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Оголошення. Про конкурс на здобуття Золотої медалі імені В.І. Вернадського Національної академії наук України у 2025 році
No full textKilling (Super)Algebras Associated to Connections on Spinors
No full textWe generalise the notion of a Killing superalgebra, which arises in the physics literature on supergravity, to general dimension, signature, and choice of spinor module and Dirac current. We also allow for Lie algebras as well as superalgebras, capturing a set of examples previously defined using geometric Killing spinors on higher-dimensional spheres. Our definition requires a connection on a spinor bundle - provided by supersymmetry transformations in the supergravity examples and by the Killing spinor equation on the spheres - and we obtain a set of sufficient conditions on such a connection for the Killing (super)algebra to exist. We show that these Lie (super)algebras are filtered deformations of graded subalgebras of (a generalisation of) the Poincaré superalgebra and then study such deformations abstractly using Spencer cohomology. In the highly supersymmetric Lorentzian case, we describe the filtered subdeformations which are of the appropriate form to arise as Killing superalgebras, lay out a classification scheme for their odd-generated subalgebras, and prove that, under certain technical conditions, there exist homogeneous Lorentzian spin manifolds on which these deformations are realised as Killing superalgebras. Our results generalise previous work in the 11-dimensional supergravity literature.The author would like to thank José Figueroa-O’Farrill, under whose supervision this work was done, for his guidance and patience. Thanks also to Andrea Santi, James Lucietti, C.S. Shahbazi, and the sorely missed Paul de Medeiros for many enlightening conversations and helpful comments. Finally, thanks to the anonymous referees, whose comments and suggestions greatly improved the quality and clarity of this work. This work was carried out with scholarship funding from the Science and Technology Facilities Council (STFC) and the School of Mathematics at the University of Edinburgh. This work previously appeared as part of the author’s Ph.D. Thesis [8] but has not been published elsewhere. Some changes in notation and terminology have been made for this version to aid comparison with other work, and there are also some minor changes in exposition and corrections; in particular, Lemma 3.3 and its proof have been updated
Sustainable Development Marketing in the Pharmaceutical Market in Ukraine
No full textВ процесі дослідження було визначено основні напрями впровадження фармацевтичного маркетингу сталого розвитку. Встановлено, що в Україні зростає інтерес до екологічно сертифікованих товарів, етичного бізнесу та прозорої комунікації із зацікавленими сторонами, проте існують бар’єри: низька поінформованість споживачів, обмежені інвестиційні ресурси, недостатній розвиток інституційного середовища.
Відзначено, що характерними рисами маркетингу сталого розвитку є сприяння задоволенню базових людських потреб охорони здоров’я без яких не є можливим ефективний розвиток добробуту суспільства в цілому.Відзначено, що характерними рисами маркетингу сталого розвитку є сприяння задоволенню базових людських потреб охорони здоров’я без яких не є можливим ефективний розвиток добробуту суспільства в цілому.
Ключові слова: маркетинг сталого розвитку, фармацевтичне підприємство, екологічний маркетинг, соціальна відповідольність.
Kruhlikova V. V. Sustainable Development Marketing in the Pharmaceutical Market in Ukraine.
The article reveals the essence of sustainable development marketing and analyzes the features of its application in the Ukrainian pharmaceutical market in conditions of martial law and global challenges.
Modern business models are increasingly oriented towards the principles of sustainable development, which encompass economic efficiency, social responsibility, and environmental safety. This topic is especially important for Ukraine, given the need to increase the competitiveness of pharmaceutical companies and build consumer trust.
The research used an analysis of scientific sources, statistical data, and regulatory legal acts; a generalization of international experience and a comparative analysis of Ukrainian practices were conducted.
The main directions of implementation of pharmaceutical marketing of sustainable development are determined: ecological marketing (eco-marketing), social marketing, corporate social responsibility. It is revealed that in Ukraine there is a growing interest in ecologically certified products, ethical business and transparent communication with stakeholders, however, there are barriers: low consumer awareness, limited investment resources, insufficient development of the institutional environment.
Recommendations for Ukrainian pharmaceutical companies are proposed: integrating sustainability principles into marketing strategies, strengthening information campaigns to raise consumer environmental awareness, adapting international standards of sustainable development, and using digital tools for communications and transparency.
It is noted that the characteristic features of sustainable development marketing are the promotion of meeting basic human health needs, without which effective development of the well-being of society as a whole is not possible. The practice of implementing EU sustainable development marketing approaches in the field of providing the population with medicines in Ukraine is highlighted.
It has been found that under the influence of the dynamic system of sustainable development, new types and types of marketing are being formed, such as ecological marketing, green marketing, ethical marketing, socially responsible marketing, as well as innovative marketing
Проблеми працевлаштування випускників вищих навчальних закладів на ринку праці в умовах війни та повоєнного відновлення
No full textThe article examines the current problems of employment of graduates of higher education institutions of Ukraine. The process of transformation of the regulatory and legislative framework of the labor market regarding employment of graduates of higher education institutions during the period of Ukraine's independence is studied. It is proven that the graduate employment system has moved from state distribution to a market-oriented model with an emphasis on skills, digital tools, and partnerships with business and is viewed as a complex ecosystem that connects the graduate, the higher education institution, the employer, the state, and the international community. A categorical apparatus has been determined in accordance with the regulatory and legislative framework on the problem of employment of graduates of the real sector of the economy. The state of validity of the regulatory and legislative framework regarding the employment of graduates of higher education institutions of Ukraine has been monitored. The study proposed a set of recommendations aimed at improving approaches to regulating and supporting the employment of higher education graduates, in particular: updating and modernizing the regulatory framework that defines mechanisms for promoting youth employment; introduction of modern statistical reporting forms that will provide complete, reliable and comparative information on the employment results of graduates by region, specialty and form of study and will become the basis for conducting high-quality monitoring; regulation of the activities of employment departments of higher education institutions by approving state requirements for their structure, functions and responsibilities; integration of national educational registers, in particular, Unified State Electronic Database for Educational Information, with international information systems. The need for deepening interaction between higher education institutions, employers, and state institutions is substantiated in order to ensure the successful integration of young professionals into the modern labor market. It was emphasized that such cooperation should be systematic, technologically supported, and focused on the real needs of the economy, especially in the context of the war and post-war development of the state.У статті розглядаються актуальні проблеми працевлаштування випускників вищих навчальних закладів України. Досліджено процес трансформації нормативно-правової бази ринку праці щодо працевлаштування випускників вищих навчальних закладів за період незалежності України. Доведено, що система працевлаштування випускників перейшла від державного розподілу до ринково-орієнтованої моделі з акцентом на навички, цифрові інструменти та партнерство з бізнесом і розглядається як складна екосистема, що пов'язує випускника, вищий навчальний заклад, роботодавця, державу та міжнародну спільноту. Визначено категоріальний апарат відповідно до нормативно-правової бази з проблеми працевлаштування випускників реального сектору економіки. Проведено моніторинг стану обґрунтованості нормативно-правової бази щодо працевлаштування випускників вищих навчальних закладів України. У дослідженні запропоновано комплекс рекомендацій, спрямованих на вдосконалення підходів до регулювання та підтримки працевлаштування випускників вищих навчальних закладів, зокрема: оновлення та модернізація нормативно-правової бази, що визначає механізми сприяння працевлаштуванню молоді; впровадження сучасних форм статистичної звітності, які нададуть повну, достовірну та порівняльну інформацію про результати працевлаштування випускників за регіонами, спеціальностями та формами навчання та стануть основою для проведення якісного моніторингу; регулювання діяльності відділів працевлаштування вищих навчальних закладів шляхом затвердження державних вимог до їх структури, функцій та обов'язків; інтеграція національних освітніх реєстрів, зокрема Єдиної державної електронної бази освітньої інформації, з міжнародними інформаційними системами. Обґрунтовано необхідність поглиблення взаємодії між вищими навчальними закладами, роботодавцями та державними установами з метою забезпечення успішної інтеграції молодих спеціалістів у сучасний ринок праці. Було наголошено, що така співпраця має бути системною, технологічно забезпеченою та орієнтованою на реальні потреби економіки, особливо в умовах воєнного та повоєнного розвитку держави
Quantum Modularity for a Closed Hyperbolic 3-Manifold
No full textThis paper proves quantum modularity of both functions from ℚ and -series associated to the closed manifold obtained by −1/2 surgery on the figure-eight knot, 4₁(−1, 2). In a sense, this is a companion to the work of Garoufalidis-Zagier, where similar statements were studied in detail for some simple knots. It is shown that quantum modularity for closed manifolds provides a unification of Chen-Yang's volume conjecture with Witten's asymptotic expansion conjecture. Additionally, we show that 4₁(−1, 2) is a counterexample to previous conjectures of Gukov-Manolescu relating the Witten-Reshetikhin-Turaev invariant and the Ẑ() series. This could be reformulated in terms of a ''strange identity'', which gives a volume conjecture for the Ẑ invariant. Using factorisation of state integrals, we give conjectural but precise -hypergeometric formulae for generating series of Stokes constants of this manifold. We find that the generating series of Stokes constants is related to the 3d index of 4₁(−1, 2) proposed by Gang-Yonekura. This extends the equivalent conjecture of Garoufalidis-Gu-Mariño for knots to closed manifolds. This work appeared in a similar form in the author's Ph.D. Thesis.This work was carried out throughout my doctoral studies and therefore owes agreat debt to my supervisors Stavros Garoufalidis and Don Zagier. Their constant sharing of ideas and perspectives has been invaluable to the completion of this work. I would also like to thank Dongmin Gang, Mauricio Romo, and Masahito Yamazaki for sharing some of their code early on in this project. Again, I would like to thank Dongmin Gang for sharing a computation of the 3d index of 4₁(−1, 2) proposed in [26]and the question of whether this could be found in the Stokes constants. I thank Jie Gu, Marcos Mariño, and Matthias Storzer for various conversations throughout this project and Sergei Gukov for suggestions to improve the manuscript. Finally, I would like to thank the referees for many helpful suggestions. The work of the author has been supported by the Max-Planck-Gesellschaft with the Max Planck Institute for Mathematics in Bonnand the Southern University of Science and Technology's International Center for Mathematics in Shenzhen
Comomentum Sections and Poisson Maps in Hamiltonian Lie Algebroids
No full textIn a Hamiltonian Lie algebroid over a pre-symplectic manifold and over a Poisson manifold, we introduce a map corresponding to a comomentum map, called a comomentum section. We show that the comomentum section gives a Lie algebroid morphism among Lie algebroids. Moreover, we prove that a momentum section on a Hamiltonian Lie algebroid is a Poisson map between proper Poisson manifolds, which is a generalization that a momentum map is a Poisson map between the symplectic manifold to dual of the Lie algebra. Finally, a momentum section is reinterpreted as a Dirac morphism on Dirac structures.The authors would like to thank Antonio Miti and the referees for their useful discussion and comments. Especially, they would like to thank the anonymous referees for their relevant contributions to improve the paper. This work was supported by JSPS Grants-in-Aid for Scientific Research Number 22K03323
On the dynamic problem of optimal set partitioning with fixed centers under uncertainty
No full textУ цьому дослідженні створено комплексну математичну та обчислювальну основу для розв’язання динамічних задач ОРМ за умов невизначеності. Даний підхід поєднує теорію оптимального розбиття множин із сучасними методами штучного інтелекту, зокрема нечіткою логікою, теорією нечітких множин і нейронечіткими системами.In this study, we develop a comprehensive mathematical and computational framework for solving dynamic OSP problems under uncertainty. Our approach integrates the theory of optimal set partitioning with modern artificial intelligence techniques, particularly fuzzy logic, fuzzy set theory, and neuro-fuzzy systems
Completing the pages of P.O. Kulish’s genealogy
No full textДослідження доповнює сторінки родоводу визначного українського культурного діяча – письменника Пантелеймона Олександровича Куліша. У статті наведена інформація з документів, які раніше залишалися поза увагою дослідників, що висвітлюють походження воронізького роду Кулішів. До обігу уводиться родовідне дерево Кулішів, складене батьком письменника – Олександром Андрійовичем Кулішем. За результатами опрацювання присяг та ревізій Воронізької сотні подаються нові відомості про Пантелеймонового прадіда, сотенного воронізького отамана Івана Куліша, уводяться нові імена, які належали до членів родини, простежується їхній життєвий шлях. Уперше оприлюднено витяги зі сповідних розписів церков містечка Вороніж за 1739 р., 1756 р. та метричної книги воронізької Трьохсвятительської церкви за 1802–1811-і роки, що суттєво доповнить знання про воронізьку родину Кулішів.The research complements the genealogy pages of the prominent Ukrainian cultural figure and writer Panteleimon Oleksandrovych Kulish, born in the northern town of Voronezh. The article provides information from previously unknown archival documents that shed light on the origins of the Kulish family of Voronezh. The genealogy tree of the Kulish family, compiled by the writer’s father, Oleksandr Andriiovych Kulish, is introduced. Based on the results of the processing of oaths and revisions of the Voronezh hundred, new information about Panteleimon’s great-grandfather, the centurion Voronezh ataman Ivan Kulish, is presented, new names belonging to family members are introduced, and their life paths are traced. Extracts from the confessional records of the town of Voronezh for 1739, 1756, and the metric book of the Voronezh Trinity Church for 1802-1811 are published, significantly supplementing knowledge about the Voronezh Kulish family. For the first time in this study, the writer’s genealogy is derived from previously unlit archival documents, new family members are identified, a graphical genealogy tree is presented, and specific birth dates of individual family members, including Panteleimon’s father – Oleksandr Andriiovych, are named
Some Spherical Function Values for Hook Tableaux Isotypes and Young Subgroups
No full textA Young subgroup of the symmetric group N, the permutation group of {1, 2, …, }, is generated by a subset of the adjacent transpositions {(, +1)∣1 ≤ ₂ > ⋯ > ₚ ≥ 0), thus it is isomorphic to the direct product ₙ₁ × ₙ₂ × ⋯ ×ₙₚ. The interval {1, 2, …, } is a union of disjoint sets ⱼ = { ∣ λᵢ = ⱼ}. The orbit of λ under the action of N (by permutation of coordinates) spans a module λ, the representation induced from the identity representation of ₙ. The space λ decomposes into a direct sum of irreducible N-modules. The spherical function is defined for each of these; it is the character of the module averaged over the group ₙ. This paper concerns the value of certain spherical functions evaluated at a cycle that has no more than one entry in each interval ⱼ. These values appear in the study of eigenvalues of the Heckman-Polychronakos operators in the paper by . Gorin and the author [arXiv:2412:01938]. In particular, the present paper determines the spherical function value for N-modules of hook tableau type, corresponding to Young tableaux of shape [ − , 1ᵇ].The author is grateful to the referees whose careful reading and detailed suggestions helped to improve this paper
The impact of artificial intelligence as a disruptive and closing technologies on industrial economics: a set of tasks for scientific comprehension and resolution
No full textУ статті розглянуто вплив штучного інтелекту (ШІ) на економіку промисловості з двох різних позицій: як підривної та закриваючої технології. Визначено такі ключові поняття: економіка промисловості, ШІ, підривна та закриваюча технологія. Здійснено порівняльний аналіз впливу ШІ на ринки, продукти, домінуючі компанії на ринку, інститути й інвестиційну привабливість. Обґрунтовано, що ШІ має ознаки обох технологій, і сформульовано перелік ключових завдань для наукового осмислення та вирішення проблем визначення впливу ШІ на економіку промисловості, зокрема щодо розроблення відповідної економічної теорії, методики оцінювання впливу, мінімізації ризиків та актуалізації державної промислової політики.This article investigates the impact of Artificial Intelligence (AI) on the industrial economy, analyzing it from the perspective of two competing theories: disruptive and closing innovation. The research is highly relevant due to the significant growth in investments (Nvidia's capitalization surpassed $5 trillion in October 2025) and AI's influence on global industrial production. This is particularly crucial for Ukraine, given the prospects for the transfer of military-oriented AI into the civilian economy.
The literature review identifies two main groups of academics: proponents (AI as the core of Industry 4.0) and critics (AI primarily automates existing tasks, potentially leading to "over-automation" and a decrease in GDP).
This contradiction forms the basis for two competing hypotheses:
1. AI is a Disruptive Innovation, which changes markets and creates new players.
2. AI is a Closing Innovation, which merely improves existing products and strengthens the position of current market leaders.
A comparative analysis of AI was conducted based on criteria such as the impact on the product, the customer, market dominance, and the institutional space. The study demonstrates that AI represents a complex innovative phenomenon that simultaneously exhibits characteristics of both types of technologies:
- Closing Role: AI improves existing platforms and products of market giants (Microsoft Copilot, Google AI Overviews, Siri), thereby strengthening their dominance.
- Disruptive Role: AI creates fundamentally new products (ChatGPT, Grok), attracts new customers, and shapes new specialized legislation.
The dual nature of AI presents several challenges, notably the lack of economic theory and tools for quantitative assessment of its effects at the micro-, meso-, and macro-levels.
A list of key scientific challenges requiring resolution is formulated:
1. Defining the theoretical foundations of AI's micro-, meso-, and macro-level impact as both disruptive and closing technologies.
2. Substantiating the assessment methodology and testing the hypothesis regarding AI's statistically significant impact.
3. Identifying economic constraints, minimizing risks, and systemizing directions for stimulating AI adoption.
4. Substantiating recommendations for updating Ukraine's national industrial policy, institutional regulation (including taxation), and ensuring the economic efficiency of AI utilization.
Understanding the dual nature of AI is crucial for economic forecasting and strategizing. Although AI possesses powerful disruptive potential, its implementation is currently dominated by incumbent large companies, which does not lead to the "disruption" of their positions. Addressing the outlined challenges is necessary for the urgent actualization of Ukraine's industrial policy