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Were the Novhorod-Siverskyi Bohuns descendants of Ivan Bohun?
No full textУ статті на основі значної кількості архівного матеріалу зроблено спробу з’ясувати достовірність твердження про проживання нащадків Івана Богуна в Новгороді-Сіверському в кінці XVIII – на початку XIX століть.The article, based on a substantial amount of archival material, attempts to determine the accuracy of the claim that descendants of Ivan Bohun lived in Novhorod-Siverskyi at the end of the 18th and the beginning of the 19th centuries
Comparative analysis of cognitive and behavioral properties of modern language models
No full textМета даної роботи — виконати порівняльний аналіз когнітивних і поведінкових властивостей сучасних великих і малих мовних моделей та оцінити прояви суб’єктності за п’ятьма маркерами: лінія «Я», ініціативність, автономність реакцій, вольова активність, континуальність особистісної лінії.This study conducts a comparative analysis of the cognitive and behavioral properties of contemporary large and small language models and assesses manifestations of subjectness across five markers: self-representation («I-line»), initiative, autonomy of responses, volitional activity, and continuity of the personal narrative.Дослідження виконано в межах науково-дослідної роботи «Розроблення дослідного зразка експертної сис-теми підтримки прийняття рішень на основі ШІ» (Договір No365/1769 від 28.05.2025 між Інститутом кіберне-тики імені В.М. Глушкова НАНУкраїнита Тернопільським національниммедичним університетом імені І.Я. Горбачевського МОЗ України) та науково-дослідних робіт НАН України «Розробити теоретичніза-сади і функціональну модель комп’ютера для обробки складних інформаційних структур» (No0124U002317) і «Розробити засоби підтримки технологій віртуалізації та їх використання в комп’ютерній інженерії та інших застосуваннях» (No 0124U001826)
A-Type Open SL(2, ℂ) Spin Chain
No full textFor the noncompact open SL(2, ℂ) spin chain, the eigenfunctions of the special matrix element of the monodromy matrix are constructed. The key ingredients of the whole construction are local Yang-Baxter -operators, -operator, and raising operators obtained by reduction from the -operator. The calculation of various scalar products and the proof of orthogonality are based on the properties of the -operator and demonstrate its hidden role. The symmetry of eigenfunctions with respect to the reflection of the spin variable → 1 − is established. The Mellin-Barnes representation for eigenfunctions is derived, and equivalence with the initial coordinate representation is proved. The transformation from one representation to another is grounded on the application of the -type Gustafson integral generalized to the complex field.We are grateful to N. Belousov, S. Khoroshkin, and A. Manashov for fruitful discussions. The work was supported by the Theoretical Physics and Mathematics Advancement Foundation BASIS (S.D. and P.A.) and by the Ministry of Science and Higher Education of the Russian Federation (P.A.), agreement 075-15-2025-344 dated 29/04/2025 for Saint Petersburg Leonhard Euler International Mathematical Institute at PDMI RAS
A story of a family: Filonovych Sofia Vasylivna from Filonivka Street in the village of Dubovychi
No full textУ представленому дослідженні йдеться про родину Філоновичів: Василя Яковича та Марію Гаврилівну, які проживали в кінці ХІХ – ХХ ст. у селі Дубовичі Глухівського повіту Чернігівської губернії; їхніх нащадків; ідеологічні погляди представників фамілії; політичний конфлікт з радянською владою; життєдіяльність та внесок у державотворчу справу; слід в історії України.The Filonovych family of Cossack starshyn (foremen) is well-known in Ukrainian historical circles. In the 18th century Filon purchased an estate near the village of Dubovychi. During the Hetmanate (1648–1782), those lands first belonged to the Hlukhiv separate Zaseym Cossack military hundred, then to the Krolevets Cossack hundred of the Nizhyn Regiment. Later, those were the territories of Chernihiv region and for a long time of Hlukhiv district. Since the second half of the 20th century they belonged to Krolevets district of Sumy region. According to the new administrativeterritorial division since July 2020 up to now Dubovychi is a part of the Krolevets separate territorial communitу of Konotop district of Sumy region. Today Filonivka is one of the village streets. And it is not only the Filonovych families who live there.
Vasyl Zakharovich Filonovych (1894–1987) was an outstanding personality – a military figure, a general-coronet of the Ukrainian Army of the Ukrainian People’s Republic government in exile.
One of the first commanders of the Ukrainian Insurgent Army, Hordiy Kostiantynovych Vrotnovsky, was baptized in Dubovychi in the Church of the Nativity of the Virgin. His mother Nadiia is from the Filonovych family.
The presented study (research) deals with the Filonovych family of Vasyl Yakovych and Maria Gavrylivna as well as their descendants. They lived in the village of Dubovychi, Hlukhiv district, Chernihiv province at the end of the 19th – 20th centuries. They were fighters for Ukrainian statehood. The family was pro-Ukrainian minded, they shared nationalist ideas of independence against the Bolshevik occupation of Ukraine. In the 1930s, there was a political conflict between the family and the Soviet authorities. The family was subjected to repressions. Here is the story of the life and contribution of the Filonovych family to the state-building cause, about their place in the history of Ukraine
Functional modules and algorithms for synthesis of digital visual image of dynamic marine situation in a precision real-time geoinformation system
No full textУ статті представлено розроблені алгоритми та функціональні модулі синтезу цифрового зорового образу морської ситуації, які покращують ефективність прийнятих рішень з боку кожного користувача системи в зоні своєї відповідальності. Такий ефект досягається внаслідок підвищення точності та швидкості обробки вхідних даних з подальшим наданням високоточного кінцевого результату як об’єктивної інформації, закладеної в цілісному візуальному образі поточної ситуації.The purpose of the work is to develop algorithms and functional modules for the synthesis of a digital visual image of the marine situation, which ensure the improvement of the quality of decision-making by each user of the system by increasing the accuracy and speed of processing input data and providing a highly accurate final result in the form of an objective, adequate reality, and a holistic picture of the situation.Це дослідження виконано за підтримки НАН України (проєкт 0124U001826)
Bridging the logistics gap: Smart-Synergy and artificial intelligence in building sustainable supply chains
No full textУ статті розглянуто феномен «логістичного пробілу» в українській економіці як систематичну невідповідність між потребами ринку та фактичними можливостями існуючих ланцюгів постачань в умовах тривалих шоків, воєнних ризиків та регуляторного тиску (ESG, «зелений курс»). Запропоновано концепцію переходу від вразливих лінійних ланцюгів постачань до стійких багаторівневих логістичних мереж на основі моделі Smart-Synergy. Особливу увагу приділено ролі штучного інтелекту в трансформації ланцюгів постачань: від прогнозування попиту та виявлення вузьких місць до сценарного моделювання, оптимізації маршрутів, управління ризиками та підтримки прийняття рішень у реальному часі.The article examines the phenomenon of the “logistics gap” in the Ukrainian economy as a systematic mismatch between market needs and the actual capabilities of existing supply chains under conditions of prolonged shocks, war-related risks, and regulatory pressure (ESG, the “Green Deal”). The author proposes a concept for transitioning from vulnerable linear supply chains to sustainable multi-level logistics networks based on the Smart-Synergy model, which combines resilient logistics (ResiLog), flexible infrastructure solutions under the “logistics as a service” model (FlexHub), environmentally oriented innovations (GreenChain, ReLoop Logistics), as well as the intelligent components SmartFlow, DataChain, and CrowdRoute. Special attention is paid to the role of artificial intelligence in transforming supply chains: from demand forecasting and bottleneck detection to scenario modelling, route optimization, risk management, and real-time decision support. Based on a systematization of approaches to building adaptive logistics ecosystems, the article demonstrates how the integration of Smart-Synergy and AI solutions can help narrow the logistics gap, reduce CAPEX and OPEX, decrease disruption-related losses and the carbon footprint, and enhance the investment attractiveness of Ukrainian enterprises by ensuring compliance with contemporary requirements of international markets and post-war reconstruction programmes. The article formulates practical guidelines for business and public policy on a phased transition to sustainable logistics networks capable of supporting economic growth and recovery under conditions of high uncertainty
Linear Independence for ⁽¹⁾₁ by Using ⁽¹⁾₂
No full textIn the previous paper, the authors proved linear independence of the combinatorial spanning set for the standard ⁽¹⁾ℓ-module (Λ₀) by establishing a connection with the combinatorial basis of Feigin-Stoyanovsky's type subspace (Λ₀) of ⁽¹⁾2ℓ-module (Λ₀). In this note, we extend this argument for ⁽¹⁾₁ ≅ ⁽¹⁾₁ to all standard ⁽¹⁾₁-modules (Λ). In the proof, we use a coefficient of an intertwining operator of the type ((Λ₂)(Λ₁) (Λ₁)) for standard ⁽¹⁾₂-modules.We are deeply honored to contribute this work to an issue dedicated to Jim Lepowsky– an exceptional mathematician whose work has significantly shaped our scientific paths, a wonderful friend, and one of the kindest people that we know. This work was supported by the project “Implementation of cutting-edge research and its application as part of the Scientific Center of Excellence for Quantum and Complex Systems, and Representations of Lie Algebras”, PK.1.1.02, European Union, European Regional Development Fund. Also, this work has been supported by the Croatian Science Foundation under the project IP-2022-10-9006
Killing Superalgebras in 2 Dimensions
No full textWe provide some examples of Killing superalgebras on 2-dimensional pseudo-Riemannian manifolds within the theoretical framework established in [SIGMA 21 (2025), 081, 61 pages]. We compute the Spencer cohomology group H²’²(₋; ) and filtered deformations of the non-chiral flat model (Euclidean and Poincaré) superalgebra for various Dirac currents and show these arise as Killing superalgebras for (imaginary) geometric Killing and skew-Killing spinors in both Riemannian and Lorentzian signature.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 for their comments and suggestions, which 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 [3] 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