Development of singularities for the compressible Euler equations with external force in several dimensions

We consider solutions to the Euler equations in the whole space from a certain class, which can be characterized, in particular, by finiteness of mass, total energy and momentum. We prove that for a large class of right-hand sides, including the viscous term, such solutions, no matter how smooth initially, develop a singularity within a finite time. We find a sufficient condition for the singularity formation, "the best sufficient condition", in the sense that one can explicitly construct a global in time smooth solution for which this condition is not satisfied "arbitrary little". Also compactly supported perturbation of nontrivial constant state is considered. We generalize the known theorem by Sideris on initial data resulting in singularities. Finally, we investigate the influence of frictional damping and rotation on the singularity formation.Comment: 23 page

Nonlinear effects in tunnelling escape in N-body quantum systems

We consider the problem of tunneling escape of particles from a multiparticle system confined within a potential trap. The process is nonlinear due to the interparticle interaction. Using the hydrodynamic representation for the quantum equations of the multiparticle system we find the tunneling rate and time evolutions of the number of trapped particles for different nonlinearity values.Comment: 10 pages, 3 figure

Beneficial impact of human placenta extracts on erythrocyte membrane thermostability

PURPOSE: To study the influence of human placenta extract (HPE) and its individual fractions on the thermal stability of human erythrocyte membrane. METHODS: HPE fractions were isolated by gel chromatography. Thermal hemolysis of erythrocytes, exposed to 55°C was measured spectrophotometrically. Cytosol microvscosity and barrier function of erythrocyte membranes at hyperthermia were investigated by EPR spin probe TEMPON. Thermal denaturation of erythrocyte membrane proteins were studied by differential scanning calorimetry. RESULTS: Pre-treatment of erythrocytes with HPE or its fractions inhibited thermal hemolysis. Low-molecular fractions (below 4 kDa and 12-20 kDa) were the most effective in thermal hemolysis inhibition ((31.7±3.3) % and (31.5±3.2) %, respectively). The latter fractions markedly reduced the hyperthermia (55°C)-induced permeability of erythrocytes for ferricyanide ions and inhibited the thermo-induced structural transitions in erythrocyte membrane between 40 and 50°C, which are associated with cytoskeletal proteins. HPE fractions reversibly increased the denaturation temperatures of erythrocyte membrane proteins, except that of spectrin, and enlarged the enthalpy of denaturation of all membrane proteins. CONCLUSIONS: HPE and its individual fractions increased the thermal stability of erythrocyte membranes and erythrocytes. This effect was attributed to the reversible binding of some low molecular ingredient of HPE to the integral proteins and consequent stabilization of their interaction with under-membrane cytoskeleton

Antimicrobial activity of quantum dots: an experimental study

Тhe purpose of the study is to analyze their antimicrobial activity in a bacteriological laboratory.Цель работы – анализ противомикробной активности в условиях бактериологической лаборатории

Laboratory Analysis of the Anti-Infectious Activity of Quantum Dots and Bioconjugates Based on Them in the Aspect of the Prospects for the Treatment of Inflammatory Diseases of the Eye. Experimental Research (Part 3)

This article presents the third part of an experimental study on the prospects and possibilities of using quantum dots and bioconjugates created on their basis in the treatment of inflammatory diseases of the eye. Taking into account the previously obtained results on the possibility of “safe” use of CdTe/Cd and InP/ZnSe/ZnS quantum dots on an animal model under conditions of intravitreal administration, the aim of the current stage was to analyze their antimicrobial activity in a bacteriological laboratory. Materials and methods. As QDs, we took two types of artificial fluorophores capable of generating superoxide radicals synthesized according to a special technical assignment at the Federal State Unitary Enterprise “Research Institute of Applied Acoustics”, Dubna, Moscow Region: type 1 - colloidal solution of QD CdTe/Cd MPA 710 10 % of the mass. Type 2 - colloidal solution of QD InP/ZnSe/ZnS 650 10 % wt. The study included “museum” and nosocomial strains of microorganisms, and the activity of points was assessed using the disk-diffusion method, followed by an assessment of the zones of inhibition of bacterial growth. Concentrations of 0.1 %, 0.01 %, and 0.001 % quantum dots were tested, as well as solutions of bioconjugates (antibiotic + quantum dots) of Vancomycin, Levofloxacin, Ceftazidime and Cefotaxime. Results. Based on the data obtained, it was concluded that quantum dots potentiate the action of the sensitivity of individual microorganisms, both outpatient and hospital strains. © 2022 Ophthalmology Publishing Group. All rights reserved