A unification of some matrix factorization results

A unification of some factorization results regarding products of positive-definite matrices, commutators, and products of involutions is presented. This topic was first presented by Sourour for fields with, in the latter two classes, sufficiently many elements in terms of the order of the matrix being factored. The current presentation is valid for matrices over any field with at least four elements, and is independent of the order of the matrix being factored.     

Principles for the characterisation and the value assignment of the candidate reference material in the new ISO Guide 35:2017

Accreditation and Quality Assurance - The production of reference materials (RMs) is a key activity for the improvement and maintenance of a worldwide coherent measurement system. General...     

Idempotent factorization of matrices

Necessary and sufficient conditions are presented for a square matrix over an arbitrary field to be a product of k ≥ 1 idempotent matrices of prescribed nullities.     

Surface modification of bulk n-InAs (111)A etched in bromine–methanol

X-ray photoelectron spectroscopy, field emission scanning electron microscopy, Raman and photoluminescence spectroscopy were used to evaluate the surface properties of n-type InAs (111)A etched in a 1% Br–methanol solution. Etching completely removes the native oxides from the surface and enhances the photoluminescence response. The adsorption of bromine onto the InAs surface leads to the formation of In–Br_x and As–Br_x bonds (x = 1, 2, 3) as inferred from changes in the In 3d_3/2;5/2 and As 3d core level binding energies. The etch rate is found to decrease due to strong anisotropic effects and the high volatility of the bromine species. A 1 min Br–methanol etch was found to enhance the photoluminescence intensity by a factor of 3, probably due to a reduction in the surface state density upon de-oxidation of the surface. This is thought to be due to reductions in the surface state density. The presence of native oxides enhances both the surface accumulation layer and the surface state density.     

Type II GaSb/GaAs quantum dot/ring stacks with extended photoresponse for efficient solar cells

We report on the fabrication of GaAs based p–i–n solar cells containing 5 and 10 layers of type II GaSb quantum rings grown by molecular beam epitaxy. Solar cells containing quantum rings show improved efficiency at longer wavelengths into the near-IR extending up to 1500 nm and show enhanced short-circuit current under 1 sun illumination compared to a GaAs control cell. A reduction in the open-circuit voltage is observed due to the build-up of internal strain. The MBE growth, formation and photoluminescence of single and stacked layers of GaSb/GaAs quantum rings are also presented.     

A note on medieval microfabrication: the visualization of a prayer nut by synchrotron‐based computer X‐ray tomography

One of the most fascinating objects in the Rijksmuseum (Amsterdam, The Netherlands) is an early 16th century prayer nut. This spherical wooden object measures 4 cm in diameter and consists of two hemispheres connected with a small hinge so that it can be opened. The interior of the nut holds wood carvings with scenes from the life of Christ. These miniature reliefs show an incredible degree of finish with carving details well beyond the millimetre scale. In the present paper it is shown how synchrotron‐based computer X‐ray tomography revealed the structure and fabrication method of the bead. The central part of the relief was cut from a single piece of wood, rather than assembled from multiple components, underlining the extraordinary manual dexterity of its maker. In addition, a piece of fibrous material contained in the inner structure of the bead is revealed. This may have served as a carrier for an odorous compound, which would be in line with the religious function of the prayer nut.     

Determination of metal ion content of beverages and estimation of target hazard quotients: a comparative study

Background  

Considerable research has been directed towards the roles of metal ions in nutrition with metal ion toxicity attracting particular attention. The aim of this study is to measure the levels of metal ions found in selected beverages (red wine, stout and apple juice) and to determine their potential detrimental effects via calculation of the Target Hazard Quotients (THQ) for 250 mL daily consumption.