how the continuous spontaneous localization (CSL) theory of statevector reduction is achieved as a limiting case of this model, exactly as Brownian motion is a limiting case of ordinary random walk. Finally, a slightly different but completely equivalent form of the CSL equations suggested by the simple model given here is discussed.     

Jupiter's Great Red Spot and zonal winds as a self-consistent,one-layer,quasigeostrophic flow

We present the point of view that both the vortices and the east-west zonal winds of Jupiter are confined to the planet's shallow weather layer and that their dynamics is completely described by the weakly dissipated, weakly forced quasigeostrophic (QG) equation. The weather layer is the region just below the tropopause and contains the visible clouds. The forcing mimics the overshoot of fluid from an underlying convection zone. The late-time solutions of the weakly forced and dissipated QG equations appear to be a small subset of the unforced and undissipated equations and are robust attractors. We illustrate QG vortex dynamics and attempt to explain the important features of Jupiter's Great Red Spot and other vortices: their shapes, locations with respect to the extrema of the east-west winds, stagnation points, numbers as a function of latitude, mergers, break-ups, cloud morphologies, internal distributions of vorticity, and signs of rotation with respect to both the planet's rotation and the shear of their surrounding east-west winds. Initial-value calculations in which the weather layer starts at rest produce oscillatory east-west winds. Like the Jovian winds, the winds are east-west asymmetric and have Karman vortex streets located only at the west-going jets. From numerical calculations we present an empirically derived energy criterion that determines whether QG vortices survive in oscillatory zonal flows with nonzero potential vorticity gradients. We show that a recent proof that claims that all QG vortices decay when embedded in oscillatory zonal flows is too restrictive in its assumptions. We show that the asymmetries in the cloud morphologies and numbers of cyclones and anticyclones can be accounted for by a QG model of the Jovian atmosphere, and we compare the QG model with competing models.     

Bengazoles C-G from the Sponge Jaspis sp. Synthesis of the Side Chain and Determination of Absolute Configuration

Five new antifungal bengazoles (C-G) were isolated and fully characterized from a marine sponge of the genus Jaspis sp. Bengazoles C-G, together with the known bengazoles A and B, comprise a homologous series of n, iso, and anteiso fatty acid esters (C(13)-C(16)) of the same heterocyclic bis(oxazolyl)methanol parent. The complete relative and absolute configurations of the bengazoles were determined by application of the modified Mosher method and interpretation of exciton coupling in the CD spectra of the tetra-p-bromobenzoate derivatives of bengazole A and that of a model tetrol synthesized in seven steps from L-fucose.     

Nonresonant third-order susceptibility measurements in the nematic liquid crystal K18

We have observed a large nonresonant third-order nonlinear susceptibility, X ⁽³⁾ (-; , 0, 0) in the isotropic phase of a nematic liquid crystal 4-n-hexyl-4-cyanobiphenyl (K18). The highest value of X ⁽³⁾ obtained at 632.8 nm is 1.16274×10^-18 m²V^-2 corresponding to a temperature 29.3°C. The observed second-order pretransitional temperature T ^* from our measurements is 1.2°C below the first-order nematic to isotropic transition temperature. The dependence of the Kerr constant on (T-T ^*)^-1 is found to be in good agreement with the predictions of the Landau-de Gennes model.     

X-ray and molecular mechanics studies on the sesquiterpene lactone eupatocunin-o-bromobenzoate — An unusual case of disorder involving atropisomerism

The molecular structure of the cytotoxic sesquiterpene lactone eupatocunin has been determined by X-ray crystallographic analysis of theo-bromobenzoate derivative. Two structural isomers, arising from hindered rotation, are present within the single crystal. The molecules are disordered (ratio 0.750.25) with the bromine atom occupying alternate ortho positions on the aromatic ring. Molecular mechanics has been used to examine the energies of molecular conformation by torsion angle variation.     

On-line preconcentration strategies for trace analysis of metabolites by capillary electrophoresis

Analysis of low concentrations of metabolites is required for new fields of biological research, such as metabolomics. In this review, recent work in our laboratory aimed at developing improved strategies for on-line sample preconcentration of metabolites by capillary electrophoresis (CE) is presented. Dynamic pH junction, sweeping and dynamic pH junction-sweeping represent three complementary methods for electrokinetic focusing of large volumes of sample directly on-capillary. Focusing selectivity and focusing efficiency are two factors that can be used to assess the suitability of each method for different classes of metabolites. Buffer properties can be selected to enhance the focusing of specific types of metabolites based on knowledge of the analyte physicochemical properties. The application of on-line preconcentration CE for trace analysis of metabolites in real samples of interest, such as biological fluids and cellular extracts, is also demonstrated. Under optimum conditions, up to three orders of magnitude increase in concentration sensitivity can be realized for several classes of metabolites, including catecholamines, purines, nucleosides, nucleotides, amino acids, steroids and coenzymes. Recent work on hyphenating on-line preconcentration with multiplexed CE is highlighted as a promising platform for sensitive and high-throughput analyses of metabolites.     

Studies in alkylation. I. Synthesis and reactions of spiro[oxirane-2,4-piperidines]

Spiro[oxirane-2, 4′-piperidines] have been prepared by the action of dimethyloxosulfonium methylide on 4-piperidones. The spiro[oxirane-2,4′-piperidines] act as alkylating agents to introduce (4-hydroxy-4-piperidyl) methyl moieties onto heteroaromatic compounds such as 4(3H)-quinazolone.     

Nonrigid molecule effects in molecules with linear or nongeometrically equivalent equilibrium configurations

A theoretical study is made of the states of nonrigid molecules, extending earlier work to apply Longuet–Higgins' symmetry group of feasible permutation/inversions in two previously untreated cases. The first involves nonrigid molecule processes between different stereoisomers, that is between molecular equilibrium configurations of different geometrical shapes. The second takes into account nonrigid molecule processes in linear molecules. The theory is applied to the specific case of nonrigid molecule effects in the butyl ion C₄H (case i), and the form of the nonrigid molecule energy levels and spectra are determined. The theory is also applied to determine the nonrigid molecule energy levels in linear H₂F₂ (case ii).     

Composition dependence of the structural chemistry and magnetism of Ca2.5Sr0.5(Ga,Co)1+xMn2−xO8

Polycrystalline samples of bilayered brownmillerite-like Ca_2.5Sr_0.5GaCo_0.15Mn_1.85O₈ and Ca_2.5Sr_0.5Ga_1.2Mn_1.8O₈ have been prepared and characterised by magnetometry and neutron diffraction over a wide temperature range. The structural chemistry and magnetic properties are compared to those of Ca_2.5Sr_0.5GaMn₂O₈. Ga enrichment has a significant effect on the former but not on the latter, whereas changes in both occur when paramagnetic Co³⁺ cations enter the parent phase on the 4-coordinate sites. The coupling between the environment around the 4-coordinate cations and the transition to an antiferromagnetic ordered state that was observed in Ca_2.5Sr_0.5GaMn₂O₈ is not apparent in the cation-substituted compositions, although both show long-range antiferromagnetic order at low temperatures.