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

Quantitative mass spectrometry-based proteomics: An overview

In recent decades, mass spectrometry has moved more than ever before into the front line of protein-centered research. After being established at the qualitative level, the more challenging question of quantification of proteins and peptides using mass spectrometry has become a focus for further development. In this chapter, we discuss and review actual strategies and problems of the methods for the quantitative analysis of peptides, proteins, and finally proteomes by mass spectrometry. The common themes, the differences, and the potential pitfalls of the main approaches are presented in order to provide a survey of the emerging field of quantitative, mass spectrometry-based proteomics

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

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

Propagator of a Charged Particle with a Spin in Uniform Magnetic and Perpendicular Electric Fields

We construct an explicit solution of the Cauchy initial value problem for the time-dependent Schroedinger equation for a charged particle with a spin moving in a uniform magnetic field and a perpendicular electric field varying with time. The corresponding Green function (propagator) is given in terms of elementary functions and certain integrals of the fields with a characteristic function, which should be found as an analytic or numerical solution of the equation of motion for the classical oscillator with a time-dependent frequency. We discuss a particular solution of a related nonlinear Schroedinger equation and some special and limiting cases are outlined.Comment: 17 pages, no figure

The role of procalcitonin and lactate at single determination in the intensive care unit in the diagnosis and prognosis of hypovolemic and distributive (septic) shock

The aim of this study was to critically analyze the information value of the blood plasma content of lactate and procalcitonin (PCT) in patients with septic and hypovolemic shockЦель исследования — критический анализ информационной ценности содержания лактата и прокальцитонина (ПКТ) в плазме крови у пациентов с септическим и гиповолемическим шоко