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Small Volume Bodies of Constant Width with Tetrahedral Symmetries
No full textFor every ≥ 2, we construct a body ₙ of constant width 2 in ⁿ with small volume and symmetries of a regular -simplex. ₂ is the Reuleaux triangle. To the best of our knowledge, ₃ was not previously constructed, and its volume is smaller than the volume of other three-dimensional bodies of constant width with tetrahedral symmetries. While the volume of ₃ is slightly larger than the volume of Meissner's bodies of width 2, it exceeds the latter by less than 0.137%. For all large , the volume of ₙ is smaller than the volume of the ball of radius 0.891.We would like to thank anonymous referees for carefully reading the paper and providing valuable feedback. A. Arman acknowledges support in part by a postdoctoral fellowship of the Pacific Institute for the Mathematical Sciences. A. Bondarenko was supported in part by Grant 334466 of the Research Council of Norway, and A. Prymak was supported by NSERC of Canada Discovery Grant RGPIN-2020-05357. D. Radchenko acknowledges funding by the European Union (ERC, FourIntExP, 101078782)
Weak Gauge PDEs
No full textGauge PDEs generalise the AKSZ construction when dealing with generic local gauge theories. Despite being very flexible and invariant, these geometrical objects are usually infinite-dimensional and are difficult to define explicitly, just like standard infinitely-prolonged PDEs. We propose a notion of a weak gauge PDE in which the nilpotency of the BRST differential is relaxed in a controllable way. In this approach, a nontopological local gauge theory can be described in terms of a finite-dimensional geometrical object. Moreover, among the equivalent weak gauge PDEs describing a given system, a minimal one can usually be found and is unique in a certain sense. In the case of a Lagrangian system, the respective weak gauge PDE naturally arises from its weak presymplectic formulation. We prove that any weak gauge PDE determines the standard jet-bundle Batalin-Vilkovisky formulation of the underlying gauge theory, giving an unambiguous physical interpretation of these objects. The formalism is illustrated by a few examples, including the non-Lagrangian self-dual Yang-Mills theory and a finite jet bundle. We also discuss possible applications of the approach to the characterisation of those infinite-dimensional gauge PDEs that correspond to local theories.We wish to thank K. Druzhkov, I. Krasil’shchik, A. Mamekin, M. Markov, A. Verbovetsky, and especially I. Dneprov and A. Kotov for fruitful discussions. The authors are also grateful to the anonymous referees for their valuable suggestions and comments that helped to improve the manuscript. Maxim Grigoriev, supported by the ULYSSE Incentive Grant for Mobility in Scientific Research [MISU] F.6003.24, F.R.S.-FNRS, Belgium, also at Lebedev Physical Institute and Institute for Theoretical and Mathematical Physics, Lomonosov MSU
Uniformity of Strong Asymptotics in Angelesco Systems
No full textLet ₁ and ₂ be two complex-valued Borel measures on the real line such that supp μ₁ = [α₁, ₁] < supp ₂ = [α₂, ₂] and dᵢ()=−ᵢ()d/2πi, where ᵢ() is the restriction to [αᵢ, ᵢ] of a function non-vanishing and holomorphic in some neighborhood of [αᵢ, ᵢ]. Strong asymptotics of multiple orthogonal polynomials is considered as their multi-indices (₁, ₂) tend to infinity in both coordinates. The main goal of this work is to show that the error terms in the asymptotic formulae are uniform with respect to min{₁, ₂}.The research was supported in part by a grant from the Simons Foundation, CGM-706591. The author is grateful to the anonymous referees for their careful reading of the manuscript and helpful suggestions
Δ Invariants of Plumbed Manifolds
No full textWe study the minimal -exponent Δ in the BPS -series Ẑ of negative definite plumbed 3-manifolds equipped with a spinc-structure. We express the Δ of Seifert manifolds in terms of an invariant commonly used in singularity theory. We provide several examples illustrating the interesting behaviour of Δ for non-Seifert manifolds. Finally, we compare Δ invariants with correction terms in Heegaard-Floer homology.We are grateful to Sergei Gukov, Mrunmay Jagadale, and Sunghyuk Park for useful discussions. Wewould also like to thank the anonymous referees for their valuable suggestions. A. Némethi was partially supported by ‘Élvonal (Frontier)’ Grant KKP 144148. J. Svoboda was supported by the Simons Foundation Grant, New structures in low-dimensional topology. S. Harichurn was supported by the 2020 FirstRand FNB Fund Education Scholarship Award and the University of KwaZulu-Natal’s 2024 Vincent Maphai Scholarship Award
Siverian settlement «Monastyryshche»
No full textСтаття присвячена дослідженню роменської археологічної культурі, що існувала протягом VIII–Х ст. на території Дніпровського Лівобережжя і суміжних районів Росії та Білорусі. Роменська культура є одним із компонентів формування давньоруської культури. Носіями роменської культури було східнослов’янське племінне об’єднання сіверян.The article is devoted to the Romanian archaeological culture that existed during the 8th-10th centuries. on the territory of the Dnieper Left Bank and adjacent regions of Russia and Belarus. Romanian culture is one of the components of the formation of ancient Russian culture. The bearers of Roma culture were the East Slavic tribal association of northerners
Strategic principles of personnel management of industrial enterprises in the context of workforce development
No full textСтаття присвячена науковому обґрунтуванню стратегічних засад управління персоналом промислових підприємств у контексті розвитку робочої сили в умовах воєнних і повоєнних трансформацій економіки. Розкрито особливості сучасної кадрової політики промислового сектору, зокрема виклики, пов’язані з дефіцитом кваліфікованих кадрів та цифровізацією HR-процесів. Обґрунтовано, що ключовими напрямами підвищення кадрової стійкості є впровадження людиноцентричних моделей управління, розвиток внутрішніх систем навчання, розширення програм соціального партнерства та адаптація державних стратегій людського розвитку до потреб промисловості. Запропоновано рекомендації щодо вдосконалення кадрової політики підприємств шляхом посилення взаємодії з освітніми інституціями, цифрової трансформації HR-систем і створення механізмів моніторингу компетентностей працівників.The article is devoted to the study of the strategic principles of personnel management of industrial enterprises in the context of workforce development in the context of war and post-war economic transformations. It is determined that the personnel policy of the Ukrainian industry is undergoing significant structural changes under the influence of demographic decline, labor migration, mobilization processes and technological modernization. It is proved that the modern model of personnel management should combine a short-term response to crisis challenges with long-term strategies for the development of human capital. The role of a people-centered approach in personnel policy, which involves the development of competencies, continuous learning, digitalization of HR processes and strengthening of social dialogue, is revealed. It is shown that an effective personnel management strategy should be based on the integration of state and corporate mechanisms, in particular through the development of dual education, the introduction of digital platforms for monitoring competencies and the expansion of partnerships between business and educational institutions. It is substantiated that in the conditions of post-war recovery, personnel security, the development of internal training systems, the creation of flexible forms of employment and the formation of a corporate culture of resilience are of particular importance. The article emphasizes that the modernization of industry is impossible without updating approaches to human resources management, because it is the quality of the workforce that determines the ability of enterprises to innovative growth. Strategic guidelines for enterprises are proposed: the development of internal training systems, the digital transformation of HR processes, the creation of mechanisms for motivating and supporting employees, as well as the integration of social and labor aspects into the strategic planning process. It is concluded that the formation of an effective system of strategic personnel management will contribute to increasing labor productivity, strengthening the human resource potential of industry and ensuring the long-term sustainability of the national economy in the conditions of global competition.Дослідження виконано в межах «Комплексного наукового дослідження щодо актуалізації промислової політики України на принципах Індустрій 4.0 та 5.0» Інституту економіки промисловості НАН України за рахунок бюджетних коштів, спрямованих на забезпечення проведення державними науковими установами наукових досліджень і науково-технічних (експериментальних) розробок за результатами державної атестації та бюджетної теми «Забезпечення повоєнної розбудови промисловості України робочою силою»(КПКВК6541030, ДР № 0124U003622)
From the experience of oral history research on the everyday life of Chernihiv region residents during the Russian-Ukrainian war in 2022–2024
No full textМета статті полягає в узагальненні досвіду усноісторичних досліджень повсякденного життя мешканців Чернігівщини під час російсько-української війни у 2022–2024 рр., які проводять викладачі та студенти Навчально-наукового інституту історії та соціогуманітарних дисциплін імені О. М. Лазаревського Національного університету «Чернігівський колегіум» імені Т. Г. Шевченка під час етнографічної практики. Особлива увага була спрямована на з’ясування емоційно-психологічного стану населення, особливостей поведінки людей, їхньої реакції на заходи окупантів, а також основних життєвих стратегій та способів виживання мешканців населених пунктів під час активної фази бойових дій.The purpose of the article is to summarize the experience of oral history research on the everyday life of residents of Chernihiv region during the Russian-Ukrainian war in 2022–2024, conducted by teachers and students of the Lazarevsky Educational and Research Institute of History and Socio-Humanitarian Disciplines of the National University «Chernihiv Collegium» named after T. G. Shevchenko during ethnographic practice. Particular attention was paid to finding out the emotional and psychological state of the population, the peculiarities of people’s behavior, their reaction to the occupiers’ actions, as well as the main life strategies and ways of survival of the inhabitants of the settlements during the active phase of hostilities
Influence of leadership style on motivation, productivity, and administrative decisions of managers and executives
No full textУ статті здійснено аналіз впливу стилю лідерства на мотивацію, продуктивність і управлінські рішення менеджерів та управлінців. Розглянуто сучасні підходи до класифікації стилів, їхній зв’язок із результативністю, мотиваційним кліматом і груповою динамікою. Визначено роль лідерських компетенцій та психологічних навичок взаємодії у підвищенні ефективності командної роботи й досягненні стратегічних цілей суб’єкта господарювання. Акцент зроблено на відмінностях ролей менеджера й управлінця та практичній значущості розвитку професійних компетенцій для оптимізації управління й формування конкурентних переваг. Матеріали можуть стати у пригоді науковцям, викладачам, студентам і практикам управління.The article presents a comprehensive analysis of the impact of leadership style on the motivation, productivity, and managerial decisions of managers and executives in an enterprise. Contemporary theoretical approaches to the classification of leadership styles and their influence on the effectiveness of managerial activities are examined. The key components determining the performance of managers and executives are identified, including motivational factors, productivity levels, decision-making, the ability to self-organize, and adapt to changes in a dynamic business environment. Special attention is paid to the conceptual and categorical apparatus used in the study, including concepts such as «leadership style», «motivation», «group dynamics», «managerial competence», «productivity», and «managerial decisions», which ensures clarity of interpretation and scientific accuracy of conclusions. The significance of leadership competencies and psychological skills in group interaction is substantiated as factors that enhance team efficiency and contribute to achieving strategic and operational goals of the enterprise. The interrelation between different leadership styles and the specifics of managerial decisions, as well as their impact on the formation of motivational climate and productivity within teams, is analyzed. Particular attention is given to distinguishing the roles of managers and executives, where managers provide operational management and task control, while executives perform strategic management functions and influence the formation of organizational culture. Emphasis is placed on the practical importance of developing leadership skills, effective group interaction, and a conceptual framework of terms and categories to improve enterprise performance, optimize decision-making processes, and create competitive advantages. The materials of the article may be useful for researchers, educators, students, managers, executives, HR specialists, and anyone involved in developing professional competencies and organizational potential