On Type I singularities of the local axi-symmetric solutions of the Navier-Stokes equations

Local regularity of axially symmetric solutions to the Navier-Stokes equations is studied. It is shown that under certain natural assumptions there are no singularities of Type I

Prognosis of recurrent myocardial infarction based on shortliffe fuzzy models using the electrical characteristics of biologically active points

This report discusses the employment of the electrical characteristics of biologically active points (BAP) in the meridian of the heart to solve the task of prognosticating recurrence of myocardial infarctions during the rehabilitation period using fuzzy decision rule

Interior regularity criteria for suitable weak solutions of the Navier-Stokes equations

We present new interior regularity criteria for suitable weak solutions of the 3-D Navier-Stokes equations: a suitable weak solution is regular near an interior point $z$ if either the scaled $L^{p,q}_{x,t}$-norm of the velocity with $3/p+2/q\leq 2$, $1\leq q\leq \infty$, or the $L^{p,q}_{x,t}$-norm of the vorticity with $3/p+2/q\leq 3$, $1 \leq q < \infty$, or the $L^{p,q}_{x,t}$-norm of the gradient of the vorticity with $3/p+2/q\leq 4$, $1 \leq q$, $1 \leq p$, is sufficiently small near $z$

Diffeomorphic approximation of Sobolev homeomorphisms

Every homeomorphism h : X -> Y between planar open sets that belongs to the Sobolev class W^{1,p}(X,Y), 1<p<\infty, can be approximated in the Sobolev norm by diffeomorphisms.Comment: 21 pages, 5 figure

Synthis and Phisical And Chemical; Properties of SiO[2]-B[2]O[3] and SiO[2]-P[2]O[5] Thin Film Systems and Powders

The SiO[2]-B[2]O[3] and SiO[2]-P[2]O[5] films were synthesized by using film forming solutions having a P[2]O[5] content of up to 30% and B[2]O[3] up to 40%. Properties of the filmforming solutions and binary oxides were examined. The physical and chemical processes occurring in the solution during the heat treatment of films were examined. The conditions for producing films of different thicknesses were determined. The kinetic parameters were calculated

Global regularity criterion for the 3D Navier-Stokes equations involving one entry of the velocity gradient tensor

In this paper we provide a sufficient condition, in terms of only one of the nine entries of the gradient tensor, i.e., the Jacobian matrix of the velocity vector field, for the global regularity of strong solutions to the three-dimensional Navier-Stokes equations in the whole space, as well as for the case of periodic boundary conditions

On the loss of continuity for super-critical drift-diffusion equations

We show that there exist solutions of drift-diffusion equations in two dimensions with divergence-free super-critical drifts, that become discontinuous in finite time. We consider classical as well as fractional diffusion. However, in the case of classical diffusion and time-independent drifts we prove that solutions satisfy a modulus of continuity depending only on the local $L^1$ norm of the drift, which is a super-critical quantity.Comment: Minor edit

Blow-up of critical Besov norms at a potential Navier-Stokes singularity

We show that the spatial norm of any strong Navier-Stokes solution in the space X must become unbounded near a singularity, where X may be any critical homogeneous Besov space in which local existence of strong solutions to the 3-d Navier-Stokes system is known. In particular, the regularity of these spaces can be arbitrarily close to -1, which is the lowest regularity of any Navier-Stokes critical space. This extends a well-known result of Escauriaza-Seregin-Sverak (2003) concerning the Lebesgue space $L^3$, a critical space with regularity 0 which is continuously embedded into the spaces we consider. We follow the "critical element" reductio ad absurdum method of Kenig-Merle based on profile decompositions, but due to the low regularity of the spaces considered we rely on an iterative algorithm to improve low-regularity bounds on solutions to bounds on a part of the solution in spaces with positive regularity

Новые комбинации и названия сосудистых растений Азиатской России.

In this paper, we present nomenclatural novelties required in the course of the preparation of the second, revised version of the checklist of vascular plants of Asian Russia. The first version was published in 2012 (Baikov 2012). At the family level, we accepted the modern classification systems (APG IV for flowering plants, PPG I for lycophytes and ferns, and GPG for gymnosperms). At the genus level, we follow the generic concepts applied for particular taxonomic groups according to the Catalogue of Life (COL; https://www.catalogueoflife.org/), version COL23.5. At the species level, we consistently apply the monotypic species concept (also known in Russia as Komarov’s concept). In total, this paper presents one new nothogenus name (× Sibirotrisetokoeleria Chepinoga nom. nov., Poaceae) and 156 new names in the rank of species, in 28 families: Amaranthaceae Juss. (1 name), Amaryllidaceae J. St.-Hil. (1), Apiaceae Lindl. (2), Asteraceae Bercht. & J.Presl (12), Boraginaceae Juss. (4), Caryophyllaceae Juss. (11), Crassulaceae J. St.-Hill. (3), Cyperaceae Juss. (8), Ericaceae Juss. (2), Fabaceae Lindl. (16), Gentianaceae Juss. (1), Geraniaceae Juss. (1), Juncaceae Juss. (1), Lamiaceae Martinov (1), Menyanthaceae Dumort. (1), Orchidaceae Juss. (1), Orobanchaceae Vent. (1), Papaveraceae Juss. (4), Plantaginaceae Juss. (1), Poaceae Barnhart (49), Polygonaceae Juss. (4), Primulaceae Batsch. ex Borkh. (6), Ranunculaceae Juss. (4), Rosaceae Juss. (5), Salicaceae Mirb. (2), Saxifragaceae Juss. (11), Vitaceae Juss. (1), Zygophyllaceae R. Br. (2 names)

Obtainment of Monoclonal Antibodies and Prospects of Their Application as Basis for Immunodiagnostic Aids for Crimean-Congo Hemorrhagic Fever Virus Detection

) as framework for the production of tools for CCHF virus detection and identification in artificially contaminated samples and clinical specimens containing CCHF antigens was proven efficient