An overlapping additive Schwarz preconditioner for interpolation on the unit sphere with spherical radial basis functions

The problem of interpolation of scattered data on the unit sphere has many applications in geodesy and Earth science in which the sphere is taken as a model for the Earth. Spherical radial basis functions provide a convenient tool for constructing the interpolant. However, the underlying linear systems tend to be ill-conditioned. In this paper, we present an additive Schwarz preconditioner for accelerating the solution process. An estimate for the condition number of the preconditioned system will be discussed. Numerical experiments using MAGSAT satellite data will be presented.     

Line intensities of acetylene: New measurements in the 1.5-μm spectral region and global modelling in the ΔP=10 series

Using the Fourier transform spectra of the acetylene molecule recorded near 1.5-μm, the intensities of 111 lines belonging to seven hot bands of the main isotopologue ¹²C₂H₂ have been retrieved by means of a multispectrum fitting procedure. Considering the density of lines in the spectra, and the fact that the measured bands are the weakest observed, the accuracy of the measurements is around 10%. At first stage, an empirical treatment of these data has been performed, leading to the vibrational transition dipole moment squared and some Herman–Wallis coefficients. Then the measured line intensities of this work and collected ones from the literature have been treated simultaneously within the framework of the effective operator approach.     

Higher-order Dirac solitons in binary waveguide arrays

We study optical analogues of higher-order Dirac solitons (HODSs) in binary waveguide arrays. Like higher-order solitons obtained from the well-known nonlinear Schrödinger equation governing the pulse propagation in an optical fiber, these HODSs have amplitude profiles which are numerically shown to be periodic over large propagation distances. At the same time, HODSs possess some unique features. Firstly, the period of a HODS depends on its order parameter. Secondly, the discrete nature in binary waveguide arrays imposes the upper limit on the order parameter of HODSs. Thirdly, the order parameter of HODSs can vary continuously in a certain range.     

THE REACTION OF TERMINAL PHOSPHINIDENE COMPLEXES WITH ELECTRON-RICH ALKYNES: A NEW APPROACH TO THE PHOSPHOLE RING

Abstract

The reaction of electron-rich alkynes such as ethoxyacetylene or propynyldiethylamine with a transient terminal phosphinidene complex such as [PhP?W(CO)₅] directly yields the corresponding phosphole complexes via a formal [2 + 2 + I] cycloaddition involving two molecules of alkyne and one phosphorus center.     

Methyl (E)-2-(2-phenylcyclopropylidene)acetate: Synthesis, isomerization, and reaction with 1,3-diphenyl-2-benzofuran

Treatment of 3-methyl-2-phenylcycloprop-2-ene-1-carboxylic acid with potassium tert-butoxide induced its isomerization into trans-2-methylidene-3-phenylcyclopropane-1-carboxylic acid which was converted into methyl ester, and heating of the latter for 1 h in toluene gave methyl (E)-2-(2-phenylcyclopropylidene)acetate. Thermal isomerization of methyl (E)-2-(2-phenylcyclopropylidene)acetate on prolonged heating in toluene afforded 5-methoxy-3-methyl-2-phenylfuran, and the reaction with 1,3-diphenyl-2-benzofuran resulted in [4 + 2]-cycloaddition at the exocyclic double bond.     

Development and validation of an ELISA kit for the detection of ricin toxins from biological specimens and environmental samples

Ricin is a toxin that can be easily extracted from seeds of Ricinus communis plants. Ricin is considered to be a major bio-threat as it can be freely and easily acquired in large quantities. A deliberate release of such toxin in civilian populations would very likely overwhelm existing public health systems, resulting in public fear and social unrest. There is currently no commercially available or FDA-approved prophylaxis such as vaccines, or therapeutic antitoxins or antidotes, available for ricin intoxication. Patient treatment is typically supportive care based on symptoms, often designed to reinforce the body’s natural response. This paper describes the development and validation of a robust ELISA test kit, which can be used to screen for ricin in biological specimens such as whole blood and faeces. Faecal specimens are shown in this study to have better diagnostic sensitivity and a wider diagnostic window compared to whole blood. From these results, it is concluded that faeces is the most suitable clinical specimen for diagnosis of ricin poisoning via the oral route. The ELISA test kit can also detect ricin in environmental samples. An advantage of this ELISA kit over other commercial off-the-shelf (COTS) detection kits currently on the market that are developed to screen environmental samples only is its ability to diagnose ricin poisoning from clinical specimens as well as detect ricin from environmental samples.     

Performance analysis of cooperative spatial multiplexing networks with AF/DF relaying and linear receiver over Rayleigh fading channels

Cooperative spatial multiplexing (CSM) system has played an important role in wireless networks by offering a substantial improvement in multiplexing gain compared with its cooperative diversity counterpart. However, there is a limited number of research works that consider the performance of CSM systems. As such, in this paper, we have derived exact performance of CSM with amplify‐and‐forward and decode‐and‐forward relays in terms of outage capacity and ergodic capacity. We have shown that CSM systems yield a unity diversity order regardless of the number of antennas at the destination and the number of relays in the networks, which is the direct result of diversity and multiplexing gain trade‐off. Our analytical expressions are corroborated by Monte‐Carlo simulations. Copyright © 2013 John Wiley & Sons, Ltd.