Collocation Methods for Weakly Singular Second-kind Volterra Integral Equations with Non-smooth Solution

Collocation type methods are studied for the numerical solutionof the weakly singular Volterra integral equation of the secondkind: where the solution (t) is assumedto have the form f(t) = x(t)+r^?(t), x and being sufficientlysmooth. The solution is approximated near zero by a linear combinationof powers of t?, and away from zero by the usual polynomialrepresentation. Convergence is proved and many numerical experimentsare carried out with examples from the literature. A comparisonis made with a method of Brunner & Norsett (1981), originallydeveloped for (1) with a smooth solution. Special attentionis paid to the numerical approximation of the so-called momentintegrals which emerge in the collocation scheme.     

无机酸洗脱对胜利褐煤微晶结构及其自燃倾向性的影响

利用XRD、Raman、XPS和FT-IR表征技术,研究无机酸洗脱(HCl、H2SO4、HCl-HF)处理的胜利褐煤微晶结构的变化,采用自行设计的表面吸附仪-GC联用装置,对样品进行不同温度的低温脉冲氧化实验,考察了煤样在不同温度下氧吸附量的变化规律,通过低温脉冲氧吸附规律与TG/DTG和固定床燃烧实验关联,考察了煤样的自燃倾向。结果表明,无机酸洗脱对矿物质的脱除使得煤结构的有序度增加,石墨化程度提高,无机酸洗脱煤样与原煤相比吸氧量明显下降。随着吸附温度的升高,各煤样吸氧量明显增加,且随着脱除矿物质程度的增加,吸氧量呈减小的趋势,导致自燃倾向降低。     

An approximate treatment of scattering based on the delta boundary operator

The development of a scheme to treat two-dimensional electromagneticscattering by electrically large, perfectly conducting bodiesis described. It incorporates the effects of surface curvatureand non-local phenomena and has the potential to provide thebasis for a general technique yielding more accurate predictionsthan the widely used physical optics method.     

Characterization of fluorocarbon-in-water emulsions with added triglyceride

Fluorocarbon-in-water emulsions are being explored clinically as synthetic oxygen carriers in general surgery. Stabilizing fluorocarbon emulsions against coarsening is critical in maintaining the biocompatibility of the formulation following intravenous administration. It has been purported that the addition of a small percentage of long-chain triglyceride results in stabilization of fluorocarbon emulsions via formation of a three-phase emulsion. In a three-phase emulsion, the triglyceride forms a layer around the dispersed fluorocarbon, thereby improving the adhesion of the phospholipid surfactant to the dispersed phase. In the present study, we examined the effect of triglyceride addition on the physicochemical characteristics of the resulting complex dispersion. In particular, we examined the particle composition and stability of the dispersed particles using a method which first fractionates (classifies) the different particles prior to sizing (i.e., sedimentation field-flow fractionation). It was determined that the addition of a long-chain triglyceride (soybean oil) results in oil demixing and two distinct populations of emulsion droplets. The presence of the two types of emulsion droplets is not observed via light scattering techniques, since the triglyceride droplets dominate the scattering due to a large difference in the refractive index between the particles and the medium as compared to fluorocarbon droplets. The growth of the fractionated fluorocarbon emulsion droplets was followed over time, and it was found that there was no difference in growth rates with and without added triglyceride. In contrast, addition of medium-chain-triglyceride (MCT) oils results in a single population of emulsion droplets (i.e., a three-phase emulsion). These emulsions are not stable to droplet coalescence, however, as significant penetration of MCT into the phospholipid lipid interfacial layer results in a negative increment in the monolayer spontaneous curvature, thereby favoring water-in-oil emulsions and resulting in destabilization of the emulsion to the effects of terminal heat sterilization or mechanical stress.     

Structure-property relationships for carbochain fluoropolymers

Polyvinyl fluoride (PVF), polyvinylidene fluoride (PVDF) and polychlorotrifluoroethylene (PCTFE) were studied by differential calorimetry at normal pressure in the temperature interval 130–555 K, and by pressure dilatometry in the temperature interval 303–545 K and in the pressure range 14–70 MPa. Pressure derivatives of the melting temperature,dT _m/dP, were used to calculate the true melting entropy S _m from the Clausius-Clapeyron equation, while equilibrium values of the melt specific volume were treated according to the Simha-Somcynsky cell theory. Comparison of the experimental data for PVF, PVDF and PCTFE with pertinent published data for polyethylene (PE) and polytetrafluoroethylene (PTFE) showed that a steady decrease of S _m and of the conformational contribution to S _m reflects the increase of the equilibrium chain stiffness as the hydrogen atoms of the hydrocarbon chain (PE) are substituted with bulkier fluorine and/or chlorine atoms (PCTFE, PTFE), while a concomitant drop of the pressure reducing parameter from the cell model and an increase of melt compressibility and the derivative,dT _m/dP, should be attributed to the increase of the free volume fraction of the melt in the series, PE to PTFE.     

A 14 Parameter Study of UHPLC’s for Method Development Transfer and Troubleshooting

Five ultra-high pressure liquid chromatography (UHPLC) instruments were compared to one another by examining the overall system performance and key functions of the system parts including: pump, auto-sampler, thermo-stated column compartment, and the detector. The five UHPLC systems used in this study were: ThermoFisher Vanquish, Agilent 1290 Infinity I, Agilent 1290 Infinity II, Waters Acquity I-Class, and Shimadzu Nexera X2. The identities of the systems were blinded in the results and discussion section to use this study for scientific purposes only rather than for competition and marketing. The following tests were performed to evaluate and compare the five UHPLC systems: injector linearity and precision, sample carryover, sample (autosampler) temperature accuracy, column temperature accuracy and precision, pressure ripple, pump mixing accuracy, flow rate accuracy, detector drift and noise, detector linearity, wavelength accuracy, extra-column volume, and dwell volume determination. This study presents an approach on how to test the performance of UHPLC systems along with potential problems that analysts may face when using the UHPLC systems, examples of such issues are: retention time irreproducibility, low sensitivity, method transfer failure, etc.