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Man vs time: the features of сhrono-fiction in S. Krzhizhanovsky's story "Memories of the Future" 人与时间:S.克日扎诺夫斯基小说《回忆未来》的时空虚构特征
Pub Date : 2022-12-30 DOI: 10.26565/2227-1864-2022-91-10
Tatiana Shekhovtsova, Veronika Yaskova
The purpose of the article is to clarify the features of сhrono-fiction in S. Krzhizhanovsky 's story "Memories of the Future". An understanding of the author's concept and plot function of time travel, a systematic description of different levels of poetics of the story (type of hero, plot-composition structure, space-time structure, narrative organization) are offered.The relevance of the study is determined by the interest of modern literary studies in the problems of science fiction and сhrono-fiction as its variety, as well as the insufficient study of S. Krzhizhanovskyi 's work in this aspect.The plot of the story is subordinated to the idea of time travel and its implementation. The work presents multidimensional time and changing space, but the description of the future as a specific historical epoch does not receive a detailed social and everyday characteristic. The most important thing is the process of movement in time, its experience by the hero and the spiritual evolution of the characters.The storyteller's focus is on the formation of an idea in the hero's mind and its transformation under the influence of the journey. Time becomes a theme, a problem, a hero, a participant in the conflict and the main component of the artistic structure of the story. Time can be attributed to the system of characters of the work, since it is with him that the inventor Sterer, who corresponds to the archetype of a cultural hero, enters into a dispute and a duel. As the plot develops, the relationship between the main character and the surrounding reality, historical time, changes. This is the essence of the plot of formation, to which the hero-inventor and a secondary character - his biographer Stynskyi - are related. Sterer 's transformation is sudden, Stynsky 's transformation is gradual, which ensures the openness of the finale.Chrono-fiction Krzhizhanovsky 's work differs from other authors' сhrono-fiction in that the writer is not interested in either the world of the past or the world of the future. He is interested in the development of the idea within the hero, and the hero within the idea, the struggle with time and its consequences for man. Krzhizhanovsky 's story does not reveal the content of Sterer 's dystopia, which plagued its author. The very fact of its creation as a result of the hero's formation is important.
本文旨在阐明s .克日扎诺夫斯基小说《未来的回忆》的叙事小说特征。通过对作者时间旅行概念和情节功能的理解,对故事的不同诗学层面(主人公类型、情节构成结构、时空结构、叙事组织)进行了系统的描述。现代文学研究对科幻小说和科幻小说-小说的多样性问题的兴趣,以及对s . krzhzhanovsky在这方面的工作的研究不足,决定了研究的相关性。故事情节从属于时间旅行的概念及其实现。作品呈现了多维的时间和变化的空间,但对未来的描述作为一个特定的历史时代,并没有得到详细的社会和日常特征。最重要的是时间运动的过程,主人公的经历和人物的精神演变。故事讲述者关注的是主人公思想的形成及其在旅途影响下的转变。时间成为一个主题,一个问题,一个英雄,一个冲突的参与者和故事艺术结构的主要组成部分。时间可以归因于作品的人物体系,因为正是与他一起,发明家斯特尔,一个符合文化英雄原型的人,进入了一场争论和决斗。随着情节的发展,主人公与周围现实、历史时间的关系发生了变化。这是小说情节形成的本质,与主人公发明家和他的传记作者斯廷斯基有关。斯特尔的转变是突然的,斯廷斯基的转变是渐进的,这保证了结局的开放性。克日扎诺夫斯基的作品不同于其他作家的时间小说,他对过去的世界和未来的世界都不感兴趣。他感兴趣的是英雄思想的发展,英雄思想的发展,与时间的斗争及其对人类的影响。柯日扎诺夫斯基的故事并没有揭示困扰作者的斯特尔反乌托邦的内容。它的创造是英雄形成的结果,这一事实非常重要。
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引用次数: 0
Target orientations of the development of state policy for the sustainable development of the "green" economy in Ukraine 乌克兰“绿色”经济可持续发展国家政策发展的目标方向
Pub Date : 2022-12-30 DOI: 10.26565/2311-2379-2022-103-15
Y. Bilovitska
The purpose of the article is to determine the target guidelines for the state policy of sustainable development of the "green" economy in Ukraine. The article uses general scientific and special research methods, the use of which contributed to the solution of the problem in the process of obtaining theoretical and practical results. When studying literary sources, the monographic method was used. The study of concepts, developments, approaches in order to generalize the results of scientific developments of domestic and foreign researchers to solve the problems of formation and implementation of the state policy for the sustainable development of the "green" economy, the method of systematization was used. The methods of classification, induction and deduction were used to determine the targets to which the state policy of sustainable development of the "green" economy should be directed. The abstract-logical method is used for theoretical generalizations and the formation of conclusions. It is proved that the complexity of the problem of formation and implementation of the state policy for the sustainable development of the "green" economy provides for the use of a long-term strategic approach, which will harmoniously integrate such a policy into the public administration system of Ukraine, which is in the process of reforming and adapting to European legislation, which is supported by a number of international obligations. It has been determined that the goal of state policy is to stabilize and improve the state of the environment of Ukraine in order to create an environmentally friendly natural environment for the life and health of the population, the introduction of an ecologically balanced system of nature management and the conservation of natural ecosystems, which are important for all life on planet Earth. The article proposes the Conceptual provisions for the development of a strategy for the state policy of sustainable development of the "green" economy in Ukraine, providing for a gradual move away from the traditional economy (with its areas of activity that are not energy and resource efficient and pollute the environment) to the "green" economy (which is based on qualitative structural shifts, innovative activities and industries that do not harm the environment, efficient use of natural resources, etc.).
本文旨在确定乌克兰“绿色”经济可持续发展国家政策的目标指导方针。文章采用了一般科学和专门的研究方法,在获得理论和实践成果的过程中,这些方法的使用有助于问题的解决。在研究文献来源时,采用了专题研究的方法。概念、发展、方法的研究为了总结国内外研究人员的科学发展成果,解决国家政策的形成和实施问题,采用了系统化的方法,实现“绿色”经济的可持续发展。采用分类法、归纳法和演绎法确定了“绿色”经济可持续发展国家政策应指向的目标。抽象逻辑方法用于理论概括和结论的形成。事实证明,“绿色”经济可持续发展国家政策的形成和实施问题的复杂性为使用长期战略方法提供了条件,这将使这一政策与乌克兰的公共行政系统和谐地结合起来,乌克兰正处于改革和适应欧洲立法的过程中,这得到了一些国际义务的支持。已经确定,国家政策的目标是稳定和改善乌克兰的环境状况,为人民的生命和健康创造一个环境友好的自然环境,建立一个生态平衡的自然管理系统,保护自然生态系统,这对地球上的所有生命都很重要。文章提出了制定乌克兰“绿色”经济可持续发展国家政策战略的概念性规定,规定逐步从传统经济(其活动领域能源和资源效率不高,污染环境)转向“绿色”经济(其基础是质量结构转变、创新活动和不损害环境的产业、有效利用自然资源等)。
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引用次数: 0
Trends in the spread of excessive economic inequality in the modern world and prospects for overcoming it 现代世界过度经济不平等的蔓延趋势和克服这种不平等的前景
Pub Date : 2022-12-30 DOI: 10.26565/2311-2379-2022-103-03
T. Kim, H. Ilin
The study is devoted to the problem of excessive economic inequality, which leads to lagging behind developing countries, especially the countries with lower middle and low income, to an increase in the population at the level of extreme poverty, depriving them of the opportunity to receive education, decent work, and income to ensure the quality of life. Based on the Madison Project's database of historical statistics, the authors show that since the 1820s, economic disparity between developed and developing countries has steadily increased. And since the 1960s, this inequality in the level of economic development, measured by the average GDP per capita according to the PPP, began to grow rapidly. The authors put forward assumptions about the negative impact on this trend of international economic and financial institutions, which, through cooperation with developing countries, implement liberal principles in the domestic and foreign policies of these countries. Economic liberalization was carried out by all developed countries to overcome the public financial crisis caused by excessive public spending on economic growth and social protection in the 1970s. Later, international organizations began to transfer this experience to countries with economies in transition and developing countries in the form of stabilization programs, development programs, etc. But the consequence of liberal reforms in these countries was the destruction of their economic systems, institutions, values, culture, and even the memory of the historical path which makes them weaker and more dependent. Analyzing changes in such indicators as the average GDP per capita according to the PPP of the countries of the world, the incomes of various categories of the population, the trade balance index, the index of the economic complexity of the country's exports, the authors prove that the economic inequality between the countries of the Western Branch and Western Europe (according to Maddison's classification) and all other countries at these only increases. Therefore, the implementation of the unified liberal recommendations of international organizations to improve economic mechanisms and state and social institutions in most countries of the world has devastating consequences: loss of competitiveness, technological backwardness, negative trade balance, public debt, inflation, unemployment, and the growth of excessive economic inequality. To overcome it, the countries of the world should apply certain balanced instruments of protectionist policy.
这项研究致力于解决过度的经济不平等问题,这导致落后于发展中国家,特别是中低收入国家,导致极端贫困人口增加,剥夺了他们接受教育、体面工作和收入以确保生活质量的机会。根据麦迪逊项目的历史统计数据库,作者表明,自19世纪20年代以来,发达国家和发展中国家之间的经济差距稳步扩大。自20世纪60年代以来,这种经济发展水平的不平等,以购买力平价的人均GDP衡量,开始迅速增长。作者对国际经济和金融机构对这一趋势的负面影响提出了假设,这些机构通过与发展中国家的合作,在这些国家的国内外政策中执行自由主义原则。经济自由化是所有发达国家在20世纪70年代为克服经济增长和社会保护方面的过度公共支出造成的公共财政危机而进行的。后来,国际组织开始以稳定计划、发展计划等形式将这一经验传授给经济转型期国家和发展中国家。但这些国家自由改革的后果是破坏了它们的经济制度、制度、价值观、文化,甚至是对历史路径的记忆,这使他们变得更弱、更依赖。分析根据世界各国购买力平价计算的人均国内生产总值、各类人口收入、贸易平衡指数、国家出口经济复杂性指数等指标的变化,作者证明,在这一点上,西方分支和西欧国家(根据麦迪森的分类)与所有其他国家之间的经济不平等只会加剧。因此,在世界上大多数国家,执行国际组织关于改善经济机制、国家和社会机构的统一自由主义建议会产生毁灭性后果:竞争力丧失、技术落后、贸易负平衡、公共债务、通货膨胀、失业和经济不平等加剧。为了克服这一问题,世界各国应采用某些平衡的保护主义政策工具。
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引用次数: 0
Transformation of the social-economic and political values in Ukraine to the European Union values 乌克兰社会经济和政治价值观向欧盟价值观的转变
Pub Date : 2022-12-30 DOI: 10.26565/2311-2379-2022-103-01
Міжнародна економіка, O. Nosova
The article aims to analyze basic value approaches and define the main and decisive factors of values transformation. The research methods include descriptive analysis, institutional approach, and economic and statistical methods. The hypothesis of the study is to study how public perceptions have changed in extreme conditions (military conflict) towards European integration values. The broad scope of economic and sociological works reveals the necessity of a special analysis of the European integration and regional values adaptation in Ukraine and defines the problem for study, use, and dissemination of knowledge of the European Union values. The analysis of various value theories identifies the urgency and necessity of human behavior from the human value estimation study. We estimate how economic development depends on economic, political, and social values transformation and the overall indicators (market and democracy) reforms in Ukraine. We apply data from surveys to the comparing the population’s attitude toward European values since Ukrainian independence. The designation of core values allows formulating a strategy and intensifying a more sustainable strategy of political and social-economic development.
本文旨在分析价值转换的基本途径,界定价值转换的主要和决定性因素。研究方法包括描述性分析、制度方法、经济和统计方法。该研究的假设是研究公众在极端条件下(军事冲突)对欧洲一体化价值观的看法是如何变化的。广泛的经济和社会学著作揭示了对乌克兰的欧洲一体化和区域价值观适应进行专门分析的必要性,并定义了研究、使用和传播欧盟价值观知识的问题。通过对各种价值理论的分析,从人的价值估计研究中确定了人的行为的紧迫性和必要性。我们估计经济发展如何取决于乌克兰的经济、政治和社会价值观转变以及总体指标(市场和民主)改革。我们将调查数据应用于比较乌克兰独立以来民众对欧洲价值观的态度。指定核心价值观可以制定一项战略,并加强更可持续的政治和社会经济发展战略。
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引用次数: 2
Notes on two lyrics by Lina Kostenko 莉娜·科斯滕科对两首歌词的注释
Pub Date : 2022-12-30 DOI: 10.26565/2227-1864-2022-91-08
J. Wright
Many of the lyrics of Lina Kostenko are so immediately engaging that a reader may fail to notice their great complexity and internal structure. In the present article, the author analyzes two such lyrics in some detail, using techniques that might be called structuralist. The analyses, however, begin with no pre-selected methodological framework, but simply start where the lyrics themselves seem to suggest and follow that thread of thought, examining various aspects of the poems. The interpretations built on these analyses are significantly richer than a superficial reading would allow, and therefore, the results may be of interest not only to scholars of Ukrainian poetry, but to the general reader, as well. In the first lyric examined, two lines that are almost lexically identical lead to an examination of a complex mirror-structure that reveals a picture of a continuum between the extremes of metaphor and metonym. A morphological peculiarity of the poem then reveals that it is a response and rebuke to a lyric by the Russian poet Fyodor Tyutchev. With attention paid to the poem’s intricate structure and to the work to which it is a response, the analysis reveals that Kostenko’s lyric may have an anti-imperial meaning that was invisible to the authorities at the time of its publication.In the analysis of the second lyrics, the author begins with a large and memorable rhyme-set, examination of which leads to observations that reveal the unusual self-similar structure of the poem. Further analysis reveals the poem to be a work of verbal art that functions on multiple levels of organization at the same time. After the two analyses, the author makes broader remarks about his general impression of Kostenko’s extremely masterful work, a brief suggestion about introducing this work to anglophone students of Ukrainian literature, and a suggestion for future work on Kostenko’s poetry.
莉娜·科斯坚科的许多歌词是如此引人入胜,以至于读者可能没有注意到它们的复杂性和内部结构。在这篇文章中,作者运用结构主义的技巧对这两首歌词进行了详细的分析。然而,分析没有预先选择的方法框架,而是简单地从歌词本身似乎暗示的地方开始,并遵循这条思路,检查诗歌的各个方面。建立在这些分析上的解释比肤浅的阅读要丰富得多,因此,结果可能不仅对乌克兰诗歌学者感兴趣,而且对普通读者也感兴趣。在研究的第一首抒情诗中,两行几乎在词汇上相同的句子导致了对复杂镜像结构的研究,揭示了隐喻和转喻两个极端之间连续统一体的图景。这首诗的词形特征揭示了它是对俄罗斯诗人费奥多尔·秋切夫(Fyodor Tyutchev)的一首抒情诗的回应和谴责。通过对这首诗复杂的结构和它所回应的作品的关注,分析揭示了科斯坚科的歌词可能具有一种反帝国主义的含义,而这种含义在出版时是当局所看不到的。在对第二首歌词的分析中,作者从一个庞大而令人难忘的押韵集开始,通过对押韵集的研究,作者发现了这首诗不同寻常的自相似结构。进一步的分析表明,这首诗是一种语言艺术,同时在多个层次的组织中起作用。在这两方面的分析之后,作者对科斯坚科这部极其精湛的作品的总体印象作了更广泛的评论,并就如何向学习乌克兰文学的英语学生介绍这部作品提出了简短的建议,并对今后研究科斯坚科诗歌的工作提出了建议。
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引用次数: 0
Research of cross-cultural management of business activities in European markets 欧洲市场商业活动的跨文化管理研究
Pub Date : 2022-12-30 DOI: 10.26565/2311-2379-2022-103-04
V. Yevtushenko, E. Lisenyi, Vu Zieu Lin
Globalization of business, promotion of economic interests to the markets of other countries, processes of unification and creation of common economic space require knowledge of national customs and national culture. Culture is, first of all, predictability. The ability to understand and use the features of national cultures, interpersonal communications and business ethics in global business is an important task of cross-cultural management. The success of international companies in Europe in providing high quality products and services depends, on the one hand, on the dynamics of the growing economic environment and, on the other hand, on the adoption of global quality standards and procedures. As the European market becomes more and more global, the products and services offered by international companies around the world face the challenges of a multicultural environment, not only at the level of customer relations, but also deep inside the companies, at the level of employees. The article describes the characteristics of cross-cultural management of enterprises in the European markets, identifies the barriers to its implementation, and considers the most effective solutions in the field of cross-cultural personnel management. Cross-cultural management of enterprises in the European markets is, first of all, the creation and application of technologies for managing cultural diversity in the context of globalization, which successfully operate in different cultures, prevention of intercultural conflicts. As a solution, the development of intercultural competencies, training of global managers in Europe in key aspects of intercultural interaction, introduction and active use of advanced digital technologies, as well as building a management system are proposed. Knowledge management provides the necessary technological support for cross-cultural management of European enterprises to improve knowledge sharing, their effective use in the activities of multinational companies and international joint ventures in Europe.
商业全球化、向其他国家市场促进经济利益、统一进程和创造共同经济空间,都需要了解民族风俗和民族文化。文化首先是可预测的。在全球商业中理解和运用民族文化、人际交往和商业道德的特点是跨文化管理的一项重要任务。在欧洲的国际公司能否成功提供高质量的产品和服务,一方面取决于不断增长的经济环境的动态,另一方面也取决于全球质量标准和程序的采用。随着欧洲市场变得越来越全球化,世界各地的国际公司提供的产品和服务面临着多元文化环境的挑战,不仅在客户关系层面,而且在公司内部和员工层面。本文描述了欧洲市场企业跨文化管理的特点,确定了实施跨文化管理所面临的障碍,并考虑了跨文化人事管理领域最有效的解决方案。欧洲市场企业的跨文化管理首先是在全球化背景下创造和应用管理文化多样性的技术,这些技术在不同文化中成功运作,防止文化间冲突。作为一种解决方案,建议发展跨文化能力,在跨文化互动的关键方面培训欧洲的全球管理人员,引入和积极使用先进的数字技术,以及建立管理系统。知识管理为欧洲企业的跨文化管理提供了必要的技术支持,以改善知识共享,并在跨国公司和国际合资企业在欧洲的活动中有效利用知识。
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引用次数: 1
Clinical trials market: state and prospects, IT segment 临床试验市场:现状和前景,IT部门
Pub Date : 2022-12-30 DOI: 10.26565/2311-2379-2022-103-07
The article provides an overview of the development of the global and Ukrainian clinical trials market and indicates that the field of clinical research is very promising and its development correlates with the development of technologies in the world, which in turn are developing quickly and successfully. The COVID-19 pandemic has shown that global pharmaceuticals, applying the best clinical research methods, are able to find effective solutions in very short periods of time. The market is stable, because it refers to the protection of human health. According to forecasts, the clinical trials market will grow along with the growth of investments in it. Ukraine has a good medical base with a large infrastructure and a fairly developed IT sector, which makes it promising to open contract research organizations (CROs) in the country, in particular, those specialized in statistical analysis of research and clinical programming. A large number of CROs, including those in Ukraine, cooperate with large sponsors-corporations, which are mostly foreign ones. This helps develop the domestic economic market and provides a high level of income for employees, because the industry is highly specialized and high-tech. The authors offer a basic model of IT project dynamics, which reflects the process of its implementation and allows displaying the dynamics of various indicators (given the total number of project tasks). The object of simulation is a newly established IT firm (startup), and a typical project faced by a statistical CRO is considered. The model can be used for planning short-term or long-term activities of the firm in the field of clinical research. Since the market and the field of clinical research as a whole is developing and growing, starting one’s own CRO with statistical specialization can be considered as a promising business in Ukraine.
本文概述了全球和乌克兰临床试验市场的发展情况,指出临床研究领域非常有前景,其发展与世界技术发展密切相关,而世界技术发展又迅速而成功。COVID-19大流行表明,全球制药公司采用最佳临床研究方法,能够在很短的时间内找到有效的解决方案。市场稳定,因为它指的是对人体健康的保护。据预测,临床试验市场将随着投资的增长而增长。乌克兰拥有良好的医疗基础设施和相当发达的信息技术部门,因此有望在该国开设合同研究组织,特别是专门从事研究统计分析和临床方案编制的合同研究组织。包括乌克兰的cro在内的大量cro与大型赞助公司合作,而这些赞助公司大多是外国公司。这有助于发展国内经济市场,并为员工提供高水平的收入,因为该行业高度专业化和高科技。作者提供了一个IT项目动态的基本模型,该模型反映了其实现的过程,并允许显示各种指标的动态(给定项目任务的总数)。模拟的对象是一家新成立的IT公司(创业公司),并考虑了统计CRO面临的一个典型项目。该模型可用于规划公司在临床研究领域的短期或长期活动。由于市场和临床研究领域作为一个整体正在发展和成长,在乌克兰开始自己的统计专业CRO可以被认为是一个有前途的业务。
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引用次数: 0
The explicit form of the switching surface in admissible synthesis problem 可容许综合问题中开关曲面的显式形式
Pub Date : 2022-12-24 DOI: 10.26565/2221-5646-2022-96-03
V. I. Korobov, O. Vozniak
In this article we consider the problem related to positional synthesis and controllability function method and more precisely to admissible maximum principle. Unlike the more common approach the admissible maximum principle method gives discontinuous solutions to the positional synthesis problem. Let us consider the canonical system of linear equations $dot{x}_i=x_{i+1}, i=overline{1,n-1}, dot{x}_n=u$ with constraints $|u| le d$. The problem for an arbitrary linear system $dot{x} = A x + b u$ can be simplified to this problem for the canonical system. A controllability function $Theta(x)$ is given as a unique positive solution of some equation $Phi(x,Theta) = 0$. The control is chosen to minimize derivative of the function $Theta(x)$ and can be written as $u(x) = -d text{ sign}(s(x,Theta(x)))$. The set of points $s(x,Theta(x)) = 0$ is called the switching surface, and it determines the points where control changes its sign. Normally it mbox{contains} the variable $Theta$ which is given implicitly as the solution of equation $Phi(x, Theta) = 0$. Our aim in this paper is to find a representation of the switching surface that does not depend on the function $Theta(x)$. We call this representation the explicit form. In our case the expressions $Phi(x, Theta)$ and $s(x, Theta)$ are both polynomials with respect to $Theta$, so this problem is related to the problem of finding conditions when two polynomials have a common positive root. Earlier the solution for the 2-dimensional case was known. But during the exploration it was found out that for systems of higher dimensions there exist certain difficulties. In this article the switching surface for the three dimensional case is presented and researched. It is shown that this switching surface is a sliding surface (according to Filippov's definition). Also the other ways of constructing the switching surface using the interpolation and approximation are proposed and used for finding the trajectories of concrete points.
本文考虑了位置综合和可控性函数法的相关问题,更确切地说,考虑了可容许最大值原理。与一般的方法不同,可容许极大原理法给出了位置综合问题的不连续解。让我们考虑带约束的正则线性方程组$dot{x}_i=x_{i+1}, i=overline{1,n-1}, dot{x}_n=u$$|u| le d$。对于任意线性系统$dot{x} = A x + b u$的问题可以简化为正则系统的问题。给出了可控性函数$Theta(x)$作为方程$Phi(x,Theta) = 0$的唯一正解。选择控制以最小化函数$Theta(x)$的导数,可以写成$u(x) = -d text{ sign}(s(x,Theta(x)))$。点的集合$s(x,Theta(x)) = 0$被称为切换面,它决定了控制改变其符号的点。通常是mbox{contains}变量$Theta$隐式地给出方程$Phi(x, Theta) = 0$的解。我们在本文中的目标是找到不依赖于$Theta(x)$函数的切换曲面的表示。我们称这种表示为显式。在我们的例子中,表达式$Phi(x, Theta)$和$s(x, Theta)$都是关于$Theta$的多项式,所以这个问题与寻找两个多项式有一个公正根的条件有关。之前二维情况的解是已知的。但在探索过程中发现,对于高维系统存在一定的困难。本文提出并研究了三维情况下的开关曲面。证明了该开关曲面是一个滑动曲面(根据Filippov的定义)。此外,还提出了利用插值法和近似法构造切换曲面的其他方法,并将其用于寻找具体点的轨迹。
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引用次数: 0
Homogeneous approximation for minimal realizations of series of iterated integrals 迭代积分级数最小实现的齐次逼近
Pub Date : 2022-12-24 DOI: 10.26565/2221-5646-2022-96-02
D. M. Andreieva, S. Ignatovich
In the paper, realizable series of iterated integrals with scalar coefficients are considered and an algebraic approach to the homogeneous approximation problem for nonlinear control systems with output is developed. In the first section we recall the concept of the homogeneous approximation of a nonlinear control system which is linear w.r.t. the control and the concept of the series of iterated integrals. In the second section the statement of the realizability problem is given, a criterion for realizability and a method for constructing a minimal realization of the series are recalled. Also we recall some ideas of the algebraic approach to the description of the homogeneous approximation: the free graded associative algebra, which is isomorphic to the algebra of iterated integrals, the free Lie algebra, the Poincar'{e}-Birkhoff-Witt basis, the dual basis and its construction by use of the shuffle product, the definition of the core Lie subalgebra, which defines the homogeneous approximation of a control system. In the third section we show how to find the core Lie subalgebra of the systems that is a realization of the one-dimensional series of iterated integrals without finding the system itself. The result obtained is illustrated by the example, in which we demonstrate two methods for finding the core Lie subalgebra of the realizing system. In the last section it is shown that for any graded Lie subalgebra of finite codimension there exists a one-dimensional homogeneous series such that this Lie subalgebra is the core Lie subalgebra for its minimal realization. The proof is constructive: we give a method of finding such a series; we use the dual basis to the Poincar'{e}-Birkhoff-Witt basis of the free associative algebra, which is built by the core Lie subalgebra, and the shuffle product in this algebra. As a consequence, we get a classification of all possible homogeneous approximations of systems that are realizations of one-dimensional series of iterated integrals.
本文考虑了标量系数迭代积分的可实现级数,提出了一种具有输出的非线性控制系统齐次逼近问题的代数方法。在第一部分中,我们回顾了线性非线性控制系统的齐次逼近的概念,以及控制和迭代积分级数的概念。第二部分给出了可实现性问题的表述,给出了可实现性的判据和构造该级数的最小可实现的方法。我们还回顾了描述齐次逼近的代数方法的一些思想:与迭代积分代数同构的自由梯度结合代数,自由李代数,庞加莱-伯克霍夫-维特基,对偶基及其用洗牌积的构造,核心李子代数的定义,它定义了控制系统的齐次逼近。在第三节中,我们展示了如何在不找到系统本身的情况下找到系统的核心李子代数,即一维迭代积分序列的实现。通过算例说明了所得到的结果,并给出了求实现系统核心李子代数的两种方法。在最后一节中,我们证明了对于任何有限余维的阶李子代数,存在一个一维齐次级数,使得该李子代数是其最小实现的核心李子代数。证明是建设性的:我们给出了一种求这样一个级数的方法;利用核心李子代数建立的自由结合代数的Poincar {e}-Birkhoff-Witt基的对偶基,以及该代数中的shuffle积。因此,我们得到了所有可能的齐次逼近系统的分类,这些系统是一维迭代积分序列的实现。
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引用次数: 0
Vyacheslav O. Rezunenko (1941 - 2022) Obituary
Pub Date : 2022-12-07 DOI: 10.26565/2221-5646-2022-96-04
V. I. Korobov, O. Lazorenko, S. O. Masalov, A. Rezounenko
On August 28, 2022, a docent at the Department of High mathematics and informatics of V. N. Karazin Kharkiv National University Vyacheslav Oleksijovich Rezunenko passed away. The bright memory of Vyacheslav Oleksijovich Rezunenko, a real scientist and a wonderful man, forever remains in the hearts of his colleagues, students and friends.
2022年8月28日,哈尔科夫国立大学高等数学与信息系讲解员维亚切斯拉夫·奥列克西约维奇·列祖年科去世。维亚切斯拉夫·奥列克西约维奇·列祖年科是一位真正的科学家,一位了不起的人,他的光辉记忆永远留在他的同事、学生和朋友们的心中。
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引用次数: 0
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Visnik Kharkivs''kogo natsional''nogo universitetu imeni VN Karazina Seriia Ekonomika
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