Effective semi-analytic integration for hypersingular Galerkin boundary integral equations for the Helmholtz equation in 3D

We deal with the Galerkin discretization of the boundary integral equations corresponding to problems with the Helmholtz equation in 3D. Our main result is the semi-analytic integration for the bilinear form induced by the hypersingular operator. Such computations have already been proposed for the bilinear forms induced by the single-layer and the double-layer potential operators in the monograph The Fast Solution of Boundary Integral Equations by O. Steinbach and S. Rjasanow and we base our computations on these results.     

Foliations of asymptotically flat manifolds by surfaces of Willmore type

The goal of this paper is to establish the existence of a foliation of the asymptotic region of an asymptotically flat manifold with positive mass by surfaces which are critical points of the Willmore functional subject to an area constraint. Equivalently these surfaces are critical points of the Geroch–Hawking mass. Thus our result has applications in the theory of general relativity.     

Estimating summary functionals in multistate models with an application to hospital infection data

Inhomogeneous Markov chains are a relevant framework for analysing event histories. The fundamental estimator in the presence of incompletely observed data is the Nelson-Aalen estimator of the multivariate cumulative hazards. It may be summarised in terms of probability estimates via the empirical transition matrix. The empirical transition matrix has only slowly entered applications, one reason being previous lack of software. In a number of applications, further summary measures are desired. We illustrate how they may be computed from the empirical transition matrix and why bootstrapping their variance works. In contrast, computing such summaries outside the present framework has typically led to biased results. As an example, we consider in more detail hospital stay following infectious complication. This summary quantity is often considered by clinical decision makers, but reliable estimates require modelling the timing of infection as in the present set-up. In this context, we also derive new summary measures that further distinguish between patients discharged and patients deceased.     

Atmospheric pressure chemical vapour deposition of selenium and tellurium films by UV laser photolysis of diethyl selenium and diethyl tellurium

Excimer laser‐induced photolysis of gaseous diethyl selenium and diethyl tellurium (C₂H₅)₂M (M = Se, Te) is controlled by cleavage of both M? C bonds, it yields C₁–C₄ hydrocarbons (ethene as major product) and results in chemical vapour deposition of selenium films and nanosized tellurium powder. The selenium and tellurium properties were characterized by X‐ray photoelectron spectroscopy and Scanning electron Microscopy techniques. Copyright © 2001 John Wiley & Sons, Ltd.     

A class of quasi-variational inequalities for adaptive image denoising and decomposition

We introduce a class of adaptive non-smooth convex variational problems for image denoising in terms of a common data fitting term and a support functional as regularizer. Adaptivity is modeled by a set-valued mapping with closed, compact and convex values, that defines and steers the regularizer depending on the variational solution. This extension gives rise to a class of quasi-variational inequalities. We provide sufficient conditions for the existence of fixed points as solutions, and an algorithm based on solving a sequence of variational problems. Denoising experiments with spatial and spatio-temporal image data and an adaptive total variation regularizer illustrate our approach.     

The effect of mixing methods on the dispersion of carbon nanotubes during the solvent-free processing of multiwalled carbon nanotube/epoxy composites

Several solvent-free processing methods to disperse multiwalled carbon nanotubes (MWCNTs) in bisphenol F-based epoxy resin were investigated, including the use of a microfluidizer (MF), planetary shear mixer (PSM), ultrasonication (US) and combinations. The processed mixture was cured with diethyl toluene diamine. Three complimentary techniques were used to characterize the dispersion of the MWCNTs in cured composite samples: optical microscopy, micro Raman spectroscopy, and scanning electron microscopy (SEM). For sample MF + PSM, optical micrographs and Raman images showed reduced agglomeration and a homogeneous distribution of MWCNTs in the epoxy matrix. SEM analysis of fractured specimen after tensile testing revealed breakage of nanotubes along the fracture surface of the composite. A comparison of the MWCNT dispersion in the epoxy samples processed using different methods showed that a combination of MF and PSM processing yields a more homogeneous sample than the PSM or US + PSM processed samples. Mechanical testing of the composites showed about 15% improvement in the tensile strength of samples processed by the MF + PSM method over other methods. Thermogravimetric analysis (TGA) results showed a small decrease in the onset degradation temperature for poorly dispersed samples produced by PSM compared with the well-mixed samples (MF + PSM). These results strongly suggest that the MF + PSM processing method yield better-dispersed and stronger MWCNT/epoxy composites. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2013