Fixed points and lines in 2-metric spaces

We consider bounded 2-metric spaces satisfying an additional axiom, and show that a contractive mapping has either a fixed point or a fixed line.     

Empirical estimation of the proportional hazard premium for heavy-tailed claim amounts

The asymptotic normality of the sample proportional hazard premium for heavy-tailed claim amounts with infinite variance cannot be obtained by classical results for L-statistics. In this paper, we propose an alternative estimator for this class of premiums and we establish its asymptotic normality.     

Biotreatment on Cellulose Fluff Pulp: Quaternary Ammonium Salts Finish and Grafting with β-cyclodextrin

For its potential performances to be expanded, cellulose needs to be processed in different ways. Therefore, an object of the present work was to provide a chemical modification of cellulose through: a specific finish with two quaternary ammonium salts (namely Aliquat 336 and Aliquat 1529, respectively). Chemical grafting of β-cyclodextrin derivative (β-CD) onto fibers followed by the inclusion of benzoic acid in the grafted CD cavities as a probe chemical. Physicochemical properties and performances of the untreated and treated fibers have been determined with infrared spectra, microscopy, swelling measurements, antimicrobial finishing tests, and dye adsorption. Our results show that cellulose fibers can be efficiently modified with no significant changes in its structural and surface properties; the treated fibers show an attractive behavior in swelling, dye adsorption and antibacterial activity.     

An enhanced immobilization of BSA biomolecule on anionic hydrogels: swelling and adsorption modeling

The three-dimensional structure of hydrogels plays a leading role in several areas of applications. The hydrogels are more and more used as systems of immobilized and controlled release of biomolecules in biotechnology and bio-pharmacy industries. To improve protein adsorption capacity in poly(acrylamide) hydrogels, maleic acid co-monomer was included into the reaction mixture during hydrogel synthesis. So, hydrogels of poly(acrylamide) and its copolymers with diprotic maleic acid were prepared by copolymerization and chemical crosslinking with N,N′-methylene bis-acrylamide. Swelling behavior in distilled water, in physiological saline and in bovine serum albumin (BSA) solutions was studied. Influence of initial BSA concentration on hydrogel swelling and BSA adsorption was investigated. The high amount of maleic acid present in the hydrogels has a significant effect on the swelling behavior and BSA adsorption. Results showed that the pH sensitivity of hydrogels resulted in the high amount of adsorbed BSA. The adsorption isotherms were described by Langmuir and Freundlich models. The thermodynamic parameter (ΔG _ads ⁰ ) was determined for all obtained hydrogels. We demonstrated the favorable character and reversibility of the BSA adsorption process.     

Influence of the solvent on the extraction of copper(II) from nitrate medium using salicylideneaniline

Different solvents including cyclohexane, dichloromethane, chloroform, toluene, 1-octanol, and methyl isobutyl ketone (MIBK) have been evaluated in extracting copper(II) from nitrate medium by salicylideneaniline. Extracted species differs from solvent to solvent: CuL₂ in cyclohexane, toluene, 1-octanol, and methyl isobutyl ketone. However, in dichloromethane or chloroform, there are two complexes of the type CuL₂ and CuL₂(HL). The extraction constants and percentage of extraction (%E) are calculated for different solvents. Solvent played an important role in recovering copper(II) from the aqueous solution, thus affecting the extraction equilibrium and extraction efficiency. The nonpolar solvent showed better performance than the polar solvent. The maximum extraction efficiency was 85.75% at pH?=?4.5, which was from cyclohexane.     

Adsorption isotherms and retention behavior of 1,1'-bis(2-naphthol) on CHIRIS AD1 and CHIRIS AD2 columns

The separation of the atropoisomers of 1,1'-bis(2-naphthol) was studied on CHIRIS AD1 and CHIRIS AD2, two Pirkle-type chiral stationary phases. Satisfactory selectivity was found only on CHIRIS AD2. The ternary mobile phases comprised hexane, dichloromethane and methanol. The effects of their composition and of the temperature on the retention under analytical conditions and on the single-component and competitive isotherms were investigated. The retention of the R- and S-isomers on CHIRIS AD1 and CHIRIS AD2 is controlled by the enthalpic contribution to adsorption, but the effect of the mobile phase on the retention should be attributed mainly to the entropic contribution. The adsorption of the less retained R-isomer is controlled by the achiral interactions, which are the same as for the S-isomer. The single-component and competitive isotherms of the R- and S-isomers are adequately described by the sum of a Langmuir term for the achiral contribution to adsorption and a linear-term characterising the selective or chiral adsorption of the S-isomer in the concentration range experimentally available, i.e. within the solubility limit of 1,1'-bis(2-naphthol).     

XPS analysis of chitosan–hydroxyapatite biomaterials: from elements to compounds

Chitosan (Cs) and hydroxyapatite (Ha) were analysed by X‐ray photoelectron spectroscopy (XPS). Phosphorylated Cs microparticles and hybrid Cs/Ha microparticles were prepared and analysed by XPS before and after immersion in a solution 1.5 times more concentrated than a simulated body fluid (SBF). The accuracy of spectrum recording, peak decomposition and peak component assignment was insured by a post‐control of charge stabilization, and by the examination of correlations between spectral data guided by stoichiometry and charge balance. The concentration of organic oxygen was determined from the concentrations of the oxidized forms of carbon, allowing a sharper insight into speciation and O 1s peak shape. This indicated that the hydroxide ion of Ha, and hydrogenophosphate if present, give a contribution near 532.4 eV, which overlaps with organic oxygen. As a result of immersion in the 1.5*SBF solution, the formation of CaCO₃ and of Ha material occurred. A quantification could be made for the constituents of biomaterial interest, contaminating salts and paraffin oil residues from the microparticle manufacturing process. The uncertainties regarding the nature of the model calcium phosphate used and the best marker for calcium carbonate were addressed by comparing the possible effect on the output, which was facilitated by using ternary composition diagrams. Whatever their formulation, the native microparticles were found to be coated by a thick layer of paraffin oil. The induction of calcium carbonate and phosphate precipitation or the retention of precipitates by the microparticles was favored by the presence of phosphate in the initial formulation either by phosphorylation or by incorporation of Ha. Copyright © 2013 John Wiley & Sons, Ltd.     

Computational study on the encapsulation of ethylparaben into β-cyclodextrin

Two models namely A and B were considered to investigate the inclusion process of ethylparaben into β-CD cavity by means PM3, HF/6-31G (d) and B3LYP/6-31G (d). The obtained results with PM3 method clearly indicate that the formed complexes are energetically favored with or without solvent; the B complex is found more favored than A complex. The calculated deformations energies show that the geometry of β-CD is deformed in the complexation process on the other hand the ethylparaben do not undergo deformation. Finally, From NBO analysis, the donor and acceptor interactions between ethylparaben and β-CD were analyzed and discussed.     

General decay for a coupled Lamé system of nonlinear viscoelastic equations

In this paper, we consider a coupled Lamé system of nonlinear viscoelastic equations with general source terms. Under some suitable conditions on the initial data and the relaxation functions, we prove an asymptotic stability result of global solution taking into account that the kernel is not necessarily decreasing. This work generalizes and improves earlier results in the literature.     

FIXED POINT THEOREMS FOR MAPPINGS SATISFYING IMPLICIT RELATION ON TWO COMPLETE AND COMPACT METRIC SPACES

First, the implicit relations were given. A common fixed point theorem was proved for two mappings satisfying implicit relation functions. A further fixed point theorem was proved for mappings satisfying implicit relation functions on two compact metric spaces.