A posteriori error estimates for FEM with violated Galerkin orthogonality

This article investigates Petrov‐Galerkin discretizations of operator equations with linearly stable operators, where the residual does not belong to the annihilator W of the discrete test space W_h. Conforming and nonconforming methods are considered separately, and for the treatment of the nonconforming situation the concept of elliptic lifting is introduced. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 241–259, 2002; DOI 10.1002/num.1005     

Homogeneous ZnO Nanoparticles by Flame Spray Pyrolysis

Zinc oxide (ZnO) nanoparticles were made by flame spray pyrolysis (FSP) of zinc acrylate–methanol–acetic acid solution. The effect of solution feed rate on particle specific surface area (SSA) and crystalline size was examined. The average primary particle diameter can be controlled from 10 to 20nm by the solution feed rate. All powders were crystalline zincite. The primary particle diameter observed by transmission electron microscopy (TEM) was in agreement with the equivalent average primary particle diameter calculated from the SSA as well as with the crystalline size calculated from the X-ray diffraction (XRD) patterns for all powders, indicating that the primary particles were rather uniform in diameter and single crystals. Increasing the solution feed rate increases the flame height, and therefore coalescence and/or surface growth was enhanced, resulting in larger primary particles. Compared with ZnO nanoparticles made by other processes, the FSP-made powder exhibits some of the smallest and most homogeneous primary particles. Furthermore, the FSP-made powder has comparable BET equivalent primary particle diameter with but higher crystallinity than sol–gel derived ZnO powders.     

The Poisson Voronoi Tessellation II. Edge Length Distribution Functions

This paper presents a method for the determination of the distribution function of the length of the 'typical' edge of the Poisson Voronoi tessellation. The method is based on distributional properties of the configuration of the centres in the neighbourhood of the 'typical' vertex. The distribution and density functions of the edge lengths are given in double integral form for various dimensions. Analogous characteristics are considered for two-dimensional sections through higher-dimensional Poisson Voronoi tessellations.     

On bounded time-dependent perturbations of operator cosine functions

In this note it is shown that the Cauchy problem associated with the infinitesimal generatorA of a strongly continuous operator cosine function remains uniformly well-posed under bounded time-dependent perturbations ofA.     

Current Interruption at Powers up to 1 GW with Crossed-Field Tubes

This paper describes the current interruption and voltage holdoff capabilities of a wide range of crossed-field tubes (XFTs). The XFTs investigated have active electrode areas ranging from 96 to 8000 cm2 with mean diameters from 2 to 56 cm. For the larger XFTs, currents up to 10 kA have been interrupted at voltages up to 100 kV, corresponding to a switched power of 1 GW. Experiments have shown the peak interruptible current to vary linearly with tube radius. The mechanism responsible for the limitation may be related to the self-generated magnetic field, but other factors are also shown to play a role.     

Novel halogenated imidazoles. Chloroimidazoles

With one exception chloroimidazoles containing an unalkylated ring nitrogen have been ignored. Procedures are described using hypochlorite solution that permit the synthesis of 4,5-dichloroimidazole and 2,4,5-trichloroimidazole. Various bromoimidazoles are also converted to chloroimidazoles in refluxing hydrochloric acid.