Pub Date : 2023-05-03DOI: 10.29235/2524-2369-2023-68-2-123-129
I. U. Yalyntsava
The article is devoted to the comparative study of the modern Russian and Belarusian languages at the morphemic level. It is proved that it is the contrastive study that makes it possible to reveal the features of the morphemic organization of the equivalent lexical units of the Russian and Belarusian languages, to clearly see the real degree of lexical coincidence and mismatch of closely related languages using the example of morphemic word structures. The article gives a classification of interlingual Russian and Belarusian adjective color correlates depending on the nature of their morphemic structure. The coincidence of both the structures themselves as a whole and individual morphemes, as well as their specific differences, which indicates the national specificity of each of the compared closely related languages. The conclusion is made about the importance of this type of research in solving an urgent problem in Russian linguistics – establishing the similarity and difference between two closely related languages at the morphemic level, which will contribute to a deeper understanding of the ways of development of the word-formation systems of the Belarusian and Russian languages, the features of their correlation and interaction in the conditions of state bilingualism.
{"title":"Morphemic structure of russian and belarusian adjective color names: general and specific","authors":"I. U. Yalyntsava","doi":"10.29235/2524-2369-2023-68-2-123-129","DOIUrl":"https://doi.org/10.29235/2524-2369-2023-68-2-123-129","url":null,"abstract":"The article is devoted to the comparative study of the modern Russian and Belarusian languages at the morphemic level. It is proved that it is the contrastive study that makes it possible to reveal the features of the morphemic organization of the equivalent lexical units of the Russian and Belarusian languages, to clearly see the real degree of lexical coincidence and mismatch of closely related languages using the example of morphemic word structures. The article gives a classification of interlingual Russian and Belarusian adjective color correlates depending on the nature of their morphemic structure. The coincidence of both the structures themselves as a whole and individual morphemes, as well as their specific differences, which indicates the national specificity of each of the compared closely related languages. The conclusion is made about the importance of this type of research in solving an urgent problem in Russian linguistics – establishing the similarity and difference between two closely related languages at the morphemic level, which will contribute to a deeper understanding of the ways of development of the word-formation systems of the Belarusian and Russian languages, the features of their correlation and interaction in the conditions of state bilingualism. ","PeriodicalId":20584,"journal":{"name":"Proceedings of the National Academy of Sciences of Belarus, Medical series","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83368591","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 : 2023-05-03DOI: 10.29235/2524-2369-2023-68-2-104-111
N. Balich
The article presents conceptual foundations of a theoretical and applied study of life strategies of the rural youth. An integral model for the analysis of life strategies has been proposed, aimed at identifying the main factors that shape, promote and hinder the implementation of various youth strategies in the context of life plans and orientations, requests, motivations, values of this social group, as well as taking into account the needs and prospects for the development of rural areas, agrarian industries. A method of empirical study of the life strategies of the rural youth has been proposed in the form of a scheme with the allocation of specific components of the analysis of socio-economic, socio-cultural and leisure, consumer strategies, as well as strategies for professional self-realization. Particular attention is paid to the demand for methods of managing regional development: strategic planning, project approach, which are used after studying of scientific literature and conducting surveys among the local population to model the socio-cultural development of rural areas on the basis of public opinion, statistical indicators of economic, social, cultural development. The importance of applying an interdisciplinary approach is noted, with taking into account the specifics of a particular region and the socio-demographic characteristics of young people, the need to develop indicators for assessing the effectiveness of the functioning of the economy, culture, education, healthcare both in the republic and in its rural areas, regions.
{"title":"Conceptual foundations of research of life strategies of rural youth in Belarus","authors":"N. Balich","doi":"10.29235/2524-2369-2023-68-2-104-111","DOIUrl":"https://doi.org/10.29235/2524-2369-2023-68-2-104-111","url":null,"abstract":"The article presents conceptual foundations of a theoretical and applied study of life strategies of the rural youth. An integral model for the analysis of life strategies has been proposed, aimed at identifying the main factors that shape, promote and hinder the implementation of various youth strategies in the context of life plans and orientations, requests, motivations, values of this social group, as well as taking into account the needs and prospects for the development of rural areas, agrarian industries. A method of empirical study of the life strategies of the rural youth has been proposed in the form of a scheme with the allocation of specific components of the analysis of socio-economic, socio-cultural and leisure, consumer strategies, as well as strategies for professional self-realization. Particular attention is paid to the demand for methods of managing regional development: strategic planning, project approach, which are used after studying of scientific literature and conducting surveys among the local population to model the socio-cultural development of rural areas on the basis of public opinion, statistical indicators of economic, social, cultural development. The importance of applying an interdisciplinary approach is noted, with taking into account the specifics of a particular region and the socio-demographic characteristics of young people, the need to develop indicators for assessing the effectiveness of the functioning of the economy, culture, education, healthcare both in the republic and in its rural areas, regions. ","PeriodicalId":20584,"journal":{"name":"Proceedings of the National Academy of Sciences of Belarus, Medical series","volume":"107 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74936854","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 : 2023-05-03DOI: 10.29235/2524-2369-2023-68-2-112-122
V. N. Borovskaya
The article draws attention to the issue of opening transit along the river the Neman in Soviet-Polish relations 1921–1931. The solution of the issue was complicated by tense Polish-Lithuanian relations due to the unresolved territorial disputes between the parties. Organization of free transit along the river the Neman was important not only for establishing favorable trade relations between Poland and the Soviet state. The political and economic interests of the Soviet republics were significantly complicated by the uncertain status of the Neman: its declaration as an international river from Grodno to the mouth allowed Western states to interfere in the internal affairs of Lithuania and link Poland with Memel, regardless of the implementation of the Hymans plan. The signing of the Riga Peace Treaty and the beginning of the New Economic Policy became the starting point in a gradual process of transition from a real assessment of the international situation, but the foreign policy actions of the Soviet state were, as before, contradictory. The unresolved status of the disputed territories was added, which increased the level of conflict in the region. The nomination of the USSR of new requirements to the Polish leadership on the passage of wood along the river Neman did not lead desired results. Neither the Polish-Lithuanian negotiations in September-October 1925, nor the Soviet-Lithuanian meeting in November-December 1925 changed the case of timber rafting along the Neman.
{"title":"The issue of opening transit along the river Neman in the system of Soviet-Polish relations (1921–1931)","authors":"V. N. Borovskaya","doi":"10.29235/2524-2369-2023-68-2-112-122","DOIUrl":"https://doi.org/10.29235/2524-2369-2023-68-2-112-122","url":null,"abstract":"The article draws attention to the issue of opening transit along the river the Neman in Soviet-Polish relations 1921–1931. The solution of the issue was complicated by tense Polish-Lithuanian relations due to the unresolved territorial disputes between the parties. Organization of free transit along the river the Neman was important not only for establishing favorable trade relations between Poland and the Soviet state. The political and economic interests of the Soviet republics were significantly complicated by the uncertain status of the Neman: its declaration as an international river from Grodno to the mouth allowed Western states to interfere in the internal affairs of Lithuania and link Poland with Memel, regardless of the implementation of the Hymans plan. The signing of the Riga Peace Treaty and the beginning of the New Economic Policy became the starting point in a gradual process of transition from a real assessment of the international situation, but the foreign policy actions of the Soviet state were, as before, contradictory. The unresolved status of the disputed territories was added, which increased the level of conflict in the region. The nomination of the USSR of new requirements to the Polish leadership on the passage of wood along the river Neman did not lead desired results. Neither the Polish-Lithuanian negotiations in September-October 1925, nor the Soviet-Lithuanian meeting in November-December 1925 changed the case of timber rafting along the Neman. ","PeriodicalId":20584,"journal":{"name":"Proceedings of the National Academy of Sciences of Belarus, Medical series","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86777300","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 : 2023-05-03DOI: 10.29235/2524-2369-2023-68-2-95-103
O. Y. Knaus
The period of the second half of the XX – beginning of the XXI centuries is marked by the creation of new forms of dialogue between the Eastern and Western Christian Churches. The conceptual basis for the communication of confessions is openness, the desire to know the “Other”, overcoming the difficulties of dialogue, mutual respect, and the desire for unity. In the religious space of the Republic of Belarus, the Orthodox and Roman Catholic denominations form the core of the religious structure of society. The interaction of the Churches lies in several planes: social, theological, cultural and educational. The purpose of this study is to identify the main manifestations and features of the institutional Orthodox-Catholic dialogue in the Republic of Belarus. The study is based on material from the official media of the Orthodox and Roman Catholic Churches. The author comes to the conclusion that a significant role in the development of communications between confessions belongs to the Orthodox hierarch – Metropolitan Philaret (Vakhromeev), the first Patriarchal Exarch of All Belarus and the Hero of Belarus. The thirty-year period under consideration (the period of existence of sovereign Belarus) is divided by the author into two stages: 1990–2015 – centralization of dialogue, conditionally since 2016 – decentralization of communications.
{"title":"Dynamics of the development of the orthodox-catholic institutional dialogue in the Republic of Belarus (1990–2022)","authors":"O. Y. Knaus","doi":"10.29235/2524-2369-2023-68-2-95-103","DOIUrl":"https://doi.org/10.29235/2524-2369-2023-68-2-95-103","url":null,"abstract":"The period of the second half of the XX – beginning of the XXI centuries is marked by the creation of new forms of dialogue between the Eastern and Western Christian Churches. The conceptual basis for the communication of confessions is openness, the desire to know the “Other”, overcoming the difficulties of dialogue, mutual respect, and the desire for unity. In the religious space of the Republic of Belarus, the Orthodox and Roman Catholic denominations form the core of the religious structure of society. The interaction of the Churches lies in several planes: social, theological, cultural and educational. The purpose of this study is to identify the main manifestations and features of the institutional Orthodox-Catholic dialogue in the Republic of Belarus. The study is based on material from the official media of the Orthodox and Roman Catholic Churches. The author comes to the conclusion that a significant role in the development of communications between confessions belongs to the Orthodox hierarch – Metropolitan Philaret (Vakhromeev), the first Patriarchal Exarch of All Belarus and the Hero of Belarus. The thirty-year period under consideration (the period of existence of sovereign Belarus) is divided by the author into two stages: 1990–2015 – centralization of dialogue, conditionally since 2016 – decentralization of communications. ","PeriodicalId":20584,"journal":{"name":"Proceedings of the National Academy of Sciences of Belarus, Medical series","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81425115","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 : 2023-05-03DOI: 10.29235/2524-2369-2023-68-2-130-139
T. Mdivani
New musical and theatrical genres that demonstrate post-non-classical musical thinking are considered. The most common are happening, performance and instrumental theater. Genres are considered differently by V. Petrov, M. Pereverzeva, Yu. Gnirenko and M. Katunyan, but, however, without disclosing their ontology and logical basis. The main distinguishing features of the new stage forms are the openness of the structure, the creative function of the performers and temporal unlimitedness, which indicates the rhizome and rhizome thinking of the composers. It is proposed to consider the new musical and theatrical realities as non-linear, in particular dissipative, based on a non-linear type of determinism – self-determinism. On its basis, a rational construct is established in the form of self-organization (performer), or performing will, which provide the musical material with the quality of integrity. Alternative musical theater is another form of new musical stage genres that have emerged in the post-non-classical era, or in the post-modern era. It is presented by alternative opera and alternative ballet, which establish the aesthetics of consonance, antimimesis and display (instead of experience), as well as the multivariant implementation of the musical and theatrical concept (concert, theater stage, etc.). The works of the American composer D. Cage, the Russian composer V. Martynov, the Belarusian composers V. Kuznetsov, L. Simakovich, A. Korotkina were selected as analytical material.
新的音乐和戏剧流派，证明后非古典音乐思维的考虑。最常见的是发生、表演和器乐戏剧。V. Petrov, M. Pereverzeva, Yu认为类型是不同的。格尼连科和M. Katunyan，但是，没有透露他们的本体论和逻辑基础。新舞台形式的主要特点是结构的开放性、表演者的创作功能和时间的无限性，这表明了作曲家的根茎性和根茎性思维。建议将新的音乐和戏剧现实视为非线性的，特别是耗散的，基于非线性类型的决定论-自我决定论。在此基础上，以自组织(演奏者)或演奏意志的形式建立起理性结构，使音乐材料具有整体性。另类音乐剧是后非古典时代或后现代时代出现的另一种新的音乐舞台类型。它以另类歌剧和另类芭蕾的形式呈现，它们建立了和谐、反模仿和展示(而不是体验)的美学，以及音乐和戏剧概念(音乐会、戏剧舞台等)的多种变体实施。本文选取了美国作曲家凯奇、俄罗斯作曲家马尔丁诺夫、白俄罗斯作曲家库兹涅佐夫、西马科维奇、科罗特基纳的作品作为分析材料。
{"title":"About new stage genres in the music of the second half XX century","authors":"T. Mdivani","doi":"10.29235/2524-2369-2023-68-2-130-139","DOIUrl":"https://doi.org/10.29235/2524-2369-2023-68-2-130-139","url":null,"abstract":"New musical and theatrical genres that demonstrate post-non-classical musical thinking are considered. The most common are happening, performance and instrumental theater. Genres are considered differently by V. Petrov, M. Pereverzeva, Yu. Gnirenko and M. Katunyan, but, however, without disclosing their ontology and logical basis. The main distinguishing features of the new stage forms are the openness of the structure, the creative function of the performers and temporal unlimitedness, which indicates the rhizome and rhizome thinking of the composers. It is proposed to consider the new musical and theatrical realities as non-linear, in particular dissipative, based on a non-linear type of determinism – self-determinism. On its basis, a rational construct is established in the form of self-organization (performer), or performing will, which provide the musical material with the quality of integrity. Alternative musical theater is another form of new musical stage genres that have emerged in the post-non-classical era, or in the post-modern era. It is presented by alternative opera and alternative ballet, which establish the aesthetics of consonance, antimimesis and display (instead of experience), as well as the multivariant implementation of the musical and theatrical concept (concert, theater stage, etc.). The works of the American composer D. Cage, the Russian composer V. Martynov, the Belarusian composers V. Kuznetsov, L. Simakovich, A. Korotkina were selected as analytical material. ","PeriodicalId":20584,"journal":{"name":"Proceedings of the National Academy of Sciences of Belarus, Medical series","volume":"104 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82419179","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 : 2023-04-03DOI: 10.29235/1561-2430-2023-59-1-62-70
V. I. Benediktovich
In recent years, the eigenvalues of the distance matrix of a graph have attracted a lot of attention of mathematicians, since there is a close connection between its spectrum and the structural properties of the graph. Thus, quite recently an interesting result was obtained, relating the Hamiltonicity of a graph to the distance spectral radius of the graph, on the basis of which a more general conjecture about the Hamiltonicity of a graph was formulated. We confirm this conjecture put forward for a k-connected graph, when k Î{2;3}, and also establish similar sufficient conditions for the traceability of a k-connected graph, when k Î{1; 2}.
{"title":"Distance spectral radius and Hamiltonicity of a graph","authors":"V. I. Benediktovich","doi":"10.29235/1561-2430-2023-59-1-62-70","DOIUrl":"https://doi.org/10.29235/1561-2430-2023-59-1-62-70","url":null,"abstract":"In recent years, the eigenvalues of the distance matrix of a graph have attracted a lot of attention of mathematicians, since there is a close connection between its spectrum and the structural properties of the graph. Thus, quite recently an interesting result was obtained, relating the Hamiltonicity of a graph to the distance spectral radius of the graph, on the basis of which a more general conjecture about the Hamiltonicity of a graph was formulated. We confirm this conjecture put forward for a k-connected graph, when k Î{2;3}, and also establish similar sufficient conditions for the traceability of a k-connected graph, when k Î{1; 2}.","PeriodicalId":20584,"journal":{"name":"Proceedings of the National Academy of Sciences of Belarus, Medical series","volume":"362 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76516495","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 : 2023-04-03DOI: 10.29235/1561-2430-2023-59-1-51-61
H. A. Zadarazhniuk
The subject of this paper is the mixing time of random walks on minimal Cayley graphs of complex reflection groups G(m,1,n). The key role in estimating it is played by the coupling of distributions, which has been used before for the same task on symmetric groups. The difficulty with its adaptation for the current case is that there are now two components in a walk, which are to be coupled, and they influence each other’s behaviour. To solve this problem, random walks are split into several blocks for each of which the time needed for their states to match is estimated separately. The result is upper and lower bounds on mixing times of random walks on complex reflection groups, analogous to those obtained by Aldous for a symmetric group.
{"title":"An analogue of Aldous’s theorem on mixing times of a random walk for complex reflection groups","authors":"H. A. Zadarazhniuk","doi":"10.29235/1561-2430-2023-59-1-51-61","DOIUrl":"https://doi.org/10.29235/1561-2430-2023-59-1-51-61","url":null,"abstract":"The subject of this paper is the mixing time of random walks on minimal Cayley graphs of complex reflection groups G(m,1,n). The key role in estimating it is played by the coupling of distributions, which has been used before for the same task on symmetric groups. The difficulty with its adaptation for the current case is that there are now two components in a walk, which are to be coupled, and they influence each other’s behaviour. To solve this problem, random walks are split into several blocks for each of which the time needed for their states to match is estimated separately. The result is upper and lower bounds on mixing times of random walks on complex reflection groups, analogous to those obtained by Aldous for a symmetric group.","PeriodicalId":20584,"journal":{"name":"Proceedings of the National Academy of Sciences of Belarus, Medical series","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89154832","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 : 2023-04-03DOI: 10.29235/1561-2430-2023-59-1-71-80
Y. Kurochkin, I. Rybak
In this paper, we consider the problem of the classical and quantum movement of a charged particle in a two-dimensional Lobachevsky space in the presence of analogues of uniform magnetic and electric fields. Based on this consideration, equations for the conductivity for the classical and quantum Hall effect are obtained. It is shown that in Lobachevsky space the presence of a small electrical field leads to a shift of the stair structure of the quantum Hall conductivity.
{"title":"The Hall effect in Lobachevsky space","authors":"Y. Kurochkin, I. Rybak","doi":"10.29235/1561-2430-2023-59-1-71-80","DOIUrl":"https://doi.org/10.29235/1561-2430-2023-59-1-71-80","url":null,"abstract":"In this paper, we consider the problem of the classical and quantum movement of a charged particle in a two-dimensional Lobachevsky space in the presence of analogues of uniform magnetic and electric fields. Based on this consideration, equations for the conductivity for the classical and quantum Hall effect are obtained. It is shown that in Lobachevsky space the presence of a small electrical field leads to a shift of the stair structure of the quantum Hall conductivity.","PeriodicalId":20584,"journal":{"name":"Proceedings of the National Academy of Sciences of Belarus, Medical series","volume":"32 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83741588","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 : 2023-04-03DOI: 10.29235/1561-2430-2023-59-1-37-50
V. I. Korzyuk, J. V. Rudzko
In this article, we study a mixed problem in a quarter-plane for one system of differential equations, which describes vibrations in the string from viscoelastic material, which corresponds to the Maxwell model. At the bottom of the boundary, we pose the Cauchy conditions, and one of them has a discontinuity of the first kind at one point. We set a smooth boundary condition on the lateral boundary. We derive the Klein – Gordon – Fock equation for one function of the studied system. We use the method of characteristics to build the classical solution as a solution of some integral equation. We prove the uniqueness and establish conditions under which a piecewise smooth solution exists. The Cauchy problem is considered the system’s second function. We determine the conditions under which the solution of the system has sufficient smoothness
在本文中，我们研究了一个四分之一平面上的一个描述粘弹性材料弦振动的微分方程组的混合问题，它符合麦克斯韦模型。在边界的底部，我们提出了柯西条件，其中一个条件在一点上具有第一类不连续。我们在横向边界上设置了光滑边界条件。对于所研究的系统的一个函数，我们导出了Klein - Gordon - Fock方程。我们用特征方法将经典解建立为某积分方程的解。证明了该方法的唯一性，并建立了分段光滑解存在的条件。柯西问题被认为是系统的第二个函数。我们确定了系统解具有足够平滑性的条件
{"title":"Classical solution of a problem for a system of equations from mechanics with nonsmooth Cauchy conditions","authors":"V. I. Korzyuk, J. V. Rudzko","doi":"10.29235/1561-2430-2023-59-1-37-50","DOIUrl":"https://doi.org/10.29235/1561-2430-2023-59-1-37-50","url":null,"abstract":"In this article, we study a mixed problem in a quarter-plane for one system of differential equations, which describes vibrations in the string from viscoelastic material, which corresponds to the Maxwell model. At the bottom of the boundary, we pose the Cauchy conditions, and one of them has a discontinuity of the first kind at one point. We set a smooth boundary condition on the lateral boundary. We derive the Klein – Gordon – Fock equation for one function of the studied system. We use the method of characteristics to build the classical solution as a solution of some integral equation. We prove the uniqueness and establish conditions under which a piecewise smooth solution exists. The Cauchy problem is considered the system’s second function. We determine the conditions under which the solution of the system has sufficient smoothness","PeriodicalId":20584,"journal":{"name":"Proceedings of the National Academy of Sciences of Belarus, Medical series","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84486162","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 : 2023-04-03DOI: 10.29235/1561-2430-2023-59-1-18-36
Yu. V. Trubnikov, M. Chernyavsky
This article is devoted to the development of a numerical-analytical method for constructing extremes in the Chebyshev norm polynomials, given on the square of the complex plane. The studied polynomials are a generalization of the classical Chebyshev polynomials of the first kind. In the complex case there are no classical Chebyshev alternance conditions, and the Kolmogorov criterion along with the Ivanov – Remez criterion are difficult to prove for establishing the extremality property of specific polynomials. On the basis of the subdifferential construction developed by the authors of the article the extremal polinomials on the squares of the complex plane are calculated in an explicit way. The basic research methods are the methods of functional and complex mathematical analysis, as well as the Maple 2021 computer mathematics system. Methods of function theory and some general results of optimization theory are also used.
{"title":"On a numerical-analytical method for constructing extremal polynomials of a complex argument","authors":"Yu. V. Trubnikov, M. Chernyavsky","doi":"10.29235/1561-2430-2023-59-1-18-36","DOIUrl":"https://doi.org/10.29235/1561-2430-2023-59-1-18-36","url":null,"abstract":"This article is devoted to the development of a numerical-analytical method for constructing extremes in the Chebyshev norm polynomials, given on the square of the complex plane. The studied polynomials are a generalization of the classical Chebyshev polynomials of the first kind. In the complex case there are no classical Chebyshev alternance conditions, and the Kolmogorov criterion along with the Ivanov – Remez criterion are difficult to prove for establishing the extremality property of specific polynomials. On the basis of the subdifferential construction developed by the authors of the article the extremal polinomials on the squares of the complex plane are calculated in an explicit way. The basic research methods are the methods of functional and complex mathematical analysis, as well as the Maple 2021 computer mathematics system. Methods of function theory and some general results of optimization theory are also used.","PeriodicalId":20584,"journal":{"name":"Proceedings of the National Academy of Sciences of Belarus, Medical series","volume":"32 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77602331","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}
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