Comparative chemical analysis of the essential oil constituents in the bark, heartwood and fruits of Cryptocarya massoy (Oken) Kosterm. (Lauraceae) from Papua New Guinea

Exhaustive hydro-distillation of the bark, heartwood and fruits of Cryptocarya massoy (Lauraceae) afforded pale yellow-coloured oils in 0.7, 1.2 and 1.0 % yields, respectively. Detailed chemical evaluation of these distillates using GC/MS revealed the major components in the bark and the heartwood oils to be the C-10 (5,6-dihydro-6-pentyl-2H-pyran-2-one) and C-12 (5,6-dihydro-6-heptyl-2H-pyran-2-one) massoia lactones, while the major fruit oil constituent was benzyl benzoate (68.3 %). The heartwood also contained trace amounts of the C-14 (5,6-dihydro-6-nonyl-2H-pyran-2-one) massoia lactone (1.4 %) and the saturated C-10 derivative delta-decalactone (2.5 %).     

Volatile chemical constituents of Piper aduncum L and Piper gibbilimbum C. DC (Piperaceae) from Papua New Guinea

Exhaustive hydro-distillation of the leaves of Piper aduncum and fruits of Piper gibbilimbum (Piperaceae) afforded colorless and pale orange colored oils in 0.35 and 0.30 % yields, respectively. Detailed chemical analysis by GC/MS indicated the volatile constituents of Piper aduncum to be composed of dill apiole (43.3%), beta-caryophyllene (8.2%), piperitione (6.7%) and alpha-humulene (5.1%), whilst the oil of P. gibbilimbum is dominated by the gibbilimbols A-D (74.2%), with the remaining major constituents being the terpenes camphene (13.6%) and alpha-pinene (6.5%).     

A fluorous-tagged linker from which small molecules are released by ring-closing metathesis

A fluorous-tagged linker for the parallel synthesis of small- and medium-ring and macrocyclic nitrogen heterocycles using ring-closing metathesis is described. The linker was designed such that "cyclization-release" of the cyclic heterocyclic products was coupled with liberation of the active catalyst. The design of the linker was validated using a non-fluorous-tagged model. A wide range of unsaturated alcohols were used as reagents to functionalize a fluorous-tagged sulfonamide, (Z)-{N-[4-(2-(N'-3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,10-heptadecafluorodecyl)-4-methylsulfonamido)methylallyloxy]but-2-enyl}-2-nitrobenzenesulfonamide, using Fukuyama-Mitsunobu reactions; in each case, fluorous-solid-phase extraction (F-SPE) was used to purify the functionalized linker from the excess reagents. In general, the "cyclization-release" of cyclic products was triggered using a light-fluorous tagged derivative of the Grubbs-Hoveyda second-generation catalyst. After the metathesis step, F-SPE was used to purify released cyclic compounds from the fluorous-tagged linker and the fluorous-tagged catalyst. The scope and limitations of the approach were determined using a range of substrates which probed different aspects of the functionalization and metathesis steps. In the study as a whole, a wide range of small- and medium-ring and macrocyclic nitrogen heterocycles were prepared using polyene and polyenyne metathesis cascades.     

Long-time solutions of scalar nonlinear hyperbolic reaction equations incorporating relaxation I. The reaction function is a bistable cubic polynomial

We consider an initial-value problem based on a class of scalar nonlinear hyperbolic reaction–diffusion equations of the general form

$u_{\tau \tau }+u_{\tau }=u_{xx}+\epsilon (F(u)+F{(u)}_{\tau }),$

in which x and τ represent dimensionless distance and time respectively and $\epsilon >0$ is a parameter related to the relaxation time. Furthermore the reaction function, $F(u)$, is given by the bistable cubic polynomial,

$F(u)=u(1?u)(u?\mu ),$

in which $0<\mu <1/2$ is a parameter. The initial data is given by a simple step function with $u(x,0)=1$ for $x\le 0$ and $u(x,0)=0$ for $x>0$. It is established, via the method of matched asymptotic expansions, that the large-time structure of the solution to the initial-value problem involves the evolution of a propagating wave front which is either of reaction–diffusion or of reaction–relaxation type. The one exception to this occurs when $\mu =\frac{1}{2}$ in which case the large time attractor for the solution of the initial-value problem is a stationary state solution of kink type centred at the origin.     

The large-time development of the solution to an initial-value problem for the Korteweg-de Vries-Burgers equation, II: Initial data has a discontinuous expansive step

In this paper, we consider an initial-value problem for the Korteweg-de Vries-Burgers equation. The normalized Korteweg-de Vries-Burgers equation considered is given by

     

A note on the integrability of the classical portfolio selection model

We revisit the classical Merton portfolio selection model from the perspective of integrability analysis. By an application of a nonlocal transformation the nonlinear partial differential equation for the two-asset model is mapped into a linear option valuation equation with a consumption dependent source term. This result is identical to the one obtained by Cox–Huang [J.C. Cox, C.-f. Huang, Optimal consumption and portfolio policies when asset prices follow a diffusion process, J. Econom. Theory 49 (1989) 33–88], using measure theory and stochastic integrals. The nonlinear two-asset equation is then analyzed using the theory of Lie symmetry groups. We show that the linearization is directly related to the structure of the generalized symmetries.     

Catalytic Enantioselective Synthesis of α‐Chiral Azaheteroaryl Ethylamines by Asymmetric Protonation

The direct enantioselective synthesis of chiral azaheteroaryl ethylamines from vinyl‐substituted N‐heterocycles and anilines is reported. A chiral phosphoric acid (CPA) catalyst promotes dearomatizing aza‐Michael addition to give a prochiral exocyclic aryl enamine, which undergoes asymmetric protonation upon rearomatization. The reaction accommodates a broad range of N‐heterocycles, nucleophiles, and substituents on the prochiral centre, generating the products in high enantioselectivity. DFT studies support a facile nucleophilic addition based on catalyst‐induced LUMO lowering, with site‐selective, rate‐limiting, intramolecular asymmetric proton transfer from the ion‐paired prochiral intermediate.     

Cracking assisted nucleation in chemical vapor deposition of silicon nanoparticles on silicon dioxide

Deposition of sub-monolayer silicon on SiO₂/Si(1 0 0) greatly facilitates nucleation in subsequent thermal chemical vapor deposition (CVD) of silicon nanoparticles. Sub-monolayer seeding is accomplished using silicon atoms generated via disilane decomposition over a hot tungsten filament. The hot-wire process is nonselective towards deposition on silicon and SiO₂, is insensitive to surface temperature below 825 K, and gives controlled coverages well below 1 ML. Thermal CVD of nanoparticles at 1×10⁻⁴ Torr disilane and temperatures ranging from 825 to 925 K was studied over SiO₂/Si(1 0 0) surfaces that had been subjected to predeposition of Si or were bare. Seeding of the SiO₂ surface with as little as 0.01 ML is shown to double the nanoparticle density at 825 K, and densities are increased twenty fold at 875 K after seeding the surface with 30% of a monolayer.