Aziridines as a protecting and directing group. Stereoselective synthesis of (+)-bromoxone

[reaction: see text] The directing ability of an aziridine group for the epoxidation of adjacent double bonds is demonstrated. The aziridine group is also used to effectively protect a double bond in a cycloenone system for a short synthesis of the title compound.     

Efficient asymmetric synthesis of the vasopeptidase inhibitor BMS-189921

[reaction: see text] An efficient asymmetric synthesis of the vasopeptidase inhibitor BMS-189921 was accomplished. Two short enantioselective syntheses of the common key intermediate (S)-alpha-aminoazepinone 6b were developed. Olefin 3 was converted to 6b via asymmetric hydrogenation. Alternatively, enyne 12 was converted to racemic alpha-aminoazepinone 15b, which was transformed to 6b by a practical dynamic resolution.     

The kinetics of homogeneous nucleation of silver nanoparticles stabilized by polymers

The formation of Ag nanoparticles synthesized by homogeneous nucleation, stabilized by polymers (PVA and PVP) was monitored by UV–Vis spectrophotometry and transmission electron microscopy. Our aim was to differentiate between the two main phases of particle formation, i.e. nucleation and growth and to characterize their rates with the help of appropriate kinetic equations. Time resolved spectrophotometric measurements revealed that particle formation is an autocatalytic process: a slow, continuous nucleation phase (3–5 min) is followed by a rapid, autocatalytic growth phase where the maximal particle size is 5–7 nm. By freezing the reaction mixture, the process of particle growth can be followed from 5 to 40 min on TEM pictures. The first order rate constants were calculated and they are strongly depend on the polymer concentration. If the growing particles are attached by PEI to the surface of a solid support, the formation of silver nanoparticles can also be followed by atomic force microscopy (AFM) and we can control the particle growth on mica surface. The cross section analysis of the pictures show, that the particle growing process can be also monitored at solid–liquid interface.     

Arbitrage valuation and bounds for sinking-fund bonds with multiple sinking-fund dates

The paper tackles the problem of pricing, under interest-rate risk, a default-free sinking-fund bond which allows its issuer to recurrently retire part of the issue by (a) a lottery call at par, or (b) an open market repurchase. By directly modelling zero-coupon bonds as diffusions driven by a single-dimensional Brownian motion, a pricing formula is supplied for the sinking-fund bond based on a backward induction procedure which exploits, at each step, the martingale approach to the valuation of contingent-claims. With more than one sinking-fund date, however, the pricing formula is not in closed form, not even for simple parametrizations of the process for zerocoupon bonds, so that a numerical approach is needed. Since the computational complexity increases exponentially with the number of sinking-fund dates, arbitrage-based lower and upper bounds are provided for the sinking-fund bond price. The computation of these bounds is almost effortless when zero-coupon bonds are as described by Cox, Ingersoll and Ross. Numerical comparisons between the price of the sinking-fund bond obtained via Monte Carlo simulation and these lower and upper bounds are illustrated for different choices of parameters.     

Microwave-assisted synthesis of dihydropyridones from curcumin

Dihydropyridones were prepared by microwave-assisted reaction between curcumin and primary amines or their acetates in the presence of Montmorillonite (K-10) as a catalyst. The reaction was complete within a few minutes and the yield depends on the amine used.     

Algebraic approach for the exploration of the onset of chaos in discrete nonlinear dynamical systems

An algebraic approach based on the rank of a sequence is proposed for the exploration of the onset of chaos in discrete nonlinear dynamical systems. The rank of the partial solution is identified and a special technique based on Hankel matrices is used to decompose the solution into algebraic primitives comprising roots of the modified characteristic equation. The distribution of roots describes the dynamical complexity of a solution and is used to explore properties of the nonlinear system and the onset of chaos.     

Codimension one symplectic foliations and regular Poisson structures

In this short note we give a complete characterization of a certain class of compact corank one Poisson manifolds, those equipped with a closed one-form defining the symplectic foliation and a closed two-form extending the symplectic form on each leaf. If such a manifold has a compact leaf, then all the leaves are compact, and furthermore the manifold is a mapping torus of a compact leaf. These manifolds and their regular Poisson structures admit an extension as the critical hypersurface of a b-Poisson manifold as we will see in [9].     

Complementary multiplicative hyperrings

In this paper the complementary hyperstructure obtained from a multiplicative hyperring is considered. Furthermore a characterization for such hyperstructures obtained starting from a strongly distributive multiplicative hyperring is given.     

Addendum to: Comparison between different types of abstract integrals in riesz spaces

In [3] we did not give explicitly the definition of measurability for realvalued functions, with respect to finitely additive measures with values in a Dedekind complete Riesz space. We note that, in [3], all involved functions are intended to be measurable. We now report the definition of measurability, which we gave in [2] (Definition 3.2).