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.     

Solvent-Polymer Interaction. II. Measurements of Liquid Solvent Molecules Associating with Polymer Sites and of Their Transport Behavior in Polymer Membrane by Thermogravimetry,GLC, and Mass Spectrometry

The measurement of sorption and diffusion behavior of liquid ethanol and water solvent mixtures in polyurethane membrane were made simultaneously by thermogravimetry. The individual amounts of sorbed water and ethanol in the polymer membrane were estimated by thermogravimetry and differentiated by mass spectrometry. In addition, from a single dynamic thermogravimetric experiment the activation energy for solvent molecules desorbing from the polymer membrane was also determined. The thermodynamic activity of ethanol vapor in equilibrium with the ethanol-water-polyurethane system was determined by gas-liquid chromatography. The clustering functions, the mean numbers of solvent molecules in the clusters, and those associating with polymer sites were evaluated by applying simplified mathematical derivatives using the experimentally determined values of activity and volume fraction of solvent molecules. It was found that at lower ethanol concentration the tendency for ethanol molecules to cluster together is high. At higher ethanol activity, ethanol-polymer site interactions predominantly occurred.

Similar results were observed for ethanol-water molecules. However, water molecules in this particular system did not exhibit a self-associating tendency nor interact with the polymer sites. It was concluded that the Zimm-Lundberg clustering theory can be adequately applied to the interpretation of sorption and diffusion behavior of liquid ethanol-water mixtures in the polymer membrane.     

Reinforcement of Natural Rubber from Hydroxyl-Terminated Liquid Natural Rubber Grafted Carbon Black. I. Grafting of Acyl Chloride Capped Liquid Natural Rubber onto Carbon Black

Abstract

This paper deals with the grafting of acyl chloride capped liquid natural rubber (LNR–COCl) onto carbon black by the reaction of the acyl chloride group with the phenolic hydroxyl group on the surface. LNR–COCl was prepared by the reaction of hydroxyl-terminated liquid natural rubber (HTNR) with adipoyl dichloride. The percentage of grafting was estimated to be 18–21% depending on the grafting temperature and the molecular weight of HTNR used. It increased with an increase in the molecular weight of LNR–COCl. The LNR grafted onto carbon black was investigated by IR spectroscopy and by hydrolysis with a dilute THF solution of KOH. It was shown that LNR grafted onto the carbon black surface with ester bonds.     

Dimerisation and complexation of 6-(4′-t-butylphenylamino)naphthalene-2-sulphonate by β-cyclodextrin and linked β-cyclodextrin dimers

This study shows that stereochemical factors largely determine the extent to which 6-(4′-t-butylphenylamino)-naphthalene-2-sulphonate, BNS^?  and its dimer, (BNS^? )₂, are complexed by β-cyclodextrin, βCD, and a range of linked βCD dimers. Fluorescence and ¹H NMR studies, respectively, show that BNS^?  and (BNS^? )₂ form host–guest complexes with βCD of the stoichiometry βCD.BNS^?  (10^? 4 K ₁ = 4.67 dm³ mol^? 1) and βCD.BNS₂ ^2 ?  (10^? 2 K ₂′ = 2.31 dm³ mol^? 1), where the complexation constant K ₁ = [βCD.BNS^? ]/([βCD][BNS^? ]) and K ₂′ = [βCD. (BNS^? )₂]/([βCD.BNS^? ][BNS^? ]) in aqueous phosphate buffer at pH 7.0, I = 0.10 mol dm³ at 298.2 K. (The dimerisation of BNS^?  is characterised by 10^? 2 K _d = 2.65 dm³ mol^? 1.) For N,N-bis((2^AS,3^AS)-3^A-deoxy-3^A-β-cyclodextrin)succinamide, 33βCD₂su, N-((2^AS,3^AS)-3^A-deoxy-3^A-β-cyclodextrin)-N′-(6^A-deoxy-6^A-β-cyclodextrin)urea, 36βCD₂su, N,N-bis(6^A-deoxy-6^A-β-cyclodextrin)succinamide, 66βCD₂su, N-((2^AS,3^AS)-3^A-deoxy-3^A-β-cyclodextrin)-N′-(6^A-deoxy-6^A-β-cyclodextrin)urea, 36βCD₂ur, and N,N-bis(6^A-deoxy-6^A-β-cyclodextrin)urea, 66βCD₂ur, the analogous 10^? 4 K ₁ = 11.0, 101, 330, 29.6 and 435 dm³ mol^? 1 and 10^? 2 K ₂′ = 2.56, 2.31, 2.59, 1.82 and 1.72 dm³ mol^? 1, respectively. A similar variation occurs in K ₁ derived by UV–vis methods. The factors causing the variations in K ₁ and K ₂ are discussed in conjunction with ¹H ROESY NMR and molecular modelling studies.     

Photophysics of Silicon Phthalocyanines in Aqueous Media

Phthalocyanines have been used as photodynamic therapy (PDT) agents because of their uniquely favorable optical properties and high photostability. They have been shown to be highly successful for the treatment of cancer through efficient singlet‐oxygen (¹O₂) production. However, due to their hydrophobic properties, the considerations of solubility and cellular location have made understanding their photophysics in vitro and in vivo difficult. Indeed, many quantitative assessments of PDT reagents are undertaken in purely organic solvents, presenting challenges for interpreting observations during practical application in vivo. With steady‐state and time‐resolved laser spectroscopy, we show that for axial ligated silicon phthalocyanines in aqueous media, both the water:lipophile ratio and the pH have drastic effects on their photophysics, and ultimately dictate their functionality as PDT drugs. We suggest that considering the presented photophysics for PDT drugs in aqueous solutions leads to guidelines for a next generation of even more potent PDT agents.     

A convenient and sensitive method for haloacetic acid analysis in tap water by on‐line field‐amplified sample‐stacking CE–ESI‐MS

In this study, we propose a simple strategy based on flow injection and field‐amplified sample‐stacking CE–ESI‐MS/MS to analyze haloacetic acids (HAAs) in tap water. Tap water was passed through a desalination cartridge before field‐amplified sample‐stacking CE–ESI‐MS/MS analysis to reduce sample salinity. With this treatment, the signals of the HAAs increased 300‐ to 1400‐fold. The LODs for tap water analysis were in the range of 10 to 100 ng/L, except for the LOD of monochloroacetic acid (1 μg/L in selected‐ion monitoring mode detection). The proposed method is fast, convenient, and sensitive enough to perform on‐line analysis of five HAAs in the tap water of Taipei City. Four HAAs, including trichloroacetic acid, dichloroacetic acid, dibromoacetic acid, and monobromoacetic acid, were detected at concentrations of approximately 1.74, 1.15, 0.16, and 0.15 ppb, respectively.