Numerical solution of a singularly perturbed problem via exponential splines

It is proved that a spline difference scheme for a singularly perturbed self-adjoint problem, derived by using exponential cubic splines at mid-points, has second order uniform convergence in a small parameter . Numerical experiments are presented to confirm the theoretical predictions.     

Carbon-bromine cleavage by dimethyl sulfoxide: the key step of C(5) functionalization of push-pull 2-alkylidene-4-oxothiazolidine vinyl bromides

Push-pull 2-alkylidene-4-oxothiazolidine vinyl bromides undergo efficient C(5) functionalization through DMSO-assisted carbon-bromine cleavage, followed by a bromine transfer-substitution (or elimination) sequence. A mechanism for this novel transformation is proposed.     

An Efficient Route to Phenylselenoethers in the Presence of Ag2O

An efficient protocol for the preparation of phenylselenoethers from unsaturated alcohols using phenylselenenyl halides at room temperature was developed. The procedure employs phenylselenenyl chloride and bromide, some Δ ⁴- and Δ ⁵-alkenols and Ag₂O, as an additive, to generate the tetrahydropyrans or tetrahydrofurans. This method permits the preparation of cyclic phenylselenoethers in high yields and under extremely mild conditions.     

Precipitation and recrystallization of uniform CuCl particles formed by aggregation of nanosize precursors

Uniform, spherical CuCl particles were obtained by mixing aqueous solutions of CuCl ₂ and ascorbic acid in the presence of polyvinylpyrrolidone (PVP) as dispersing agent. The size and the uniformity of the resulting particles depended on the volume ratio of the reactant solutions, their concentrations, the distribution of the stabilizers, and the mixing method. The single jet precipitation yielded large spheres of broad size distributions, while the particles obtained by the double jet technique were rather uniform in size. The final colloidal CuCl particles were formed by the aggregation of nanocrystals, initially generated in the system. Depending on the pH of the reaction mixture, these particles slowly change to large CuCl crystals on aging in the mother liquor.     

Spectrophotometric method for the determination of demeclocycline using sodium molybdate as analytical reagent

By means of spectroscopic methods it has been found that demeclocycline reacts with molybdate ions forming a complex compound [MoO₃HDMTC]^2–. The relative stability constant of this compound has been determined by applying spectrophotometric methods. Under optimum conditions for complex formation a very sensitive spectrophotometric method for the estimation of demeclocycline in the concentration range 5.0–35.1 g/ml is proposed. The detection limit of the method is 2.5 g/ml of demeclocycline. The relative standard deviation (n=10) varies between 0.76% and 1.46%. The method proved to be accurate and sensitive for the analysis of the demeclocycline content in tablets.     

A simple adsorptive chronopotentiometric stripping method for determination of vitamin B 1 in pharmaceutical products

A new electroanalytical method for vitamin B1 determination, based on adsorptive chronopotentiometric stripping analysis and non-specific adsorption onto mercury film electrode, was developed and validated. Stripping chronopotentiograms showed a single well-defined oxidation wave corresponding to vitamin B1 at about − 0.43 V in citrate buffer pH 6.0. The most important experimental factors affecting the monitored electroanalytical response of vitamin B1 were investigated and optimised. Under the optimal experimental conditions, linear response of vitamin B1 was obtained in the concentration range of 5–50 mg dm−3, with the achieved limit of detection of 1.64 mg dm−3, and the limit of quantitation of 4.97 mg dm−3. A mean recovery of 97.1% and relative standard deviations of 3.75% were achieved. The developed electrochemical procedure was successfully applied for the determination of vitamin B1 in pharmaceutical products. The results of the proposed method were in good agreement with those obtained by parallel HPLC analyses, confirming an accuracy of the developed method.     

An expansion formula for fractional derivatives of variable order

In this work we extend our previous results and derive an expansion formula for fractional derivatives of variable order. The formula is used to determine fractional derivatives of variable order of two elementary functions. Also we propose a constitutive equation describing a solidifying material and determine the corresponding stress relaxation function.