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).     

A comparison of CCS tandem overload controls

In this paper we analyse issues associated with overloads in tandem switching systems in Common Channel Signalling (CCS) networks. In particular, we examine the need for, and effectiveness of, Automatic Congestion Control (ACC), a CCS mechanism which allows a congested switching system to inform adjacent CCS nodes of its level of overload, and subsequently controls the rate at which traffic is sent to the congested node. We demonstrate the critical need for end-offices and tandem switching systems to implement some form of ACC if network performance is to be maintained during congestion, especially in tandem exchanges. In addition, we find that the presently defined ACC should be expanded to allow more levels of congestion to be reported to adjacent nodes, so that a more effective, finer grained control is produced.     

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.     

Model-based automated extraction of microtubules from electron tomography volume.

We propose a model-based automated approach to extracting microtubules from noisy electron tomography volume. Our approach consists of volume enhancement, microtubule localization, and boundary segmentation to exploit the unique geometric and photometric properties of microtubules. The enhancement starts with an anisotropic invariant wavelet transform to enhance the microtubules globally, followed by a three-dimensional (3-D) tube-enhancing filter based on Weingarten matrix to further accentuate the tubular structures locally. The enhancement ends with a modified coherence-enhancing diffusion to complete the interruptions along the microtubules. The microtubules are then localized with a centerline extraction algorithm adapted for tubular objects. To perform segmentation, we novelly modify and extend active shape model method. We first use 3-D local surface enhancement to characterize the microtubule boundary and improve shape searching by relating the boundary strength with the weight matrix of the searching error. We then integrate the active shape model with Kalman filtering to utilize the longitudinal smoothness along the microtubules. The segmentation improved in this way is robust against missing boundaries and outliers that are often present in the tomography volume. Experimental results demonstrate that our automated method produces results close to those by manual process and uses only a fraction of the time of the latter.     

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.     

Echo planar imaging of perfluorocarbons

Emulsions of perfluorotributylamine (FTBA) and perflubron were evaluated for their utility in ¹⁹F echo planar imaging. Fluorine images of the emulsions were obtained in a phantom and two mice that had been predosed. Both agents, but particularly perflubron, show potential for fluorine echo planar studies because of the long spin-spin relaxation times of the CF₃ resonances. High resolution thin slice images obtained in as little as 26.6 ms are presented.