Pub Date : 2023-07-09DOI: 10.29235/1561-8358-2023-68-2-113-120
V. Rubanik, D. A. Bahrets, V. Rubanik Jr., V. I. Urban, V. Dorodeiko
The deformation behavior of the titanium nickelide alloy Ti–55.84 wt. % Ni (TiNi) with titanium nitride (TiN) coatings obtained by arc-PVD has been simulated. Differential scanning calorimetry and three-point bending test were used to study the parameters of martensitic transformations and the deformation behavior of this alloy. The values of the characteristic temperatures for the TiNi alloy that can be used in medical applications were substantiated. The elastic-force characteristics of the alloy related to the properties in the superelastic state were considered. The dependiences of the change in the phase yield strength, the stress of the unloading plateau, and the residual deformation of the TiNi samples with TiN coatings on the ambient temperature range between 6 to 37 °C were determined. Based on these dependencies, a deformation curve was obtained that can predict the mechanical behavior of a TiNi product, for example, a stent, before and during its implantation into a human body. TiNi-based shape memory alloys are widely used in various branches of medicine; therefore, the development of technological methods for manufacturing products from TiNi with high corrosion resistance is promising.
采用电弧pvd法模拟了Ti-55.84 wt. % Ni (TiNi)镍化钛合金在氮化钛(TiN)涂层下的变形行为。采用差示扫描量热法和三点弯曲试验研究了该合金的马氏体相变参数和变形行为。得到了医用钛镍合金的特征温度值。考虑了合金的弹性力特性与超弹性状态下的性能的关系。在6 ~ 37℃的环境温度范围内，测定了TiN涂层的TiNi试样的相屈服强度、卸载平台应力和残余变形的变化规律。基于这些依赖关系，获得了一条变形曲线，可以预测TiNi产品(例如支架)在植入人体之前和期间的力学行为。镍基形状记忆合金广泛应用于医学的各个分支;因此，开发高耐蚀性TiNi产品的技术方法是有前途的。
{"title":"Simulation of deformation behavior of TiNi alloy with TiN coatings for medical applications","authors":"V. Rubanik, D. A. Bahrets, V. Rubanik Jr., V. I. Urban, V. Dorodeiko","doi":"10.29235/1561-8358-2023-68-2-113-120","DOIUrl":"https://doi.org/10.29235/1561-8358-2023-68-2-113-120","url":null,"abstract":"The deformation behavior of the titanium nickelide alloy Ti–55.84 wt. % Ni (TiNi) with titanium nitride (TiN) coatings obtained by arc-PVD has been simulated. Differential scanning calorimetry and three-point bending test were used to study the parameters of martensitic transformations and the deformation behavior of this alloy. The values of the characteristic temperatures for the TiNi alloy that can be used in medical applications were substantiated. The elastic-force characteristics of the alloy related to the properties in the superelastic state were considered. The dependiences of the change in the phase yield strength, the stress of the unloading plateau, and the residual deformation of the TiNi samples with TiN coatings on the ambient temperature range between 6 to 37 °C were determined. Based on these dependencies, a deformation curve was obtained that can predict the mechanical behavior of a TiNi product, for example, a stent, before and during its implantation into a human body. TiNi-based shape memory alloys are widely used in various branches of medicine; therefore, the development of technological methods for manufacturing products from TiNi with high corrosion resistance is promising.","PeriodicalId":20584,"journal":{"name":"Proceedings of the National Academy of Sciences of Belarus, Medical series","volume":"201 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90868717","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-09DOI: 10.29235/1561-8358-2023-68-2-121-136
C. Zhdanovich, V. N. Plishch
An analytical dependence was obtained to determine the amplitude of vibrations of the rubber track in the span of the free branch of the tractor bypass between the supporting rollers. The process of oscillations of this type of track in the middle of the span of a free branch during the operation of tracked tractors of the brand “Belarus” in pull and transport modes, taking into account the speed of movement, is investigated. It is shown that the resonant modes of transverse vibrations of the rubber track at the operational ranges of the tractor operation should be taken as the determining criterion for choosing the parameters of the spans of the free branch of the bypass. The maximum values of the oscillation amplitudes of such a track in the span of the free branch of the bypass between the supporting rollers for the family of tracked tractors “Belarus” under different operating modes are calculated. A frequency analysis of oscillations was carried out and it was found that on tracked agricultural tractors with rubber tracks, a mode of occurrence of resonant oscillations in the span of the free branch of the bypass between the supporting rollers is possible. An analytical dependence has been obtained to determine the limiting distance between the supporting rollers of a tractor with a rubber track and elastic and locked suspensions according to the criterion of deducing the resonant mode of vibration of the track in the span of a free branch outside the operational range of the tractor. The values of the maximum distances between the support rollers for tractors “Belarus” 1802, 2102 and 2103 at different suspension modes are calculated. The required number of supporting rollers is determined and recommendations are given on the place of their installation. The results of these studies can be used in the creation and operation of tractors with rubber tracks
{"title":"Selecting number and location of support rollers of crawler tractor based on analysis of vibrations of upper branch of rubber track","authors":"C. Zhdanovich, V. N. Plishch","doi":"10.29235/1561-8358-2023-68-2-121-136","DOIUrl":"https://doi.org/10.29235/1561-8358-2023-68-2-121-136","url":null,"abstract":"An analytical dependence was obtained to determine the amplitude of vibrations of the rubber track in the span of the free branch of the tractor bypass between the supporting rollers. The process of oscillations of this type of track in the middle of the span of a free branch during the operation of tracked tractors of the brand “Belarus” in pull and transport modes, taking into account the speed of movement, is investigated. It is shown that the resonant modes of transverse vibrations of the rubber track at the operational ranges of the tractor operation should be taken as the determining criterion for choosing the parameters of the spans of the free branch of the bypass. The maximum values of the oscillation amplitudes of such a track in the span of the free branch of the bypass between the supporting rollers for the family of tracked tractors “Belarus” under different operating modes are calculated. A frequency analysis of oscillations was carried out and it was found that on tracked agricultural tractors with rubber tracks, a mode of occurrence of resonant oscillations in the span of the free branch of the bypass between the supporting rollers is possible. An analytical dependence has been obtained to determine the limiting distance between the supporting rollers of a tractor with a rubber track and elastic and locked suspensions according to the criterion of deducing the resonant mode of vibration of the track in the span of a free branch outside the operational range of the tractor. The values of the maximum distances between the support rollers for tractors “Belarus” 1802, 2102 and 2103 at different suspension modes are calculated. The required number of supporting rollers is determined and recommendations are given on the place of their installation. The results of these studies can be used in the creation and operation of tractors with rubber tracks","PeriodicalId":20584,"journal":{"name":"Proceedings of the National Academy of Sciences of Belarus, Medical series","volume":"5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83083065","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-06DOI: 10.29235/1561-2430-2023-59-2-168-176
M. N. Lukashevich, M. Kovalyov
In this paper, using mathematical programming methods we investigate the problem of optimally planning the inspection and repair of cargo containers at several port facilities over time. Its relevance is conditioned by the necessity of optimization of the processes of planning logistics operations. We represent a formulation of this problem and its reduction to a mixed integer linear programming (MILP). Containers have several types and levels of quality, which determine the cost of their repair. The objective function includes total costs of storage, inspection, repair, transportation of containers and penalties for both container rejection and unsatisfied consumer demand. Using the proposed model, it is possible to achieve reasonable computing time for port operations and minimize underutilization or overutilization of port capacity, preventing financial losses and increasing efficiency. Also, this model can be easily converted to solve optimization problems in other areas of logistics.
{"title":"The statement and the mathematical model of the problem of planning the inspection and repair of cargo containers","authors":"M. N. Lukashevich, M. Kovalyov","doi":"10.29235/1561-2430-2023-59-2-168-176","DOIUrl":"https://doi.org/10.29235/1561-2430-2023-59-2-168-176","url":null,"abstract":"In this paper, using mathematical programming methods we investigate the problem of optimally planning the inspection and repair of cargo containers at several port facilities over time. Its relevance is conditioned by the necessity of optimization of the processes of planning logistics operations. We represent a formulation of this problem and its reduction to a mixed integer linear programming (MILP). Containers have several types and levels of quality, which determine the cost of their repair. The objective function includes total costs of storage, inspection, repair, transportation of containers and penalties for both container rejection and unsatisfied consumer demand. Using the proposed model, it is possible to achieve reasonable computing time for port operations and minimize underutilization or overutilization of port capacity, preventing financial losses and increasing efficiency. Also, this model can be easily converted to solve optimization problems in other areas of logistics. ","PeriodicalId":20584,"journal":{"name":"Proceedings of the National Academy of Sciences of Belarus, Medical series","volume":"93 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84240984","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-06DOI: 10.29235/1561-2430-2023-59-2-121-129
V. Lepin
In this paper, we consider the maximum weight ({K1,K2},k,l)-packing problem in a graph. This problem generalizes a number of well-known problems, for example: maximum induced matching, k-separated matching, connected matching, independent set, dissociating set, k-packing. We show that in the class of cographs, a maximum weight ({K1,K2},k,l)- packing can be computed in O(n + m) time. Let Γ be a class of graphs and Γ* be a class of all simple (with respect to the modular decomposition) induced subgraphs from Γ. It is proven that if the maximum weight ({K1,K2},k,l)-packing problem can be solved in the class of graphs Г* in time O(np ), where p ≥ 2 is a constant, then this problem can be solved in the class of graphs Г in time O(np ).
{"title":"The maximum weight ({K1,K2},k,l)-packing problem in a graph","authors":"V. Lepin","doi":"10.29235/1561-2430-2023-59-2-121-129","DOIUrl":"https://doi.org/10.29235/1561-2430-2023-59-2-121-129","url":null,"abstract":"In this paper, we consider the maximum weight ({K1,K2},k,l)-packing problem in a graph. This problem generalizes a number of well-known problems, for example: maximum induced matching, k-separated matching, connected matching, independent set, dissociating set, k-packing. We show that in the class of cographs, a maximum weight ({K1,K2},k,l)- packing can be computed in O(n + m) time. Let Γ be a class of graphs and Γ* be a class of all simple (with respect to the modular decomposition) induced subgraphs from Γ. It is proven that if the maximum weight ({K1,K2},k,l)-packing problem can be solved in the class of graphs Г* in time O(np ), where p ≥ 2 is a constant, then this problem can be solved in the class of graphs Г in time O(np ). ","PeriodicalId":20584,"journal":{"name":"Proceedings of the National Academy of Sciences of Belarus, Medical series","volume":"76 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89909699","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-06DOI: 10.29235/1561-2430-2023-59-2-136-146
I. Siutsou, A. E. Kurhuzava
The initial stage of a gamma-ray burst can be described by the diffusion of radiation in the shell which is ultrarelativistically widening. We have herein considered the case when the initial energy distribution in the shell depends on the depth according to a linear law. At the same time, the slope of the initial energy distribution function determines the effective temperature and the instantaneous spectrum of the gamma-ray burst at the initial time moment, as well as the time-integrated spectrum at high frequencies. Moreover, we investigated the dependence of the instantaneous spectrum of the gamma-ray burst on the time of arrival: if it increases, the flux maximum is observed for a smaller frequency independently of the initial energy distribution in the shell. It the time of arrival is larger than 1 s, the instantaneous spectrum is independent of the initial energy distribution in the shell. The slope of the power-law part of the time-integrated spectrum at lower frequencies is the same for any initial energy distribution in the shell and it is equal to 1.98; at higher frequencies, it becomes steeper with increasing the slope of the function corresponding to the energy distribution in the shell at the initial instant of time, and it has values between –2.38 and –13.73.This allows us to explain with the help of our model a large number of gamma-ray bursts that have a typical Band spectrum.
{"title":"Dependence of the spectra of gamma-ray bursts on the initial energy distribution in the ultrarelativistically expanding shell","authors":"I. Siutsou, A. E. Kurhuzava","doi":"10.29235/1561-2430-2023-59-2-136-146","DOIUrl":"https://doi.org/10.29235/1561-2430-2023-59-2-136-146","url":null,"abstract":"The initial stage of a gamma-ray burst can be described by the diffusion of radiation in the shell which is ultrarelativistically widening. We have herein considered the case when the initial energy distribution in the shell depends on the depth according to a linear law. At the same time, the slope of the initial energy distribution function determines the effective temperature and the instantaneous spectrum of the gamma-ray burst at the initial time moment, as well as the time-integrated spectrum at high frequencies. Moreover, we investigated the dependence of the instantaneous spectrum of the gamma-ray burst on the time of arrival: if it increases, the flux maximum is observed for a smaller frequency independently of the initial energy distribution in the shell. It the time of arrival is larger than 1 s, the instantaneous spectrum is independent of the initial energy distribution in the shell. The slope of the power-law part of the time-integrated spectrum at lower frequencies is the same for any initial energy distribution in the shell and it is equal to 1.98; at higher frequencies, it becomes steeper with increasing the slope of the function corresponding to the energy distribution in the shell at the initial instant of time, and it has values between –2.38 and –13.73.This allows us to explain with the help of our model a large number of gamma-ray bursts that have a typical Band spectrum.","PeriodicalId":20584,"journal":{"name":"Proceedings of the National Academy of Sciences of Belarus, Medical series","volume":"264 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75952830","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-06DOI: 10.29235/1561-2430-2023-59-2-158-167
A. Sotsky, E. Chudakov
By analyzing the wave equations, the coincidence of the energy reflection and transmission coefficients for the s- and p-polarization waves is herein substantiated when they are incident on the interference coating from opposite directions. The coating can be characterized by an arbitrary spatial profile of the refractive index, the limiting condition is the absence of optical losses in it. Reciprocity relations are obtained for the energy reflection and transmission coefficients of natural light for a structure in the form of a plane-parallel dielectric plate with interference coatings on its opposite sides. It is shown that when a structure with an absorbing plate is illuminated in opposite directions, the energy reflection coefficients can differ, while the energy transmission coefficients always coincide. Reciprocity relations are applied to the calculation of broadband antireflective interference coatings consisting of alternate layers Nb2O5 and SiO2 deposited on a polycarbonate plate. As a result, their correctness is confirmed and it is shown that the optimized antireflection two-sided interference coating provides approximately a five times lower averaged energy reflection coefficient compared to the optimized one-sided coating.
{"title":"Reciprocity relations for interference coatings","authors":"A. Sotsky, E. Chudakov","doi":"10.29235/1561-2430-2023-59-2-158-167","DOIUrl":"https://doi.org/10.29235/1561-2430-2023-59-2-158-167","url":null,"abstract":"By analyzing the wave equations, the coincidence of the energy reflection and transmission coefficients for the s- and p-polarization waves is herein substantiated when they are incident on the interference coating from opposite directions. The coating can be characterized by an arbitrary spatial profile of the refractive index, the limiting condition is the absence of optical losses in it. Reciprocity relations are obtained for the energy reflection and transmission coefficients of natural light for a structure in the form of a plane-parallel dielectric plate with interference coatings on its opposite sides. It is shown that when a structure with an absorbing plate is illuminated in opposite directions, the energy reflection coefficients can differ, while the energy transmission coefficients always coincide. Reciprocity relations are applied to the calculation of broadband antireflective interference coatings consisting of alternate layers Nb2O5 and SiO2 deposited on a polycarbonate plate. As a result, their correctness is confirmed and it is shown that the optimized antireflection two-sided interference coating provides approximately a five times lower averaged energy reflection coefficient compared to the optimized one-sided coating. ","PeriodicalId":20584,"journal":{"name":"Proceedings of the National Academy of Sciences of Belarus, Medical series","volume":"76 3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77511075","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we propose a physics-based method of prediction high-energy solar flares (SFs) with the help of neutrino detectors utilizing coherent elastic neutrino-nucleus scattering (CEνNS). The behavior of neutrino beams passing through coupled sunspots (CSs) being the sources of future SFs is investigated. We consider the evolution of left-handed electron neutrino νeL and muon neutrino νμL beams formed in the convective zone after the passage of the Micheev – Smirnov – Wolfenstein resonance. It is assumed that the neutrinos possess the charge radius, the magnetic and anapole moments while the CS magnetic field is vortex, nonhomogeneous and has twisting. Estimations of the weakening of the neutrino beams after traversing the resonant layers are given. It is shown that for SFs this weakening could be registered by neutrino detectors of the second generation only when neutrinos have the Dirac nature.
{"title":"Prediction of solar flares using neutrino detectors of the second generation","authors":"O. Boyarkin, I. Boyarkina","doi":"10.29235/1561-2430-","DOIUrl":"https://doi.org/10.29235/1561-2430-","url":null,"abstract":"In this paper, we propose a physics-based method of prediction high-energy solar flares (SFs) with the help of neutrino detectors utilizing coherent elastic neutrino-nucleus scattering (CEνNS). The behavior of neutrino beams passing through coupled sunspots (CSs) being the sources of future SFs is investigated. We consider the evolution of left-handed electron neutrino νeL and muon neutrino νμL beams formed in the convective zone after the passage of the Micheev – Smirnov – Wolfenstein resonance. It is assumed that the neutrinos possess the charge radius, the magnetic and anapole moments while the CS magnetic field is vortex, nonhomogeneous and has twisting. Estimations of the weakening of the neutrino beams after traversing the resonant layers are given. It is shown that for SFs this weakening could be registered by neutrino detectors of the second generation only when neutrinos have the Dirac nature. ","PeriodicalId":20584,"journal":{"name":"Proceedings of the National Academy of Sciences of Belarus, Medical series","volume":"41 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80361791","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-06DOI: 10.29235/1561-2430-2023-59-2-95-109
N. Y. Kazlouskaya, Y. A. Rovba
Approximation by trigonometric Fourier series is a well-developed branch of the theory of approximation by polynomials. Methods of approximation by rational trigonometric Fourier series have not been researched so deeply yet. In particular, rational trigonometric operators of the Fejér type have not been used in the rational approximation with free poles. In this paper, we consider the approximation of the function | sin | , (0;2), ∈ s x s by rational trigonometric operators of the Fejér type. An integral representation of the remainder for the above-mentioned approximation is obtained. An estimate of approximations is found in the points of analyticity of the function | sin |s x under the condition that the corresponding system of rational functions is complete. It is shown that the order of uniform approximation in the case of approximation by rational Fejér functions with two geometrically different poles is higher than the order of approximation by trigonometric polynomials. As a result, an asymptotic estimation of the uniform approximation by trigonometric Fejér sums in the polynomial case is obtained.
三角傅立叶级数逼近是多项式逼近理论的一个发展良好的分支。有理三角傅里叶级数逼近方法的研究还不够深入。特别地，fejsamir型的有理三角算子在有自由极点的有理逼近中没有被使用。本文考虑函数| sin |，(0;2)，∈s x s用fej型的有理三角算子逼近。得到了上述近似余数的积分表示。在相应的有理函数系完备的条件下，在函数的解析点上发现了近似的估计。结果表明，用两个几何上不同极点的有理fejsamir函数逼近时，均匀逼近的阶数要高于用三角多项式逼近的阶数。得到了多项式情况下用三角fejsamir和的一致逼近的渐近估计。
{"title":"On the approximation of the | sin |s x function by rational trigonometric operators of the Fejér type","authors":"N. Y. Kazlouskaya, Y. A. Rovba","doi":"10.29235/1561-2430-2023-59-2-95-109","DOIUrl":"https://doi.org/10.29235/1561-2430-2023-59-2-95-109","url":null,"abstract":"Approximation by trigonometric Fourier series is a well-developed branch of the theory of approximation by polynomials. Methods of approximation by rational trigonometric Fourier series have not been researched so deeply yet. In particular, rational trigonometric operators of the Fejér type have not been used in the rational approximation with free poles. In this paper, we consider the approximation of the function | sin | , (0;2), ∈ s x s by rational trigonometric operators of the Fejér type. An integral representation of the remainder for the above-mentioned approximation is obtained. An estimate of approximations is found in the points of analyticity of the function | sin |s x under the condition that the corresponding system of rational functions is complete. It is shown that the order of uniform approximation in the case of approximation by rational Fejér functions with two geometrically different poles is higher than the order of approximation by trigonometric polynomials. As a result, an asymptotic estimation of the uniform approximation by trigonometric Fejér sums in the polynomial case is obtained. ","PeriodicalId":20584,"journal":{"name":"Proceedings of the National Academy of Sciences of Belarus, Medical series","volume":"39 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86479814","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-06DOI: 10.29235/1561-2430-2023-59-2-110-120
Chamila-Anuradha Naligama, O. Tsekhan
The objective of this study is to obtain the stabilizability conditions and a stabilizing composite state feedback control for the exponential stabilization of three-time-scale singularly perturbed linear time-invariant systems with multiple commensurate delays in the slow state variables and with two small parameters of perturbation (TSPLTISD). The stabilizability conditions and the stabilizing feedback do not depend on the small parameters and are valid for all of their sufficiently small values. The approach used in this work is the nondegenerate decoupling transformation that splits the TSPLTISD into three regularly dependent on the small parameters subsystems, which are lower in dimensions than the TSPLTISD. Further, the decoupled subsystems are approximated by three subsystems that do not depend on the small parameters. It is proven that the stabilizability of the approximating subsystems guarantees the robust (with respect to small parameters) stabilizability of the original TSPLTISD. Finally, we obtain a representation of a parameter free composite feedback control for the TSPLTISD, stabilizing it for all sufficiently small values of the parameters. A numerical example is given.
{"title":"Robust stabilizability and stabilization of three-time-scale linear time-invariant singularly perturbed systems with delay","authors":"Chamila-Anuradha Naligama, O. Tsekhan","doi":"10.29235/1561-2430-2023-59-2-110-120","DOIUrl":"https://doi.org/10.29235/1561-2430-2023-59-2-110-120","url":null,"abstract":"The objective of this study is to obtain the stabilizability conditions and a stabilizing composite state feedback control for the exponential stabilization of three-time-scale singularly perturbed linear time-invariant systems with multiple commensurate delays in the slow state variables and with two small parameters of perturbation (TSPLTISD). The stabilizability conditions and the stabilizing feedback do not depend on the small parameters and are valid for all of their sufficiently small values. The approach used in this work is the nondegenerate decoupling transformation that splits the TSPLTISD into three regularly dependent on the small parameters subsystems, which are lower in dimensions than the TSPLTISD. Further, the decoupled subsystems are approximated by three subsystems that do not depend on the small parameters. It is proven that the stabilizability of the approximating subsystems guarantees the robust (with respect to small parameters) stabilizability of the original TSPLTISD. Finally, we obtain a representation of a parameter free composite feedback control for the TSPLTISD, stabilizing it for all sufficiently small values of the parameters. A numerical example is given. ","PeriodicalId":20584,"journal":{"name":"Proceedings of the National Academy of Sciences of Belarus, Medical series","volume":"76 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86052998","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-06DOI: 10.29235/1814-6023-2023-20-2-168-176
B. G. Danielova, L. Persin, M. Postnikov, S. Rubnikovich, Y. Denisova, N. Pankratova, A. Rodionova, E. M. Postnikova
The aim of the work was to study the morphological state of the dentition of persons with normal occlusion according to cephalometric X-ray using extraoral parameters.A method for assessing the state of the maxillofacial system using the PoN reference line, PL line, PLV extrafacial vertical line is proposed. Schemes for determining the parameters formed on their basis are presented as well. These parameters will allow diagnosing disorders of maxillofacial system in patients with malocclusions at a higher quality level.The average values of the proposed new parameters were determined and presented in tables using extraoral parameters in persons 7–15 years old with normal occlusion. A comparative analysis of the angular and linear indices of cephalometric images in persons 7–12 and 12–15 years old with normal occlusion showed that with age the tendency of their change is identical to traditional methods.The proposed and studied angular and linear indices of cephalometric images in persons 7–15 years old with normal occlusion using extraoral parameters (PL line and PLV vertical line) are recommended for use in the practical work of orthodontists.
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