Mathematical Heritage of Sergey Naboko: Functional Models of Non-Self-Adjoint Operators

This is an overview of mathematical heritage of Sergey Naboko in the area of functional models of non-self-adjoint operators. It covers the works by Sergey in model construction, the analysis of absolutely continuous and singular spectra and the construction of the scattering theory in model terms.Comment: 14 pages. arXiv admin note: text overlap with arXiv:2204.0119

On the Finite-Time Blowup of a 1D Model for the 3D Axisymmetric Euler Equations

In connection with the recent proposal for possible singularity formation at the boundary for solutions of 3d axi-symmetric incompressible Euler's equations (Luo and Hou, 2013), we study models for the dynamics at the boundary and show that they exhibit a finite-time blow-up from smooth data.Comment: A paragraph at the end of Section 2 and an appendix discussing kinetic energy conservation are adde

USING THE METHOD KINESIOTAPING IN REHABILITATION OF CHILDREN WITH HEMIPARETIC FORM OF CEREBRAL PALSY

The study examines the impact of a new kind of impact in the rehabilitation of hemiparetic form of cerebral palsy – a method kinesiotaping “Concept 4 tapes.” Within this framework, the receptor patient unit gradually turned on, resulting in a restructuring of the program abnormal movement, the conditions of use of other methods to increase the efficiency and depth of the order of their influence.The advantage of a technique kinesiotaping is the standard approach, allowing you to apply effects diagram method to all patients without loss of efficacy of therapeutic effects

Computational study of electrostatic contribution to membrane dynamics

Electrostatics plays a crucial role in the membrane biology. Negatively charged lipids (such as PS, PA and PIP2) are subject to redistribution under the action of electrostatic forces during various signalling events. Membrane recruitment of multiple signalling proteins (such as MARCKS or Src kinase) is often maintained by positively charged polybasic domains (PD). Even though adsorption of these proteins to the cellular membrane has been extensively investigated, very little is known about how electrostatic interactions contribute to their membrane lateral dynamics. This thesis presents an investigation of the contribution of electrostatic interactions to the membrane lateral dynamics by means of novel computational tools. First, I developed a dynamic Monte-Carlo automaton that faithfully simulates lateral diffusion of the adsorbed positively charged PD of a peripheral membrane protein, as well as the dynamics of mono- (PS, PA) and polyvalent (PIP2) anionic lipids within the bilayer. This model allowed to investigate the major characteristics of protein-membrane diffusion on the uniform membrane. In agreement with earlier results, the simulations revealed the following microscopic phenomena: 1) Electrostatic lipid demixing in the vicinity of the PD; 2) PD interacts with PIP2 stronger than with monovalent lipids. On the spatially heterogeneous membrane the automaton predicted a directional drift of the PD, which was validated by a simple mean-field analytical model. The predicted phenomenon could potentially play a major role in membrane domain formation. To test this hypothesis and to investigate the membrane dynamics on larger scales I developed a continuous model, which was based on the results of the automaton simulations. The results of the continuous model and the Monte-Carlo simulations were shown to be in quantitative agreement. The continuous model allows one to simulate the electrostatic membrane dynamics on micrometer scales and can be used to describe various biologically important processes, such as endocytic cup initiation

THE RESULTS OF KINESIOTAPING IN PATIENTS WITH SCOLIOSIS

The kinesiotaping method has put into practice on the Rehabilitation and Sport medicine chair of the RNIMU named by N.I. Pirogov which is situated in the Medical Rehabilitation Department of RDKB. This method showed high treatment efficacy and results were stable and continuous. Kinesiotaping isn’t the main treatment method of scoliosis, but its good efficacy in reaching particular rehabilitation goals, potentiation of some methods of treatment of scoliosis, pain elimination and so on, support the idea to invent this method in the rehabilitation process circle in case of such difficult disease as scoliosis