Polycondensation of activated L‐valine and L‐leucine esters with various lewis acids

To develop a novel polycondensation method for the preparation of poly (amino acid)s, we screened a transition metal or a rare‐earth triflate as a Lewis acid for the polycondensation of activated amino acid esters in N,N‐dimethylformamide solutions at room temperature. The polymerizations of 4‐nitrophenyl L ‐leucinate ( 1a ) and 4‐nitrophenyl L ‐valinate ( 1b ) scarcely proceeded without any Lewis acid at room temperature. In the presence of 5 mol % metal triflates, especially scandium(III) trifluoromethanesulfonate, the polymerizations of both monomers were promoted effectively. The products, which were collected by the reaction mixture being poured into water, were recognized as poly(L ‐valine)s by Fourier transform infrared spectroscopy, gel permeation chromatography analysis, and ¹H NMR spectroscopy. These results showed that a metal triflate as a Lewis acid could coordinate to a carbonyl oxygen of activated L ‐valinate and L ‐leucinate even in a highly polar solvent, such as N,N‐dimethylformamide; therefore, the polymerizations of activated L ‐valinate and L ‐leucinate were promoted. Because steric hindrance derived from the isobutyl group in 1b was less than that of the isopropyl unit in 1a , the effect of the metals was not as sensitive for the polymerization of 1b . © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 543–547, 2007     

Pricing and risk management of interest rate swaps

This paper reformulates the valuation of interest rate swaps, swap leg payments and swap risk measures, all under stochastic interest rates, as a problem of solving a system of linear equations with random perturbations. A sequence of uniform approximations which solves this system is developed and allows for fast and accurate computation. The proposed method provides a computationally efficient alternative to Monte Carlo based valuations and risk measurement of swaps. This is demonstrated by conducting numerical experiments and so our method provides a potentially important real-time application for analysis and calculation in markets.     

A linear algebraic method for pricing temporary life annuities and insurance policies

We recast the valuation of annuities and life insurance contracts under mortality and interest rates, both of which are stochastic, as a problem of solving a system of linear equations with random perturbations. A sequence of uniform approximations is developed which allows for fast and accurate computation of expected values. Our reformulation of the valuation problem provides a general framework which can be employed to find insurance premiums and annuity values covering a wide class of stochastic models for mortality and interest rate processes. The proposed approach provides a computationally efficient alternative to Monte Carlo based valuation in pricing mortality-linked contingent claims.     

Enhanced field emission from LaB6 thin films with nanoprotrusions grown by pulsed laser deposition on Zr foil

Lanthanum hexaboride (LaB₆) films have been deposited on a zirconium foil by pulsed laser deposition method. The field emission studies of the LaB₆ deposited film have been performed in the planar diode configuration under ultra high vacuum conditions. The Fowler-Nordheim plots were found to be linear in accordance with the quantum mechanical tunneling phenomenon. A typical field emission current of 7.02 μA was drawn at an applied electric field of 2 V/μm. The field enhancement factor is calculated to be 8913 cm⁻¹, indicating that the field emission is from nanoscale protrusions present on the emitter surface. The atomic force microscope (AFM) investigation of the surface clearly shows the conical shaped nanoprotrusions of few hundred nanometers with asperities of 20-40 nm on its top. The emission current-time plot recorded at the pre-set value of emission current of 5 μA over a period of more than 3 h exhibits an initial increase and subsequent stabilization of the current. The results reveal that the LaB₆/Zr field emitter obtained by the pulsed laser deposition (PLD) is a promising cathode material for practical applications in field emission-based devices.     

On the Cauchy problem for the general relativistic perfect magnetofluid

This paper aims at the study of the Cauchy problem for the general relativistic perfect magnetofluid. The consistency and uniqueness condition to be satisfied on the hypersurface by three unknown quantities in the magnetohydrodynamic field equations is obtained. For unit magnetic permeability the result agrees in form with that of Lichnerowicz.     

Hyperfine interactions in stabilized Fe1−δO:Al3+ system

Highly stable Fe_1?δO:Al³⁺ system has been synthesized by checking the spontaneous disproportionation of FeO. The novel preparation route of incorporating non-magnetic trivalent Al³⁺ ions in the wustite lattice is followed for the preparation of solid solutions. X-ray diffraction (XRD), chemical analysis and Fe⁵⁷ Mössbauer effect are used for the characterization. The hyperfine interaction parameters reported are characteristic of high spin Fe²⁺ state which confirmed the stabilization of FeO.     

Crystal and molecular structure of 10,20-epoxy-grayanotoxin-II

The photooxidation with HgO in benzene and the hydrolysis with 2%-KOH in methanol of the grayanotoxin (GTX) derivative (4) gave a 10,20-epoxy-grayanotoxin-II(5). The crystal structure of (5) has been determined by X-ray diffraction at room temperature. The crystal is monoclinic, space group P2₁, with a = 14.248(10) Å, b = 6.670(10) Å, c = 9.990(10) Å, = 105.507(8)°, V = 914.9(2) ų, Z = 2. The structure was solved by direct methods and refined by full-matrix least squares methods to a final R1 = 0.046 (wR2 = 0.0833) for 1161 independent reflections. The molecule has a pentacyclic structure consisting of two five-membered, one six-membered, one seven-membered, and one three-membered rings. The three-membered ring is connected with the seven-membered ring by spiro-type bond.