Positive solutions for a system of difference equations with coupled multi-point boundary conditions

We investigate the existence and nonexistence of positive solutions for a system of nonlinear second-order difference equations with parameters subject to coupled multi-point boundary conditions.     

Synthesis of silicalite-1 from organo-silicic gels

Well crystallized silicalite-1 has been obtained from three sources of amorphous silica, namely, rice hull ashes, commercial Davisil, and a fume silica from Aldrich. The silicas were first dissolved in glycerol according to a recently described reaction. This reaction transforms rapidly and efficiently large surface area silicates into poly-alkoxide gels. It can be schematized as an etherification of an alcohol function of glycerol by the weakly acid surface silanol groups. The facile hydrolysis of the alkoxide permits the preparation of relatively pure and reactive silica, keeping the mesoporous character of the parent starting material. We insist on the mesoporous character of the solids obtained upon hydrolyzing the organo-silicic gel because we believe the gel plays a role of template in the secondary synthesis of mesoporous structures. The hydrolysis is carried out in presence of a structure directing agent, namely tetra-propylammonium hydroxide, TPAOH. After aging, the residue is dried and calcined. The first advantage of using the organo-silicic gel is probably related to the high degree of depolymerization of silica, witness by the C/Si ratio. The second one, more subtle to define, is to provide an intermediate silica with hydrophilic a hydrophobic regions, interfering differently with the surfactant. After calcination at 500 degrees C, well crystallized silicalite-1 is obtained. The texture of the starting silica influences the textural characteristics of the final silicalite-1.     

Multiple symmetric positive solutions for a second order boundary value problem

For the second order boundary value problem, , , , where growth conditions are imposed on which yield the existence of at least three symmetric positive solutions.

     

Synthesis and kinetics of polymerization of hydrophilic monomers: 2,3-dihydroxypropylacrylate and 2,3-dihydroxypropylmethacrylate

Unsaturated monomers containing none, one, or two hydroxyl groups were obtained by the reaction of glycerol (1,2,3-trihydroxypropane) with acrylic and methacrylic chloride. The experimental values of the mole fractions of the different monomers were compared with those theoretically obtained by considering different mechanisms involving two or seven kinetic constants. Agreement between the theoretical and experimental results could only be achieved by assuming that the reactivity of the hydroxyl groups changed with the presence of the substituents. The investigation of the radical polymerizations 2,3-dihydroxypropylacrylate (GA) and 2,3-dihydroxypro- pylmethacrylate (GM) was carried out at several temperatures in water–dioxane solutions. Ultraviolet spectroscopic techniques were used to determine the kinetic constants, and the results were compared with those obtained in the same conditions for methyl acrylate, methyl methacrylate, 2-hydroxyethylacrylate, and 2-hydroxyethylmethacrylate. The values of the ratio k_p/k_t^1/2 for the methacrylic monomer GM were higher than 0.5 L^1/2 mol^−1/2 s^−1/2 at temperatures between 50 and 65 °C. These values exceeded 2 L^1/2 mol^−1/2 s^−1/2 for the acrylic monomer GA, perhaps the highest values reported for this kind of monomer. Electron paramagnetic resonance spectroscopy was also used to study the polymerization of GM. All the polymers were soluble in the reaction mixture until very high conversions, and the gel effect was never detected at monomer concentrations equal to or lower than 1 mol L⁻¹. © 2001 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 39: 1843–1853, 2001     

Micellar electrokinetic chromatography method for the determination of sulfamethoxazole, trimethoprim and their main metabolites in human serum

A complete analytical procedure, including sample clean-up and a micellar electrokinetic chromatographic method, is presented for the determination of sulfamethoxazole, trimethoprim, and their main metabolites by using 20 mmol L(-1) borate buffer (pH 9.3), 25 mmol L(-1) sodium dodecylsulfate, and 5% v/v acetonitrile as electrolyte. The separation was carried out at 30 kV and 20 degrees C in a fused silica capillary (60.2 cm x 75 microm inner diameter) fitted with a window in the capillary cartridge of 100 x 800 microm. The detector response was linear from the limit of quantification to 3 mg L(-1) for the individual components. The limits of quantification ranged from 0.13 up to 0.24 mg L(-1). The method was applied to human serum, previously spiked at different concentrations of all the analytes, and recoveries between 95% and 108% were obtained.     

Slow dynamics of thin nematic films in the presence of adsorbed nanoparticles

Recent experiments indicate that liquid crystals can be used to optically report the presence of biomolecules adsorbed at solid surfaces. In this work, numerical simulations are used to investigate the effects of biological molecules, modeled as spherical particles, on the structure and dynamics of nematic ordering. In the absence of adsorbed particles, a nematic in contact with a substrate adopts a uniform orientational order, imposed by the boundary conditions at this surface. It is found that the relaxation to this uniform state is slowed down by the presence of a small number of adsorbed particles. However, beyond a critical concentration of adsorbed particles, the liquid crystal ceases to exhibit uniform orientational order at long times. At this concentration, the domain growth is characterized by a first regime where the average nematic domain size LD obeys the scaling law LDt approximately t1/2; at long times, a slow dynamics regime is attained for which LD tends to a finite value corresponding to a metastable state with a disordered texture. The results of simulations are consistent with experimental observations.     

Improvement of the Solubilization and Extraction of Curcumin in an Edible Ternary Solvent Mixture

A water-free, ternary solvent mixture consisting of a natural deep eutectic solvent (NADES), ethanol, and triacetin was investigated concerning its ability to dissolve and extract curcumin from Curcuma longa L. To this purpose, 11 NADES based on choline chloride, acetylcholine, and proline were screened using UV–vis measurements. A ternary phase diagram with a particularly promising NADES, based on choline chloride and levulinic acid was recorded and the solubility domains of the monophasic region were examined and correlated with the system’s structuring via light scattering experiments. At the optimum composition, close to the critical point, the solubility of curcumin could be enhanced by a factor of >1.5 with respect to acetone. In extraction experiments, conducted at the points of highest solubility and evaluated via HPLC, a total yield of ~84% curcuminoids per rhizome could be reached. Through multiple extraction cycles, reusing the extraction solvent, an enrichment of curcuminoids could be achieved while altering the solution. When counteracting the solvent change, even higher concentrated extracts can be obtained.     

Surface modification in natural fluorapatite after uranyl solution treatment

Natural fluorapatite samples were contacted with uranyl nitrate solutions (from 10⁻² to 10⁻⁶M), adjusted to pH 6.0, then, shaken for times varying between 15 minutes to 72 hours, at room temperature. After that, the solid and liquid phases were separated by centrifugation and the solid was dried at 80°C overnight. The uranium analysis of the solid samples and solutions revealed that uranium was incorporated over fluorapatite. Selected solid samples produced by contacting treatments were analyzed by X-ray diffraction (XRD) and scanning electron microscopy (SEM) techniques. XRD patterns showed the growth of uranyl species in the fluorapatite. Imaging by SEM at 20000x showed the location of uranyl compounds in a crystalline layer in the surface of fluorapatite grains. This layer was well defined for the 10⁻² M of U-contacting solution, but a saturation value was attained at 64% of uranium uptake yield. In the case of 10⁻⁴ M and lower U-contacting solution, the uranium uptake yield was near of 90% after 45 minutes. This fact suggests that natural fluorapatite has excellent properties to immobilize uranium compounds in a solution. Afterwards, the pregnant fluorapatite mineral was regenerated using an alkaline-leaching process. The uranium separated in this way is concentrated and can be handled to a final disposition.     

Cold events in thermal-neutron-induced fission of heavy nuclei

An interpretation of the cold fission events in thermal-neutron-induced fission of heavy nuclei is given. The descent from the saddle point is considered as a dynamical process with reversible coupling between collective and intrinsic degrees of freedom. The distribution function for the collective variables is expressed as a product of two terms: the adiabatical and the dynamical factors. A simple model for symmetric fission to study the mass distribution is presented. As example, the calculations are performed for the nucleus ²⁶⁴Fm. Gross features of the cold fission are discussed as well as the dependence of the theoretical mass distribution on the parameters of the model. Received: 29 April 1998 / Revised version: 11 September 1998