Numerical estimation of the piecewise constant Robin coefficient by identifying its discontinuous points

We propose a new numerical method for estimating the piecewise constant Robin coefficient in two-dimensional elliptic equation from boundary measurements. The Robin inverse problem is recast into a minimization of an output least-square formulation. A technique based on determining the discontinuous points of the unknown coefficient is suggested, and we investigate the differentiability of the solution and the objective functional with respect to the discontinuous points. Then we apply the Gauss-Newton method for reconstructing the shape of the unknown Robin coefficient. Numerical examples illustrate its efficiency and stability.     

一个新的指数削减椭圆形分布族

A new family of univariate exponential slash distribution is introduced, which is based on elliptical distributions and defined by means of a stochastic representation as the scale mixture of an elliptically distributed random variable with respect to the power of an exponential random variable. The same idea is extended to the multivariate case. General properties of the resulting families, including their moments and kurtosis coefficient, are studied. And inferences based on methods of moment and maximum likelihood are discussed. A real data is presented to show this family is flexible and fits much better than other related families.     

由从属关系定义的亚纯多叶函数的子类的某些性质

In the present paper, we introduce some new subclasses of meromorphic starlike,convex, close-to-convex and quasi-convex functions of β-reciprocal in terms of the linear operator using subordination. We obtain the coefficient estimates, convolution properties, integral preserving properties and inclusion relationships of the classes. The results presented here include several results as their special cases.     

Effect of Chain Length of Polyethylene Glycol and Crosslink Density (NCO/OH) on Properties of Castor Oil Based Polyurethane Elastomers

The equilibrium swelling study of polyurethanes (PU) was carried out in various solvents in order to calculate their solubility parameter. The kinetics of swelling and sorption have also been studied in 1,4‐dioxane at 30°C. The PU was synthesized by reacting a novel polyol (castor oil derivative and epoxy based resin, EpxR) and one of the polyethylene glycols (PEG 200, PEG 400, PEG 600) with different weight compositions, with a toluene diisocyanate (TDI) adduct (derived from toluene diisocyanate and R60 polyol). Different NCO/OH ratio viz. 1, 1.3 and 1.7 were employed in the study. The results were found to vary with the weight composition of polyol components, as well as the crosslink density of the samples. The sorption behavior is also found to vary with the molecular weight of polyethylene glycol employed in the preparations of the polyurethanes. Kinetic studies of swelling revealed that the sorption is anomalous in nature. The diffusion coefficient (D) increased with an increase in the NCO/OH ratio and decreased with an increase in chain length of polyethylene glycol. The sorption coefficient (S) decreased with an increase in crosslink density (NCO/OH) and increased with increasing polyethylene glycol (i.e., PEG 200, PEG 400, and PEG 600) moieties in the polyurethanes. The molecular weight between two crosslink points was calculated using the Flory Rehner equation (24), and hence, the number of chains per unit volume (N) and degree of crosslinking (ν) in all the samples were determined.     

Kinetic Study of Radical Polymerization VIII. A Comprehensive Study of Solution Copolymerization of Vinyl Acetate and Methyl Acrylate by 1H‐NMR Spectroscopy

Radical copolymerization reaction of vinyl acetate (VA) and methyl acrylate (MA) was performed in a solution of benzene‐d₆ using benzoyl peroxide (BPO) as the initiator at 60°C. Kinetic studies of this copolymerization reaction were investigated by on‐line ¹H‐NMR spectroscopy. Individual monomer conversions vs. reaction time, which was followed by this technique, were used to calculate the overall monomer conversion, as well as the monomer mixture and the copolymer compositions as a function of time. Monomer reactivity ratios were calculated by various linear and nonlinear terminal models and also by simplified penultimate model with r _2(VA)=0 at low and medium/high conversions. Overall rate coefficient of copolymerization was calculated from the overall monomer conversion vs. time data and k _p  . k _t ^?0.5 was then estimated. It was observed that k _p  . k _t ^?0.5 increases with increasing the mole fraction of MA in the initial feed, indicating the increase in the polymerization rate with increasing MA concentration in the initial monomer mixture. The effect of mole fraction of MA in the initial monomer mixture on the drifts in the monomer mixture and copolymer compositions with reaction progress was also evaluated experimentally and theoretically.     

Quantitative Relationships of Structure-Activity and Volume Fraction For Selected Nonpolar and Polar Narcotic Chemicals

Abstract

The relative toxicity of selected industrial organic chemicals was secured from the literature for the static 48-h Tetrahymena pyriformis 50% population growth impairment and the flow-through 96-h Pimephales promelas 50% mortality endpoints. Chemicals were selected to represent the nonpolar narcosis (aliphatic alcohols and aliphatic ketones) and polar narcosis (anilines and phenols) mechanisms of toxic action. molar volume (MV) and 1-octanol/water partition coefficient (log K _ow) data were generated for each chemical. High-quality, log K _ow dependent quantitative structure-activity relationships were observed for each chemical class and mechanism of action for both endpoints. The volume fraction (V _t) for each chemical in the target phase was determined from the toxicant concentration in the water (toxicity data), the MV, and the target/water partition coefficient (K _tw) with K _tw considered equal to K _ow ^(1-a). Analyses of target sites, by way of “a” revealed that “a” was constant for a mechanism of action regardless of chemical class, but distinct for a given test system. Mean V _t was constant for each mechanism of action regardless of chemical class or test system. These results suggest, at least for reversible physical mechanisms, that volume fraction analyses are significant in determining the mechanism of toxic action of a chemical.     

QSAR-based toxicity classification and prediction for single and mixed aromatic compounds

Quantitative structure-activity relationships (QSARs) based on the octanol/water partition coefficient were employed to predict acute toxicities of 36 substituted aromatic compounds and their mixtures. In this study, the model developed by Verhaar et al. was modified and used to calculate octanol/water partition coefficients of chemical mixtures. To validate the model, acute toxicities of these chemicals were measured to Vibrio fischeri in terms of EC⁵⁰. The results indicated that the obtained QSAR models could be used to predict toxicities of samples consisting of these substituted aromatic compounds, individually or in combinations. The obtained equations were proved to be robust enough by using the leave-one-out test method. By classifying these chemicals into two groups, polar and non-polar, the toxicities of chemical mixtures within each group can be predicted accurately from their calculated partition coefficients.