Smooth Solution of the Compressible Navier–Stokes Equations in an Unbounded Domain with Inflow Boundary Condition

The barotropic compressible Navier–Stokes equations in an unbounded domain are studied. We prove the unique existence of the solution (u, p) of the system (1.1) in the Sobolev spaceH^{k + 3} × H^{k + 2}provided that the derivatives of the data of the problem are sufficiently small, wherek ≥ 0 is any integer. The proof follows from an analysis of the linearized problem, the solvability of the continuity equation, and the Schauder fixed point theory. Similar smoothness results are obtained for a linearized form of (1.1).     

Organotellurides as a source of organometallics: application in the synthesis of (+/−)-frontalin

A masked lithium homoenolate, generated by tellurium/lithium exchange, was reacted with epoxides. The lithium compound was also converted into other organometallics such as Grignard, and cuprates and the reactivity of those organometallics with epoxides was evaluated. The same building block was employed in the synthesis of (+/−)-frontalin.     

Synthesis of optically active 6-substituted 2-(aminomethyl)chromans

Three novel, optically active, 6-substituted 2-(aminomethyl)chromans were synthesized from readily available chroman 2-carboxylic acid precursors. These chroman-containing primary amines are useful building blocks for the synthesis of chroman-derived pharmaceutical agents.     

Electron spin lifetimes in Hg0.78Cd0.22 Te and InSb

We have made direct pump–probe measurements of spin lifetimes in long wavelength narrow-gap semiconductors at wavelengths between 4 and 10 μm and from 4 to 300 K. In particular, we measure remarkably long spin lifetimes, τ_s300 ps, even at 300 K for epilayers of degenerate n-type InSb. In this material the mobility is approximately constant between 77 and 300 K, and we find that τ_s is approximately constant in this temperature range. In order to determine the dominant spin relaxation mechanism we have investigated the temperature dependence of τ_s in non-degenerate lightly n-type Hg_0.78Cd_0.22Te of approximately the same band gap as InSb, and find that τ_s varies from 356 ps at 150 K to 24 ps at 300 K. Our results, both in magnitude and temperature dependence of τ_s, imply that the Elliott–Yafet model dominates in these materials.     

One-pot synthesis of polysubstituted indoles from aliphatic nitro compounds under mild conditions

Polysubstituted indoles can be prepared directly from functionalized nitroalkanes under very mildly acidic conditions in a simple, one-pot, two-stage procedure.     

Ergodic theory and the Strong Law of Large Numbers on Riesz spaces

In [W.-C. Kuo, C.C.A. Labuschagne, B.A. Watson, Discrete-time stochastic processes on Riesz spaces, Indag. Math. (N.S.) 15 (3) (2004) 435-451], we introduced the concepts of conditional expectations, martingales and stopping times on Riesz spaces. Here we formulate and prove order theoretic analogues of the Birkhoff, Hopf and Wiener ergodic theorems and the Strong Law of Large Numbers on Riesz spaces (vector lattices).     

Transport of surface-modified iron nanoparticle in porous media and application to arsenic(III) remediation

The surface-modified iron nanoparticles (S-INP) were synthesized, characterized and tested for the remediation of arsenite (As(III)), a well known toxic groundwater contaminant of concern. The S-INP material was fully dispersed in the aqueous phase with a particle size distribution of 2–10 nm estimated from high-resolution transmission electron microscopy (HR-TEM). X-ray photoelectron spectroscopy (XPS) revealed that an Fe(III) oxide surface film was present on S-INP in addition to the bulk zero-valent Fe⁰ oxidation state. Transport of S-INP through porous media packed in 10 cm length column showed particle breakthroughs of 22.1, 47.4 and 60 pore volumes in glass beads, unbaked sand, and baked sand, respectively. Un-modified INP was immobile and aggregated on porous media surfaces in the column inlet area. Results using S-INP pretreated 10 cm sand-packed columns containing ∼2 g of S-INP showed that 100 % of As(III) was removed from influent solutions (flow rate 1.8 mL min⁻¹) containing 0.2, 0.5 and 1.0 mg L⁻¹ As(III) for 9, 7 and 4 days providing 23.3, 20.7 and 10.4 L of arsenic free water, respectively. In addition, it was found that 100% of As(III) in 0.5 mg/L solution (flow rate 1.8 mL min⁻¹) was removed by S-INP pretreated 50 cm sand packed column containing 12 g of S-INP for more than 2.5 months providing 194.4 L of arsenic free water. Field emission scanning electron microscopy (FE-SEM) showed S-INP had transformed to elongated, rod-like shaped corrosion product particles after reaction with As(III) in the presence of sand. These results suggest that S-INP has great potential to be used as a mobile, injectable reactive material for in-situ sandy groundwater aquifer treatment of As(III).     

Fast atom bombardment mass spectra of keto acid and keto ester phosphoranes

Positive-ion fast atom bombardment mass spectra of 13 keto acid and keto ester phosphoranes were examined. All compounds gave a protonated molecular ion and characteristic peaks at m/z 303, 279, 262 and 201.