Group analysis and exact solutions of a class of variable coefficient nonlinear telegraph equations

A complete group classification of a class of variable coefficient (1+1)-dimensional telegraph equations $f(x)u_{tt}=(H(u)u_x)_x+K(u)u_x$, is given, by using a compatibility method and additional equivalence transformations. A number of new interesting nonlinear invariant models which have non-trivial invariance algebras are obtained. Furthermore, the possible additional equivalence transformations between equations from the class under consideration are investigated. Exact solutions of special forms of these equations are also constructed via classical Lie method and generalized conditional transformations. Local conservation laws with characteristics of order 0 of the class under consideration are classified with respect to the group of equivalence transformations.Comment: 23 page

New results on group classification of nonlinear diffusion-convection equations

Using a new method and additional (conditional and partial) equivalence transformations, we performed group classification in a class of variable coefficient $(1+1)$-dimensional nonlinear diffusion-convection equations of the general form $f(x)u_t=(D(u)u_x)_x+K(u)u_x.$ We obtain new interesting cases of such equations with the density $f$ localized in space, which have large invariance algebra. Exact solutions of these equations are constructed. We also consider the problem of investigation of the possible local trasformations for an arbitrary pair of equations from the class under consideration, i.e. of describing all the possible partial equivalence transformations in this class.Comment: LaTeX2e, 19 page

Reduction Operators of Linear Second-Order Parabolic Equations

The reduction operators, i.e., the operators of nonclassical (conditional) symmetry, of (1+1)-dimensional second order linear parabolic partial differential equations and all the possible reductions of these equations to ordinary differential ones are exhaustively described. This problem proves to be equivalent, in some sense, to solving the initial equations. The ``no-go'' result is extended to the investigation of point transformations (admissible transformations, equivalence transformations, Lie symmetries) and Lie reductions of the determining equations for the nonclassical symmetries. Transformations linearizing the determining equations are obtained in the general case and under different additional constraints. A nontrivial example illustrating applications of reduction operators to finding exact solutions of equations from the class under consideration is presented. An observed connection between reduction operators and Darboux transformations is discussed.Comment: 31 pages, minor misprints are correcte

Autler - Townes doublet probed by strong field

This paper deals with the Autler - Townes doublet structure. Applied driving and probing laser fields can have arbitrary intensities. The explanation is given of the broadening of doublet components with the growth of probing field intensity, which was observed in experiment. The effects of Doppler averaging are discussed.Comment: 12 pages, RevTeX, 5 figures in 9 file

Singular reduction operators in two dimensions

The notion of singular reduction operators, i.e., of singular operators of nonclassical (conditional) symmetry, of partial differential equations in two independent variables is introduced. All possible reductions of these equations to first-order ODEs are are exhaustively described. As examples, properties of singular reduction operators of (1+1)-dimensional evolution and wave equations are studied. It is shown how to favourably enhance the derivation of nonclassical symmetries for this class by an in-depth prior study of the corresponding singular vector fields.Comment: 22 pages, minor correction

Analysis of Pharmacokinetic Parameters of Acetylsalicylic Acid for Prediction of Potential Nephrotoxic Effects

Nonsteroidal anti-inflammatory drugs, including acetylsalicylic acid, can have a dose-dependent nephrotoxic effect. The study of the pharmacokinetics of acetylsalicylic acid products will contribute to timely detection and correction of side effects caused by this medicinal product.The aim of the study was to evaluate potential nephrotoxic effects following a single oral administration of 75 mg of acetylsalicylic acid, based on the analysis of the pharmacokinetic parameters.Materials and methods: the study involved 24 healthy volunteers who received 75 mg of acetylsalicylic acid (tablets) once orally. The measurement of the active metabolite of acetylsalicylic acid—salicylic acid—in blood plasma was performed by HPLC/MS using an Agilent 1200 liquid chromatography system coupled to an Agilent 6140 tandem mass spectrometer. Agilent Eclipse XDB-C18 column (4.6 mm×150 mm; 5.0 μm) was used for chromatographic separation. The test procedure used in the study was validated. The results obtained were used to calculate the pharmacokinetic parameters: Cmax (maximum concentration), Tmax (time to maximum concentration), T1/2 (half-life of the drug), AUC0-t (area under the pharmacokinetic curve from 0 to the last time point of the curve), AUC0-∞ (total area under the pharmacokinetic curve from 0 to ∞), MRT (mean residence time of the drug in the blood), Kel (elimination rate constant), Cl/F (total clearance), Vd/F (apparent volume of distribution). The Statistics (22.0.0.0) software was used for statistical processing of the results.Results: T1/2 of salicylic acid in blood plasma was determined to be 1.6 ± 0.5 h, Cmax was 4523.0 ± 725.0 ng/mL, and Tmax was 0.98 ± 0.4 h. AUC0–t was equal to 16183.0 ± 3823.0 ng×h/m, Vd/F was 12.0 ± 3.1 L/kg, and MRT was 2.9 ± 0.6 h.Conclusions: the analysis of the pharmacokinetic parameters demonstrated a high absorption rate, intensive distribution, and moderate elimination rate of salicylic acid (the main metabolite of acetylsalicylic acid), indicating a low risk of nephrotoxic effects associated with the studied dose of the drug

Approaches to Pharmaceutical Analysis of Modern Peptide and Oligonucleotide Products as Illustrated by a Small Interfering RNA-Based Novel Therapeutic for the Treatment of Bronchial Asthma

Methods used to control the quality of peptide products depend on the level of development of analytical and bioorganic chemistry, and the level of instrumentation. Peptide identification is a difficult task and largely depends on the complexity of its structure. There does not exist a comprehensive and simple test, except for NMR, which, however, is rather expensive and time-consuming and involves complex data interpretations. Moreover, it does not allow for unambiguous determination of the peptide purity and formula (amino acid composition, sequence, chirality of amino acid residues). For this reason, a combination of methods is often used, including amino acid analysis, TLC/HPLC and mass spectrometry, and, less frequently, sequencing. Current international practice of peptide analysis is to use HPLC in combination with mass spectrometric, mainly tandem (HPLC-MS/MS), detection. According to literature sources the amino acid sequence of linear peptides can be analysed using various enzymes and subsequent identification of proteolysis products by mass spectrometry. This article presents approaches to the development of test methods for analysis of purity and identification testing of a small interfering RNA-based novel medicinal product, which will help standardise and control the quality of the production process

Digital receivers for low-frequency radio telescopes UTR-2, URAN, GURT

This paper describes digital radio astronomical receivers used for decameter and meter wavelength observations. This paper describes digital radio astronomical receivers used for decameter and meter wavelength observations. Since 1998, digital receivers performing on-the-fly dynamic spectrum calculations or waveform data recording without data loss have been used at the UTR-2 radio telescope, the URAN VLBI system, and the GURT new generation radio telescope. Here we detail these receivers developed for operation in the strong interference environment that prevails in the decameter wavelength range. Data collected with these receivers allowed us to discover numerous radio astronomical objects and phenomena at low frequencies, a summary of which is also presented.Comment: 24 pages, 15 figure

Comparative Dissolution Kinetics of Several Multisource Thioctic Acid Products

The relationship between dissolution and bioavailability is an example of the interdependency between the quality of a medicinal product and its safety and efficacy. The uniqueness of thioctic acid is that it can exist in an oxidised and a reduced form, showing lipophilic (lipoic acid) and hydrophilic (dihydrolipoic acid) properties. Bioavailability studies of thioctic acid are necessary to evaluate the expected therapeutic effect and mitigate side effects of the medicinal product.The aim of the study was to carry out equivalence dissolution testing to compare the release of thioctic acid from medicinal products produced by several manufacturers.Materials and methods: the study used a reference medicinal product and three multisource medicinal products by different manufacturers; more specifically, film-coated tablets containing 600 mg of thioctic acid. The experiment was carried out in dissolution media at pH of 6.8±0.05 and 1.2±0.05. Statistical analysis was performed by calculating the average amounts of the substance dissolved, the standard deviation (SD), and the relative standard deviation (RSD, %) using Microsoft Office Excel 2007.Results: The authors chose the testing conditions (dissolution media pH values of 6.8±0.05 and 1.2±0.05) taking into account the nature and characteristics of thioctic acid. The comparison of thioctic acid release profiles based on the calculation of the similarity factor (f2) showed that the dissolution profiles of multisource medicinal products 2 and 3 at pH 6.8 were equivalent to that of the reference medicinal product (more than 85% of the active pharmaceutical ingredient released within 15 minutes) and the dissolution profile of multisource medicinal product 1 was not equivalent to it (with f2 of 28).Conclusions: the established differences in the rate and degree of active ingredient release from the studied medicinal products may indicate possible differences in their pharmacological effectiveness in vivo

Group Analysis of Variable Coefficient Diffusion-Convection Equations. I. Enhanced Group Classification

We discuss the classical statement of group classification problem and some its extensions in the general case. After that, we carry out the complete extended group classification for a class of (1+1)-dimensional nonlinear diffusion--convection equations with coefficients depending on the space variable. At first, we construct the usual equivalence group and the extended one including transformations which are nonlocal with respect to arbitrary elements. The extended equivalence group has interesting structure since it contains a non-trivial subgroup of non-local gauge equivalence transformations. The complete group classification of the class under consideration is carried out with respect to the extended equivalence group and with respect to the set of all point transformations. Usage of extended equivalence and correct choice of gauges of arbitrary elements play the major role for simple and clear formulation of the final results. The set of admissible transformations of this class is preliminary investigated.Comment: 25 page