Schur complement‐based domain decomposition preconditioners with low‐rank corrections

This paper introduces a robust preconditioner for general sparse matrices based on low‐rank approximations of the Schur complement in a Domain Decomposition framework. In this ‘Schur Low Rank’ preconditioning approach, the coefficient matrix is first decoupled by a graph partitioner, and then a low‐rank correction is exploited to compute an approximate inverse of the Schur complement associated with the interface unknowns. The method avoids explicit formation of the Schur complement. We show the feasibility of this strategy for a model problem and conduct a detailed spectral analysis for the relation between the low‐rank correction and the quality of the preconditioner. We first introduce the SLR preconditioner for symmetric positive definite matrices and symmetric indefinite matrices if the interface matrices are symmetric positive definite. Extensions to general symmetric indefinite matrices as well as to nonsymmetric matrices are also discussed. Numerical experiments on general matrices illustrate the robustness and efficiency of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd.     

Global existence and uniform stability of solutions for a quasilinear viscoelastic problem

In this paper the nonlinear viscoelastic wave equation in canonical form with Dirichlet boundary condition is considered. By introducing a new functional and using the potential well method, we show that the damping induced by the viscoelastic term is enough to ensure global existence and uniform decay of solutions provided that the initial data are in some stable set. Copyright © 2006 John Wiley & Sons, Ltd.     

Investigation of the structural directing effect of (2-hydroxyethyl)trimethylammonium on distribution of the silicate anions using 29Si NMR spectroscopy

The effect of (2-hydroxyethyl)trimethylammonium (2-HETMA) cation on the equilibrium of silicate oligomers in aqueous alkaline silicate solutions was investigated using (29)Si NMR spectra. The results indicate role of structural directing of 2-HETMA in which it particularly directs the silicate species to the Q(4)(1)Q(4)(3)Q(4)(4) silicate anion. Results reveal that composition of the alcohols in solution affect the distribution of anionic species. The effect of methanol concentration is also discussed.     

The First Mitsunobu Protocol for Efficient Synthesis of α-Acyloxyphosphonates Using 4,4′-Azopyridine

Abstract

This is the first report on applying the Mitsunobu protocol for the synthesis of various α-acyloxyphosphonates using 4,4′-azopyridine and PPh₃ with diverse aromatic and aliphatic carboxylic acids. Under these conditions, diethyl azodicarboxylate (DEAD) as the traditional reagent for Mitsunobu reaction is not efficient. The insoluble pyridine hydrazine byproduct can be simply isolated and recycled to its azopyridine by an oxidation reaction and reused again.

[Supplemental materials are available for this article. Go to the publisher's online edition of Phosphorus, Sulfur, and Silicon and the Related Elements for the following free supplemental resource: Characterization data of compounds 3a–3z2 and NMR spectra.]

GRAPHICAL ABSTRACT      

Demulsification Efficiency of Some New Demulsifiers Based on 1,3,5-Triethanolhexahydro-1,3,5-triazine

This study mainly concentrates on the synthesis of three novel demulsifiers and the investigation of their demulsification efficiency. The demulsifiers were derived from 1,3,5-triethanolhexahydro-1,3,5-triazine, which was prepared by the reaction of monoethanol amine with formaldehyde. The 1,3,5-triethanolhexahydro-1,3,5-triazine was ethoxylated by introducing 20 units of ethylene oxide and then esterified at different molar ratios with oleic acid (1, 2, and 3) to give three demulsifiers, namely, E₂₀TO, E₂₀TO₂, and E₂₀TO₃. The chemical structures of the prepared demulsifiers were confirmed by ¹H NMR and FTIR spectrum. The demulsification efficiency of these demulsifiers was tested on the natural water-in-oil (w/o) emulsions (50% water content). From the obtained results, it has been found that the investigated demulsifiers have a great potential to break the w/o emulsions. The trioleat ester (E₂₀TO₃) exhibited the maximum demulsification efficiency (96%) after 120 minutes at 55°C.     

Effect of orientation of lateral methyl substituent on the thermal behaviour of the mesophase in binary systems of 4-substituted phenyl 4ʹ-(4”-alkoxy phenylazo) benzoates

Several binary systems made from two laterally substituted azo/ester isomers, namely 2?- (and 3?-) methyl-4-substituted phenyl 4?-(4?-alkoxyphenylazo) benzoates, where the length of the terminal alkoxy group = 8 and 16 carbons, while the other terminal substituent, X, varies between CH₃O, CH₃, H, Br and CN groups, were investigated using differential scanning calorimetry (DSC) and phases identified by polarised light microscope (PLM). For the sake of comparison, two another binary systems made from 2?- (or 3?-) methyl-4-substituted phenyl 4?-(4?-alkoxyphenylazo) benzoates (n = 8 and X = CH₃) each was mixed with its laterally neat analogue and similarly investigated. Results were discussed on the basis of constructed phase diagrams whereby various mesomorphic properties were observed dependent on X, n, and position of the lateral methyl group. In most of the cases, the mixtures exhibited eutectic compositions, while linear or nearly linear nematic and smectic A-composition temperature dependence were observed.     

Comparative High-Performance Liquid Chromatographic and High-Performance Thin-Layer Chromatographic Study for the Simultaneous Determination of Dapagliflozin and Metformin Hydrochloride in Bulk and Pharmaceutical Formulation

JPC – Journal of Planar Chromatography – Modern TLC - The discovery of potent antidiabetic drugs is of necessity owing to the rapid prevalence of diabetes worldwide. The investigation...