Stability estimates in nonlinear differential equations of a special kind

Quite a lot of works have been devoted to problems of stability theory and, in particular, to the use of the second Lyapunov method for this. The main ones are the following [1-7]. The main attention in these works is paid to obtaining stability conditions. At the same time, when solving practical problems, it is important to obtain quantitative characteristics of the convergence of solutions to an equilibrium position. In this paper, we consider nonlinear scalar differential equations with nonlinearity of a special form (weakly nonlinear equations). Differential equations of this type are encountered in the study of processes in neurodynamics [8,9]. In this paper, we obtain stability conditions for a stationary solution of scalar equations of this type. And also the characteristics of the convergence of the process are calculated. It is shown that the solution of stability problems is closely related to optimization problems [10-12]. Pages of the article in the issue: 67 - 71 Language of the article: Ukrainia

Methods of assessing the dynamic stability of the cutting process using UNIGRAPHICS NX

The article deals with the determination of the stability of the cutting process at the Nyquist criterion. Attention is paid to the use of CAE systems to solve this problem. The result of this method is to improve the reliability of technological operations

Structures of the eukaryotic ribosome and its translational states in situ

Ribosomes translate genetic information into primary structure. During translation, various cofactors transiently bind to the ribosome that undergoes prominent conformational and structural changes. Different translational states of ribosomes have been well characterized in vitro. However, to which extent the known translational states are representative of the native situation inside cells has thus far only been addressed in prokaryotes. Here, we apply cryo-electron tomography to cryo-FIB milled Dictyostelium discoideum cells combined with subtomogram averaging and classification. We obtain an in situ structure that is locally resolved up to 3 Angstrom, the distribution of eukaryotic ribosome translational states, and unique arrangement of rRNA expansion segments. Our work demonstrates the use of in situ structural biology techniques for identifying distinct ribosome states within the cellular environment

Study of Deformations Field in the Working Zone of Vertical Milling Machine

© 2017 The Authors. Published by Elsevier Ltd. The paper examines the questions of the static elastic deformation development during the machining with milling machines. It discusses the issues of "machine - tool - instrument - workpiece"system modelling aiming at providing the preliminary assessment of elastic deformations during the processing, which gives an opportunity to prevent defect appearance. The deformation distribution is detected for the cases when the cutting area is positioned in different points of working area of the machine. The changes of deformations for different cutting pattern are analysed, a method of determination of main axes rigidity is considered based on that. The results show that the deformation of the technological system depends not only on the geometry of the basic parts and junctions but also on their location. The modelling the whole technological system is required. Only in this case selecting the optimal tool and its location to achieve the required quality of processing is possible

Backbone and side chain NMR assignments for the ribosome binding factor A (RbfA) from Staphylococcus aureus

© 2018, Springer Nature B.V. Ribosome binding factor A (RbfA) is a 14.9 kDa adaptive protein of cold shock, which is important for bacterial growth at low temperatures. RbfA can bind to the free 30S ribosomal subunit and interacts with the 5′-terminal helix (helix I) of 16S rRNA. RbfA is important for the efficient processing of 16S rRNA and for the maturation (assembly) of 30S ribosomal subunits. Here we report backbone and side chains 1H, 13C and 15N chemical shift assignments of RbfA from Staphylococcus aureus. Analysis of the backbone chemical shifts by TALOS+ suggests that RbfA contains four α-helixes and three β-strands with α1-β1-β2-α2-α3-β3-α4 topology. Secondary structure of RbfA have KH-domain fold topology with βααβ subunit which is characterized by a helix-kink-helix motif in which the GxxG sequence is replaced by a conserved AxG sequence, where an Ala residue at position 70 forming an interhelical kink. The solution of the structure of this protein factor and its complex with the ribosome by NMR spectroscopy, X-ray diffraction analysis and cryo-electron microscopy will allow further development of highly selective substances for slowing or completely stopping the translation of the pathogenic bacterium S. aureus, which will interfere with the synthesis and isolation of its pathogenicity factors

Triplet proximity effect in FSF trilayers

We study the critical temperature T_c of FSF trilayers (F is a ferromagnet, S is a singlet superconductor), where the triplet superconducting component is generated at noncollinear magnetizations of the F layers. An exact numerical method is employed to calculate T_c as a function of the trilayer parameters, in particular, mutual orientation of magnetizations. Analytically, we consider limiting cases. Our results determine conditions which are necessary for existence of recently investigated odd triplet superconductivity in SF multilayers.Comment: 5 pages, 4 EPS figures; the style file jetpl.cls is included. Version 2: minor corrections, added reference. Version 3: minor correction

Superconductor-Ferromagnet Bi-Layers: a Comparison of s-Wave and d-Wave Order Parameters

We study superconductor-ferromagnet bi-layers, not only for s-wave but also for d-wave superconductors. We observe oscillations of the critical temperature when varying the thickness of the ferromagnetic layer for both s-wave and d-wave superconductors. However, for a rotated d-wave order parameter the critical temperature differs considerably from that for the unrotated case. In addition we calculate the density of states for different thicknesses of the ferromagnetic layer; the results reflect the oscillatory behaviour of the superconducting correlations.Comment: 11 pages, 5 figures, accepted for publication in J. Phys.: Condens. Matte

The competitiveness of the Republic of Tatarstan as a center of urban tourism of the Russian Federation

© Medwell Journals, 2016.The study comprises a set of theoretical and methodological statements and practical suggestions about the development and realization of urban tourism of the Republic of Tatarstan. The study to analyze how the Universiade 2013 influenced to the development of urban tourism in the capital and other ancient cities in Republic of Tatarstan. We investigated urban tourism in Russia and in the Republic of Tatarstan, this is one of the most developed and fast growing sector of the economy. This area is aimed at improving the quality of life of the population, increased life expectancy and disability Russian citizens. And also helps to preserve historical sites of the ancient cities of the Volga region

Development and investigation of the stressed-deformed state of the demountable foundation for support

© Published under licence by IOP Publishing Ltd. The development is demountable foundation for support, including separate reinforced concrete blocks in the form of prisms mounted on the surface of the base and pulled together by horizontal strands, and anchor devices for fixing the supports. The reinforced concrete blocks are made in the form of hollow prisms consisting of walls and square bottoms, and the strands are made in the form of bolts that tighten the walls along the top and bottom, while the anchoring devices for fixing the supports are made in the form of anchors on the bottom of the central prism and horizontal spacers between the support and the walls of the prism in its upper part. Numerical studies of the foundation have been carried out and its optimal sizes have been found in the PK Lira SAPR