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Physicochemical foundations of the creation of new functional materials based on rare earth oxides (transcript of scientific report at the meeting of the Presidium of NAS of Ukraine, June 4, 2025)
No full textУ доповіді наведено актуальні результати фундаментальних досліджень, проведених науковцями Інституту проблем матеріалознавства ім. I.М. Францевича НАН України, з вивчення фазових рівноваг у багатокомпонентних оксидних системах рідкісноземельних елементів та створення нових матеріалів на їх основі. Актуальність цих робіт зумовлена перспективністю застосування таких матеріалів у фотоніці, оптоелектроніці, сонячній енергетиці, медицині тощо.The report presents the current results of fundamental research conducted by scientists of the I.M. Frantsevich Institute for Problems of Materials Science of the NAS of Ukraine on the study of phase equilibria in multicomponent oxide systems of rare-earth elements and the creation of new materials based on them. The relevance of these works is due to the promising application of such materials in photonics, optoelectronics, solar energy, medicine, etc
«The art of a good death» as a factor of spatial-administrative transformations in the cities under the Magdeburg law: Lviv case (15th–16th c.)
No full textКонцепція «мистецтва доброї смерті» (ars bene moriendi), спричинена нищівною пандемією чуми, починаючи з XV ст., мотивувала жителів Європи більш масово укладати тестаменти для того, аби правильно завершити свої земні справи. Заповідачі-міщани, зокрема, заповідали нерухому власність у межах міста церквам, шпиталям та монастирям. Мета дослідження – продемонструвати, як цей європейський феномен вплинув на адміністративну організацію у Львові, адже в цей час церковні інституції розпоряджалися все більшою кількістю територій на передмістях саме через донації. Цей процес відбувався паралельно з примноженням нерухомості окремими представниками патриціату та продовжився також і в XVI ст. Було застосовано методи історичної топографії та картографії для локалізації наділів на львівських передмістях, що були передані за заповітами церковним інституціям. Новизна формується із міждисциплінарного перетину соціокультурних та топографічних студій, що дозволяють краще розуміти процеси трансформації простору. Висновки. Через поширення ідеї ars bene moriendi у Львові в XV–XVI ст. церковні інституції почали отримувати через заповідання великі наділи на території передмістя, котрі були виміряні та поділені відповідно до одиниці площі «лан» ще із середини XIV ст. Відтак, це стало ще одним фактором відходу від просторово-адміністративної системи, закладеної маґдебурзьким правом.The concept of «art of a good death» (ars bene moriendi), caused by the devastating plague pandemic starting in the 15th c., motivated inhabitants of Europe to sign wills more en masse to complete their earthly affairs correctly. The burgher testators, particularly, bequeathed immovable property within the city limits to churches, hospitals, and monasteries. The purpose of the study is to demonstrate how this European phenomenon affected the administrative organization in Lviv because, at that time, church institutions were managing an increasing number of suburban territories precisely through donations. This process took place in parallel with the increase of real estate by individual representatives of the patriciate and continued in the 16th c. Historical topography and cartography methods were used to locate allotments in the Lviv suburbs that were bequeathed to church institutions. The scientific novelty is formed from the interdisciplinary intersection of sociocultural and topographical studies, which allows a better understanding of the processes of space transformation. Conclusions. Due to the spread of the idea of ars bene moriendi in Lviv in the 15th–16th c. church institutions began to receive large allotments on the territory of the suburbs through bequests, which were measured and divided according to the unit of area «lan» from the middle of the 14th c. Therefore, this became another departure factor from the spatial-administrative system established by the Magdeburg law
Bilateral Bailey Lattices and Andrews-Gordon Type Identities
No full textWe show that the Bailey lattice can be extended to a bilateral version in just a few lines from the bilateral Bailey lemma, using a very simple lemma transforming bilateral Bailey pairs relative to into bilateral Bailey pairs relative to /. Using this and similar lemmas, we give bilateral versions and simple proofs of other (new and known) Bailey lattices, including a Bailey lattice of Warnaar and the inverses of Bailey lattices of Lovejoy. As consequences of our bilateral point of view, we derive new -versions of the Andrews-Gordon identities, Bressoud's identities, a new companion to Bressoud's identities, and the Bressoud-Göllnitz-Gordon identities. Finally, we give a new elementary proof of another very general identity of Bressoud using one of our Bailey lattices.The authors are grateful to Jeremy Lovejoy for very helpful comments on an earlier version of this paper. The authors also thank the anonymous referees for their very careful reading of the paper and for their great suggestions for improvement and future research directions. The authors are partially funded by the ANR COMBIN´e ANR-19-CE48-0011. JD is funded by the SNSF Eccellenza grant number PCEFP2 202784
Curves on Endo-Pajitnov Manifolds
No full textEndo-Pajitnov manifolds are generalizations to higher dimensions of the Inoue surfaces ᴹ. We study the existence of complex submanifolds in Endo-Pajitnov manifolds. We identify a class of these manifolds that do contain compact complex submanifolds and establish an algebraic condition under which an Endo-Pajitnov manifold contains no compact complex curves.My warm thanks to Liviu Ornea for suggesting this research topic and to Miron Stanciu for many useful discussions. I am grateful to the anonymous referees for their insightful and constructive suggestions, which have significantly improved the quality of this work
A Pile of Shifts II: Structure and -Theory
No full textWe discuss *-algebras associated with several different natural shifts on the Hilbert space of the -adic tree, continuing the analysis from [Banach J. Math. Anal. 19 (2025), 32, 30 pages, arXiv:2412.00854] and in particular, we describe their structure and compute the -theory groups.The authors wish to thank the referees for their very insightful comments and suggestions. It should be noted that one of the referees pointed out that some of our results can also be obtained using the theory of theToeplitz *-algebra of a *-correspondence as developed by [24]. While this gives a very intriguing alternative, possibly simpler technique of computing the -theory, we decided not to follow this approach since the theory of *-correspondence is separate from our unified approach based on coefficient algebras and crossed products by endomorphisms
Ultra-Discretization of Yang-Baxter Maps, Probability Distributions and Independence Preserving Property
No full textWe study the relationship between Yang-Baxter maps and the independence preserving (IP) property, motivated by their role in integrable systems, from the perspective of ultra-discretization. Yang-Baxter maps satisfy the set-theoretic Yang-Baxter equation, while the IP property ensures independence of transformed random variables. The relationship between these two seemingly unrelated properties has recently started to be studied by Sasada and Uozumi (2024). Ultra-discretization is a concept primarily used in the context of integrable systems and is an area of active research, serving as a method for exploring the connections between different integrable systems. However, there are few studies on how the stationary distribution for integrable systems changes through ultra-discretization. In this paper, we introduce the concept of ultra-discretization for probability distributions and prove that the properties of being a Yang-Baxter map and having the IP property are both preserved under ultra-discretization. Applying this to quadrirational Yang-Baxter maps, we confirm that their ultra-discrete versions retain these properties, yielding new examples of piecewise linear maps having the IP property. We also explore implications of our results for stationary distributions of integrable systems and pose several open questions.The authors would like to thank the anonymous referees for their valuable comments and suggestions, which helped to improve the quality and clarity of this paper
Quantum Groups, Discrete Magnus Expansion, Pre-Lie and Tridendriform Algebras
No full textWe review the discrete evolution problem and the corresponding solution as a discrete Dyson series in order to rigorously derive a generalized discrete version of the Magnus expansion. We also systematically derive the discrete analogue of the pre-Lie Magnus expansion and express the elements of the discrete Dyson series in terms of a tridendriform algebra binary operation. In the generic discrete case, extra significant terms that are absent in the continuous or the linear discrete case appear in both Dyson and Magnus expansions. Based on the rigorous discrete derivation, key links between quantum algebras, tridendriform, and pre-Lie algebras are then established. This is achieved by examining tensor realizations of quantum groups, such as the Yangian. We show that these realizations can be expressed in terms of tridendriform and pre-Lie algebras. The continuous limit, as expected, provides the corresponding non-local charges of the Yangian as members of the pre-Lie Magnus expansion.I would like to thank the anonymous referees for their constructive comments and suggestions. Support from the EPSRC research grant EP/V008129/1 is acknowledged
Artificial intelligence and modeling the spatial structure of proteins (speech at the session of the General Meeting of the Nationa l Academy of Sciences of Ukraine, April 30, 2025)
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Mykhailo Ivchenko in the Procrustean Bed of Literary Criticism
No full textМета статті – дослідити особливості прижиттєвої критики творчості Михайла Івченка, зокрема її ключові риси та суперечності. У роботі проаналізовано також тенденції впливу ідеологічного тиску на літературну рецепцію письменника, враховуючи перехід від розмаїття поглядів та оцінок до однозначного засудження його творів у контексті так званої справи СВУ як кампанії проти антирадянських «ворожих елементів». Методологічну основу дослідження становлять принципи історико-літературного та дискурсивного аналізу, що дозволяє простежити динаміку критичної оцінки й ідеологічних впливів на літературний процес. Новизна дослідження полягає у визначенні ролі прижиттєвої критики та її впливу на М. Івченка. У результаті встановлено, що критика творчості автора була глибоко політизованою та гострою, але письменник не зраджував собі, залишався послідовним та не змінював стилю. Автор наголошує на необхідності врахування історичного контексту для повнішого розуміння літературної спадщини письменника.The purpose of the article is to explore the features of the contemporary critique of Mykhailo Ivchenko’s literary work, focusing on its key traits and contradictions. The study also analyzes the influence of ideological pressure on the literary reception of the author, emphasizing the shift from a diversity of opinions and assessments to unequivocal condemnation of his works in the context of the so-called «Union for the Liberation of Ukraine» trial, which served as a campaign against anti-Soviet “hostile elements.” The methodological foundation of the research lies in the principles of historical-literary and discursive analysis, enabling a trace of the dynamics of critical assessment and ideological influences on the literary process. The novelty of the study is in identifying the role of contemporary critique and its impact on M. Ivchenko. Findings reveal that criticism of the author's work was deeply politicized and sharp, yet M. Ivchenko remained consistent, true to himself, and steadfast in his stylistic choices. The author underscores the necessity of considering the historical context to fully understand the literary legacy of the writer