30 research outputs found

### Regularization by nonlocal conditions of the incorrect problems for differential‐operator equations of the first order

„Regularization by nonlocal conditions of the incorrect problems for differential‐operator equations of the first order" Mathematical Modelling Analysis, 2(1), p. 160-166 First Published Online: 14 Oct 201

### One approach to the analytical solution of a two-dimensional nonstationary problem of heat conduction in regions with moving boundaries on the model of a half-space

With the use of the solution of the Dirichlet nonstationary problem with discontinuous unmixed boundary conditions on the surface of an isotropic half-space a two-dimensional model of the problem with a moving phase boundary is considered. The problem models, for example, the processes of freezing of moist ground or the processes of formation of ice in stagnant water if a temperature lower than the freezing temperature is prescribed on the boundary surface in a circular region of finite radius. The classical one-dimensional result follows as a particular case from solution of this problem for an infinite radius of the circle

### A method of paired integral equations in the region of laplace transforms for solving nonstationary heat conduction problems with mixed discontinuous boundary conditions

On the basis of the method developed, the solutions of four problems of mathematical physics are obtained for an infinite plate (a plane layer of thickness z = h) with assignment of mixed discontinuous boundary conditions (BC) on one of the surfaces z = 0 of the plate and unmixed BC on the other surface z = 17

### Microbiological monitoring as a component of efficient prevention and treatment of purulent-septic infections in an orthopedics and traumatology department

Efficient monitoring of circulating purulent-septic infectious agents in a clinical setting and a study on antibiotic susceptibility of isolated strains of microorganisms allows identifying changes in the pathogen structure and trends in antibiotic resistance development, which helps to determine the tactics of antibacterial therapy and elaborate appropriate measures. The aim of the study. Retrospective analysis of the results of microbiological monitoring of purulent-septic infectious (PSI) agents in the Orthopedics and Traumatology Department (OTD) of the Zaporizhzhia Central Ambulance and Emergency Care Hospital over the period 2017–2020 to determine the main antibacterial drugs for empirical therapy. Materials and methods. We analyzed the bacteriological test results of 664 clinical material samples obtained from OTD patients using bacteriological examination statistical reporting and analytical data of the WHONET 5.6 software. Results. The main PSI pathogens in the OTD were from the ESKAPE group: E. coli, S. aureus, K. pneumoniae, A. baumannii, E. faecalis, P. aeruginosa and S. epidermidis, P. mirabilis, C. amycolatum. Isolates of E. faecalis were sensitive to vancomycin, linezolid, S. aureus – to linezolid, tigecycline, netilmicin, A. baumannii – to tigecycline. All P. aeruginosa strains were resistant to ticarcillin/clavulanate, cefepime, chloramphenicol, imipenem, meropenem, aztreonam, ciprofloxacin. E. coli and K. pneumoniae were resistant to ampicillin, ticarcillin/clavulanate, aztreonam, ceftriaxone, cefepime. The number of isolates sensitive to piperacillin/tazobactam, carbapenems, levofloxacin, gentamicin, amikacin, chloramphenicol ranged from 37 % to 65 %. Conclusions. E. coli, S. aureus, K. pneumoniae, A. baumannii, E. faecalis, P. aeruginosa, S. epidermidis, P. mirabilis, C. amycolatum play an important role in the structure of PSI pathogens in the Orthopedics and Traumatology Department of Zaporizhzhia Central Ambulance and Emergency Care Hospital. The antibiotics of choice as the antibacterial empirical therapy for enterococcal infections are vancomycin, linezolid, for staphylococcal infections – vancomycin, linezolid, tigecycline, netilmicin. PSI pathogens continually evolve developing antibiotic resistance, and it is of particular importance to monitor antibiotic susceptibility of microorganisms within the OTD

### НЕОБХОДИМЫЕ УСЛОВИЯ ДЛЯ СУЩЕСТВОВАНИЯ КЛАССИЧЕСКИХ РЕШЕНИЙ УРАВНЕНИЯ КОЛЕБАНИЙ ПОЛУОГРАНИЧЕННОЙ СТРУНЫ

If the inhomogeneous equation of semi-bounded string vibration is a classical solution in the first quadrant, then the right-hand side of this equation is obviously continuous. We prove that in this case, a special integral of this right-hand side, which is a generalized solution of the inhomogeneous equation for semi-bounded string vibration, has continuous second derivatives and it is therefore a classical solution. This generalized solution differs from the known generalized solution of this equation in the presence of the upper half of the module of the spatial variable in the integrand, which is a continuous right-hand side ofthe equation. This assertion can be used to identify the corresponding necessary smoothness requirements on the right-hand side of the equation for string vibration for the existence of classical solutions of different mixed problems in the quarter and the half-plane.Если неоднородное уравнение колебаний полуограниченной струны имеет некоторое классическое решение в первой четверти плоскости, то правая часть этого уравнения очевидно непрерывна. В работе доказывается, что в этом случае специальный интеграл от этой правой части, который является лишь обобщенным решением неоднородного уравнения колебаний полуограниченной струны, имеет вторые непрерывные производные и, следовательно, является его классическим решением. Это обобщенное решение отличается от известного обобщенного решения данного уравнения в верхней полуплоскости наличием модуля от пространственной переменной в подынтегральнойфункции, которой является непрерывная правая часть уравнения. Доказанное утверждение можно использовать для выявления соответствующих необходимых требований гладкости на правую часть уравнения колебаний струны для существования классических решений различных смешанных задачах в четверти и полуполосе  плоскости