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

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

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

HATRIC-based identification of receptors for orphan ligands

Technologies for identifying receptor-ligand pairs on living cells at physiological conditions remain scarce. Here, the authors develop a mass spectrometry-based ligand receptor capture technology that can identify receptors for a diverse range of ligands at physiological pH with as few as a million cells

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

EnnCore: End-to-End Conceptual Guarding of Neural Architectures

The EnnCore project addresses the fundamental security problem of guaranteeing safety, transparency, and robustness in neural-based architectures. Specifically, EnnCore aims at enabling system designers to specify essential conceptual/behavioral properties of neural-based systems, verify them, and thus safeguard the system against unpredictable behavior and attacks. In this respect, EnnCore will pioneer the dialogue between contemporary explainable neural models and full-stack neural software verification. This paper describes existing studies' limitations, our research objectives, current achievements, and future trends towards this goal. In particular, we describe the development and evaluation of new methods, algorithms, and tools to achieve fully-verifiable intelligent systems, which are explainable, whose correct behavior is guaranteed, and robust against attacks. We also describe how EnnCore will be validated on two diverse and high-impact application scenarios: securing an AI system for (i) cancer diagnosis and (ii) energy demand response

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