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

The increase of ultrasound measurements accuracy with the use of two-frequency sounding

In the article the new method for detection of the temporary position of the received echo signal is considered. The method consists in successive emission of sounded impulses on two frequencies and also the current study is concerned with the analysis of ultrasound fluctuation propagation time to and from the deflector on every frequency. The detailed description of the mathematical tool is presented in the article. The math tool used allows the authors to decrease the measurement error with help of calculations needed

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

Use of Vasavital® in patients with diabetic retinopathy

Background: Diabetic retinopathy (DR) is a major cause of visual impairment or blindness among working-age adults worldwide. For years, researchers around the world have been trying to develop new effective pharmaceutical methods of treatment for preclinical and early DR. Purpose: To examine the effect of a one-month course of Vasavital on the function of the visual system and ocular hemodynamics (using ophthalmic rheography) in patients with non-proliferative and proliferative diabetic retinopathy (NPDR and PPDR, respectively). Material and Methods: Forty-seven type 2 diabetes patients with DR and moderate glycemic control were divided into those with NPDR (group 1 of 15 patients; 30 eyes) and those with PPDR (group 2 of 17 patients; 34 eyes). The control group was composed of 15 volunteers (30 eyes) of similar age having no systemic or eye disease. Patients received a one-month course of Vasavital-only therapy at a dose of one capsule twice a day as an outpatient treatment. They received visual acuity assessment, intraocular pressure measurement, ophthalmoscopy, biomicroscopy, perimetry, systemic blood pressure and pulse measurement, optical coherence tomography and fluorescein angiography, and ocular hemodynamics was assessed by ophthalmic rheography. Eleven patients (22 eyes) with NPDR and ten patients (20 eyes) with PPDR underwent electrophysiological studies of electrically evoked phosphene threshold (EEPT) and critical frequency of phosphene disappearance (CFPD), before and after a course of Vasavital treatment. Results: Patients reported that a one-month course of Vasavital was well-tolerated, with no new complaints. In addition, no side effects were observed. After treatment, the function of the photopic afferent system as assessed by light sensitivity at minutes 0 to 7 of adaptation improved by 33.3%-40% in patients with NPDR and by 27.2%-33.3% in patients with PPDR. In addition, there was a decrease in EEPT by 18% and 7.7%, respectively, and an increase in CFPD by 28.2% and 24.7%, respectively, for patients in groups 1 and 2. Moreover, ocular pulse blood filling improved by 27.7% in patients with NPDR and by 17.3% in patients with PPDR, and vascular tone in large-caliber vessels decreased by 8% in the former patients. Conclusion: A one-month Vasavital course administered to patients with DR had a positive effect on the visual system function and ocular circulation parameters, which provides grounds for the use of the Ginkgo biloba-based preparation as a monotherapy or as part of a combined treatment for initial functional changes in the visual system in DR

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

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