Horizon Formation in High-Energy Particles Collision

We investigate a classical formation of a trapped surface in 4-dimensional flat space-time in a process of a non-head-on collision of two high-energy particles which are treated as Aichelburg-Sexl shock waves. From the condition of the horizon volume local maximality an equation for the trapped surface is deduced. Using a known solution on the shocks we find a time-dependent solution describing the trapped surface between the shocks. We analyze the horizon appearance and evolution. Obtained results may describe qualitatively the horizon formation in higher dimensional space-time.Comment: Latex2e, 8 pages, 6 figures, references adde

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

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

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

Singular reduction modules of differential equations

The notion of singular reduction modules, i.e., of singular modules of nonclassical (conditional) symmetry, of differential equations is introduced. It is shown that the derivation of nonclassical symmetries for differential equations can be improved by an in-depth prior study of the associated singular modules of vector fields. The form of differential functions and differential equations possessing parameterized families of singular modules is described up to point transformations. Singular cases of finding reduction modules are related to lowering the order of the corresponding reduced equations. As examples, singular reduction modules of evolution equations and second-order quasi-linear equations are studied. Reductions of differential equations to algebraic equations and to first-order ordinary differential equations are considered in detail within the framework proposed and are related to previous no-go results on nonclassical symmetries.Comment: 38 pages, advanced version. Extension of results of arXiv:0808.3577 to the case of a greater number of independent variable

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

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

The Current State of the Vertebrate Animals Populations and their Role in the Persistence of Natural Zoonoses Foci in the Stavropol Territory

The aim of this study was to investigate the current state of vertebrates populations and to determine their role in maintaining natural foci of zoonoses in the Stavropol Territory in 2015–2019. Material and methods. Organ suspensions and blood samples from small mammals and birds were studied using certified diagnostic test-systems for the markers of Crimean hemorrhagic fever, West Nile fever, hemorrhagic fever with renal syndrome, tularemia, and leptospirosis pathogens. The data were statistically processed using Wilson’s method. Results and discussion. Identified have been the main reservoirs of natural-focal infections in the Stavropol Territory at the present stage: birds – for the West Nile fever virus, mammals and birds inhabiting the areas of semi-desert landscape-geographical zone – for Crimean hemorrhagic fever agent. The main natural reservoir of orthohantaviruses in the Stavropol Territory is the common vole Microtus arvalis, which lives in all landscape-geographical zones. The circulation of tularemia and leptospirosis pathogens has been established throughout the whole territory of the region, the small wood mouse Sylvaemus uralensis is of the greatest epizootic significance. Findings indicate the need for further epizootiologic monitoring of Stavropol Territory in order to identify the biocenotic patterns of the pathogens’ existence and the reasons that determine the dynamics of the epizootic process and epidemic manifestations of natural foci. It is advisable to determine the sites of long-term monitoring over the number of carriers and vectors of natural-focal infections and strengthen the epizootiological control over the territory, especially during periods of seasonal activity in carriers and vectors of natural focal infections

Epidemiological situation on Crimean-Congo Hemorrhagic Fever in the Russian Federation in 2021

The review presents an analysis of the epidemiological and epizootiological situation on Crimean-Congo hemorrhagic fever (CCHF) in the Russian Federation in 2021. 49 cases of CCHF were detected in 2021, which is 1.53 times higher than in 2020. The mortality rate was 6.1 %. Sporadic cases of CCHF were registered in the Stavropol Territory, Rostov, Volgograd Regions, the Republics of Dagestan and Kalmykia. The incidence rates of CCHF were below the long-term average annual values in the majority of the constituent entities. Epizootiological survey of stationary observation points has revealed that the number of Hyalomma marginatum imago corresponded to the average long-term indicators in 2021, the peak of H. marginatum activity was noted in the II–III decades of May. The proportion of Ixodidae tick pools positive for Crimean-Congo hemorrhagic fever (CCHF) virus markers exceeded the long-term average indexes in a number of regions. On the territory of the natural focus of CCHF, the circulation of the CCHF virus of the genetic lineages “Europe-1” and “Europe-3” was detected in 2021. Based on the analysis of the epidemiological data of the previous year and natural and climatic factors affecting the abundance and vital activity of H. marginatum ticks, risk-based quantitative forecast for the incidence of CCHF in the Stavropol Territory for 2022 has been compiled