Synthesis and axial chirality of an enantiopure aminodibenzazepinone

A route for the synthesis of (S,S)-7-amino-5-methyl-5H-dibenzo[b,d]azepin-6(7H)-one hydrochloride is disclosed. The synthesis includes a Friedel–Crafts alkylation to form the seven-membered ring and a highly efficient classical resolution. Additional studies on the enantiopure material showed the amine to be highly resistant to racemization, which led us to investigate the unexpected stability. We propose that the inherent axial chirality contained in the dibenzazepinone works to produce an interesting chirality transfer mechanism, which accounts for the observed robustness of the stereocenter. This previously unrecognized stereochemical element exists within this specific class of molecules, and they should be drawn in a manner which displays the axial chirality.     

Ion beam etching of high resolution structures in Ta2O5 for grating-assisted directional coupler applications

An investigation on thin Ta₂O₅ films patterning using argon ion beam etching (IBE) is presented. The etch rates are characterised by varying the angle of incidence of the beam onto the substrate. Ta₂O₅ gratings with a period of 2.2 μm (1.1 μm linewidth) and 0.25 μm thickness are fabricated using an angle of incidence of 0°. The resulting Ta₂O₅ grating cross sectional profiles are analysed using AFM and SEM imaging. A fabrication method is thus demonstrated which could be used to implement wavelength selective gratings in applications such as grating-assisted directional couplers (GADCs).     

Following the rules: Integrating asset allocation and annuitization in retirement portfolios

Financial advisers have developed standardized payout strategies to help Baby Boomers manage their money in their golden years. Prominent among these are phased withdrawal plans offered by mutual funds including the “self-annuitization” or default rules encouraged under US tax law, and fixed payout annuities offered by insurers. Using a utility-based framework, and taking account of stochastic capital markets and uncertain lifetimes, we first evaluate these rules on a stand-alone basis for a wide range of risk aversion. Next, we permit the consumer to integrate these standardized payout strategies at retirement and compare the results. We show that integrated strategies can enhance retirees’ well-being by 25%-50% for low/moderate levels of risk aversion when compared to full annuitization at retirement. Finally, we examine how welfare changes if the consumer is permitted to switch to a fixed annuity at an optimal point after retirement. This affords the retiree the chance to benefit from the equity premium when younger, and exploit the mortality credit in later life. For moderately risk-averse retirees, the optimal switching age lies between 80 and 85.     

Dynamics of Finger Formation in Laplacian Growth Without Surface Tension

We study the dynamics of “finger” formation in Laplacian growth without surface tension in a channel geometry (the Saffman–Taylor problem). We present a pedagogical derivation of the dynamics of the conformal map from a strip in the complex plane to the physical channel. In doing so we pay attention to the boundary conditions (no flux rather than periodic) and derive a field equation of motion for the conformal map. We first consider an explicit analytic class of conformal maps that form a basis for solutions in infinitely long channels, characterized by meromorphic derivatives. The great bulk of these solutions can lose conformality due to finite time singularities. By considerations of the nature of the analyticity of these solutions, we show that those solutions which are free of such singularities inevitably result in a single asymptotic “finger” whose width is determined by initial conditions. This is in contradiction with the experimental results that indicate selection of a finger of width 1/2. In the last part of this paper we show that such a solution might be determined by the boundary conditions of a finite body of fluid, e.g. finiteness can lead to pattern selection.     

Some algorithms of the projective-Newton method for the finite element space

The paper presents the projective-Newton method in the finite element space with curved finite elements along the boundary. The properties of this method are studied when the integrals are calculated by numerical quadrature. Some algorithms are derived when ω = {x ? R²: 0 < x₁, x₂ < 1}.     

Ozone-induced dissociation on a modified tandem linear ion-trap: Observations of different reactivity for isomeric lipids

Ozone-induced dissociation (OzID) exploits the gas-phase reaction between mass-selected lipid ions and ozone vapor to determine the position(s) of unsaturation. In this contribution, we describe the modification of a tandem linear ion-trap mass spectrometer specifically for OzID analyses wherein ozone vapor is supplied to the collision cell. This instrumental configuration provides spatial separation between mass-selection, the ozonolysis reaction, and mass-analysis steps in the OzID process and thus delivers significant enhancements in speed and sensitivity (ca. 30-fold). These improvements allow spectra revealing the double-bond position(s) within unsaturated lipids to be acquired within 1 s: significantly enhancing the utility of OzID in high-throughput lipidomic protocols. The stable ozone concentration afforded by this modified instrument also allows direct comparison of relative reactivity of isomeric lipids and reveals reactivity trends related to (1) double-bond position, (2) substitution position on the glycerol backbone, and (3) stereochemistry. For cis- and trans-isomers, differences were also observed in the branching ratio of product ions arising from the gas-phase ozonolysis reaction, suggesting that relative ion abundances could be exploited as markers for double-bond geometry. Additional activation energy applied to mass-selected lipid ions during injection into the collision cell (with ozone present) was found to yield spectra containing both OzID and classical-CID fragment ions. This combination CID-OzID acquisition on an ostensibly simple monounsaturated phosphatidylcholine within a cow brain lipid extract provided evidence for up to four structurally distinct phospholipids differing in both double-bond position and sn-substitution.