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Deformation Families of Quasi-Projective Varieties and Symmetric Projective K3 Surfaces
No full textThe main aim of this paper is to construct a complex analytic family of symmetric projective K3 surfaces through a compactifiable deformation family of complete quasi-projective varieties from CP² #9CP¯². Firstly, for an elliptic curve ₀ embedded in CP², let ≅ CP² #9CP¯² be the blow up of CP² at nine points on the image of ₀, and be the strict transform of the image. Then, if the normal bundle satisfies the Diophantine condition, a tubular neighborhood of the elliptic curve can be identified through a toroidal group. Fixing the Diophantine condition, a smooth compactifiable deformation of ∖ over a 9-dimensional complex manifold is constructed. Moreover, with an ample line bundle fixed on , complete Kähler metrics can be constructed on the quasi-projective variety ∖. So, complete Kähler metrics are constructed on each quasi-projective variety fiber of the smooth compactifiable deformation family. Then, a complex analytic family of symmetric projective K3 surfaces over a 10-dimensional complex manifold is constructed through the smooth compactifiable deformation family of complete quasi-projective varieties and an analogous deformation family.Thanks, Professor Zhou Zhang, for his course on algebraic geometry. Thanks, Professor Sho Tanimoto, for providing some useful materials. In particular, thanks to Professor Ryoichi Kobayashi for introducing this topic and giving invaluable comments. I would also like to thank the anonymous referees for their suggestions and comments
Statistical and economic analysis of the development of the tourism industry of Italy and its gastronomic segment as components of the national brand
No full textУ статті здійснено статистико-економічний аналіз розвитку туристичної галузі Італії в контексті формування її національного бренду та визначено роль гастрономічного сегмента як чинника підвищення брендової привабливості країни. На основі офіційних статистичних даних розглянуто динаміку туристичних потоків Італії у період 2018–2024 рр., обсяги витрат на міжнародний туризм, а також кількісні показники відвідуваності країни за основними ринками-донорами у 2024 р. Проаналізовано вплив туристичної сфери на формування валового внутрішнього продукту Італії у 2019–2024 рр., а також зміну індексу розвитку туристичної галузі (TTDI) за 2019–2024 рр. Приділено увагу дослідженню гастрономічного туризму як перспективного напряму розвитку туристичного сектору. Визначено тенденції зростання та прогноз вартості ринку гастрономічного туризму Італії на 2020–2027 рр. Проаналізовано динаміку Глобального індексу продовольчої безпеки (GFSI) Італії у 2018–2022 рр. та здійснено порівняння позицій країни з провідними державами світу за рейтингом продовольчої безпеки у 2022 р. Розглянуто динаміку кількості закладів, відзначених зірками «Michelin», у 2018–2024 рр. Отримані результати дають змогу комплексно оцінити взаємозв’язок між розвитком туристичної галузі, гастрономічного сегмента та формуванням національного бренду країни, а також окреслити потенційні напрями для подальшого зміцнення конкурентоспроможності Італії на світовому туристичному ринку.The article provides a statistical and economic analysis of the development of the Italian tourism industry in the context of the formation of its national brand and identifies the role of the gastronomic segment as a factor in increasing the country’s brand attractiveness. Based on official statistical data, the dynamics of tourist flows in Italy in the period 2018–2024, the volume of spending on international tourism, as well as quantitative indicators of the country’s attendance by major donor markets in 2024 are considered. The tourism industry in Italy continues to develop every year, and tourism indicators are constantly increasing. Every year, the country is visited by more and more foreign tourists who are interested in getting to know the country. It is tourists who form modern statistical indicators with which you can analyze changes in the industry. The impact of the tourism sector on the formation of Italy’s gross domestic product in 2019–2024 was analyzed, as well as the change in the tourism industry development index (TTDI) for 2019, 2021 and 2024. The tourism sector in Italy plays an important role in the formation of the gross domestic product indicator, which is reflected in the general state of the country’s economy. According to the data, the Travel & Tourism Development Index (TTDI) for Italy demonstrates certain dynamics, due to fluctuations in the component indicators that form the overall index. Particular attention is paid to the study of gastronomic tourism as a promising direction for the development of the tourism sector. Growth trends and a forecast for the value of the Italian gastronomic tourism market for 2020–2027 (in billion US dollars) were determined. In the context of ensuring the quality of gastronomic products, the dynamics of the Global Food Security Index (GFSI) of Italy in 2018–2022 were analyzed and the country’s positions were compared with the leading countries of the world in the food security rating in 2022. Additionally, the dynamics of the number of establishments awarded Michelin stars in 2018–2024 were considered, which reflects the level of development of the gastronomic industry and its contribution to strengthening the image of Italy as a world center of culinary culture. The results obtained make it possible to comprehensively assess the relationship between the development of the tourism industry, the gastronomic segment and the formation of the country’s national brand, as well as to outline potential areas for further strengthening Italy’s competitiveness in the global tourism market
On Integrable Nets in General and Concordant Chebyshev Nets in Particular
No full textWe consider general integrable curve nets in Euclidean space as a particular integrable geometry invariant with respect to rigid motions and net-preserving reparameterisations. For their description, we first give an overview of the most important second-order invariants and relations among them. As a particular integrable example, we reinterpret the result of I.S. Krasil'shchik and M. Marvan (see Section 2, Case 2 in [Acta Appl. Math. 56 (1999), 217-230]) as a curve net satisfying an ℝ-linear relation between the Schief curvature of the net and the Gauss curvature of the supporting surface. In the special case when the curvatures are proportional (concordant nets), we find a correspondence to pairs of pseudospherical surfaces of equal negative constant Gaussian curvatures. Conversely, we also show that two generic pseudospherical surfaces of equal negative constant Gaussian curvatures induce a concordant Chebyshev net. The construction generalises the well-known correspondence between pairs of curves and translation surfaces.This research received support from MŠMT under RVO 47813059. The author is grateful to Evgeny Ferapontov and Jan Cieśliński for the introduction to integrable surfaces and thought-provoking discussions that inspired this particular research
Toda-Type Presentations for the Quantum K Theory of Partial Flag Varieties
No full textWe prove a determinantal, Toda-type, presentation for the equivariant K theory of a partial flag variety Fl(₁, …, ₖ; ). The proof relies on pushing forward the Toda presentation obtained by Maeno, Naito, and Sagaki for the complete flag variety Fl(), via Kato's KT(pt)-algebra homomorphism from the quantum K ring of Fl() to that of Fl(₁, …, ₖ; ). Starting instead from the Whitney presentation for Fl(), we show that the same pushforward technique gives a recursive formula for polynomial representatives of quantum K Schubert classes in any partial flag variety which do not depend on quantum parameters. In an appendix, we include another proof of the Toda presentation for the equivariant quantum K ring of Fl(), following Anderson, Chen, and Tseng, which is based on the fact that the K-theoretic J-function is an eigenfunction of the finite difference Toda Hamiltonians.The authors thank Dave Anderson, Linda Chen, Takeshi Ikeda, Shinsuke Iwao, Peter Koroteev, Takafumi Kouno, Satoshi Naito, Daisuke Sagaki, Mark Shimozono, and Kohei Yamaguchi for useful discussions and sharing insights related to this work. L.M. was partially supported by NSF grant DMS-2152294, and gratefully acknowledges the support of Charles Simonyi Endowment, which provided funding for the membership at the Institute of Advanced Study during the 2024-25 Special Year in ‘Algebraic and Geometric Combinatorics’. D.O. gratefully acknowledges support from the Simons Foundation. Finally, we are grateful to two anonymous referees for their valuable suggestions, which helped us improve the exposition of this paper
Decision-making in selecting information and analytical systems for corporate IT cluster enterprises
No full textУ даному дослідженні розглядаються підходи до вибору систем інформаційно-аналітичного забезпечення в діяльності підприємств корпоративного ІТ-кластера. Метою дослідження є визначення критеріїв та чинників, що впливають на ефективний вибір таких систем з урахуванням специфіки взаємодії в межах ІТ-кластера та потреб цифрової трансформації бізнес-процесів.
Дослідження ґрунтується на аналізі наукових джерел, нормативної бази, корпоративної практики ІТ-підприємств, а також результатах порівняльного аналізу сучасних платформ інформаційно-аналітичного забезпечення. У роботі здійснено характеристику ключових типів інформаційно-аналітичних систем, що використовуються в ІТ-кластерах, зокрема систем бізнес-аналітики (BI), управління ресурсами підприємства (ERP), управління даними (DMS), управління проєктами (PMS) та взаємовідносинами з клієнтами (CRM).
У результаті встановлено, що вибір інформаційно-аналітичних систем для підприємств ІТ-кластера має враховувати не лише функціональні та технічні характеристики програмного забезпечення, а й рівень інтеграції в корпоративне середовище, масштабованість, безпеку даних та сумісність із інфраструктурою партнерських організацій.
У процесі дослідження запропоновано використання методів системного аналізу, експертного оцінювання, кластерного моделювання та аналізу ієрархій (AHP). Загальним результатом дослідження є формування алгоритму прийняття рішень щодо вибору інформаційно-аналітичних систем з урахуванням стратегічних цілей ІТ-кластера, що може бути використано як методичне підґрунтя в подальших дослідженнях та практичній діяльності підприємств.Purpose. This article explores the process of selecting information and analytical support systems (IASS) for enterprises operating within a corporate IT cluster. The study aims to identify the key selection criteria, technological factors, and integration challenges that influence the effectiveness of such systems in the context of digital transformation and inter-organizational collaboration.
Methods. The research is grounded in the analysis of scientific literature, regulatory frameworks, industry reports, and corporate practices of IT enterprises. The methodological approach includes system analysis, expert evaluation, and comparative analysis of modern IASS platforms. Particular attention is paid to the integration potential, scalability, and security aspects of the systems under consideration.
Results. The study reveals that the choice of IASS in the IT cluster environment should be based not only on functional capabilities but also on strategic alignment with cluster goals, interoperability with partner infrastructures, and adaptability to evolving business needs. The findings emphasize the advantages of hybrid models that combine centralized and decentralized data architectures with cloud-based services to ensure flexibility and efficiency. A decision-making algorithm for IASS selection is proposed to support enterprises in developing a sustainable digital strategy.
Conclusions. The outcomes of the study provide a conceptual and practical basis for selecting and implementing IASS in corporate IT clusters. The proposed framework can serve as a guideline for IT managers, analysts, and policymakers involved in building integrated digital ecosystems and enhancing analytical capabilities at the organizational level
Numerators in Parametric Representations of Feynman Diagrams
No full textThe parametric representation has been used for a long time for the evaluation of Feynman diagrams. As a dimension-independent intermediate representation, it allows a clear description of singularities. Recently, it has become a choice tool for the investigation of the type of transcendent numbersappearing in the evaluation of Feynman diagrams. The inclusion of numerators has, however, stagnated since the groundwork of Nakanishi. I here show howto greatly simplify the formulas through the use of Dodgson identities. In the massless case in particular, reduction to the completion of a vacuum graph allows for a strong reduction of the maximal power of the Symanzik polynomial in the denominator.I would like to thank the anonymous referees for their criticisms and suggestions. They addressed serious shortcomings in previous versions of this work to make it more readable, both in terms of the precise results established and the way they can be derived. Any remaining difficulties are nevertheless of my entire responsibility
Social Housing in the System of Social Protection and Reproduction of the Labor Potential of the Population of Ukraine
No full textМасштабні руйнування житлового фонду України внаслідок воєнної агресії зумовили нову хвилю наукових дискусій щодо ролі соціального житла в системі соціального захисту та відтворення трудового потенціалу. Проблематика набуває особливого значення у зв’язку з масовим внутрішнім переміщенням населення, ризиком довгострокових демографічних втрат та зростанням нерівності на ринку праці. Водночас житло розглядається не лише як гуманітарний ресурс, а як стратегічний чинник формування економічної безпеки, що впливає на зайнятість, здоров’я та продуктивність працівників, а також на регіональний розвиток у післявоєнний період.The large-scale destruction of Ukraine's housing stock as a result of military aggression has sparked a new wave of scientific debate on the role of social housing. This role has manifested itself in the system of social protection and reproduction of labor potential. The current issues are particularly important in connection with the mass internal displacement of the population, the risk of long-term demographic losses, and growing inequality in the labor market. At the same time, housing is seen not only as a humanitarian resource, but also as a strategic factor in shaping economic security. This factor affects employment, health, worker productivity, and regional development in the post-war period.
The aim of the study is to provide a theoretical and practical justification for the mechanism of providing social housing as a component of the social protection system and the reproduction of labor potential in wartime and post-war conditions. The objectives of the article are to identify current trends in the development of social housing in Ukraine and its impact on employment and productivity. The authors also set themselves the task of describing innovative management models and developing concepts for housing clusters as a new tool for regional recovery.
The methodological basis was provided by systemic and structural-functional approaches. This allowed social housing to be considered as an element of a complex socio-economic system. The publication uses comparative analysis methods to compare Ukrainian and European practices, statistical analysis to identify the scale of losses and assess restoration needs. The authors used graphical visualization to build models and diagrams of housing clusters.
The results of the study showed that social housing in Ukraine is transforming from an auxiliary tool of social policy into a key element of the strategy for restoring labor potential. It has been established that the quality of housing conditions directly affects the physical and mental health of the population, stress levels, family stability, and the integration of displaced persons into communities, which ultimately determines labor productivity. It has been substantiated that the restoration of the housing stock has a multiplier effect, contributing to the revitalization of the construction sector, related industries, and local labor markets. A concept of housing clusters has been proposed, with social housing at its core. Infrastructure, entrepreneurship, and communities are formed around this core. This, in turn, ensures long-term socio-economic stability.
The scientific novelty of the study lies in the interpretation of social housing as a multifunctional tool: it is not only social protection, but also a catalyst for the restoration of labor potential, demographic stabilization, and regional development. For the first time, a model of housing clusters has been proposed that integrates housing, social services, business infrastructure, and digital services into a single ecosystem.
The practical significance of the results obtained lies in the possibility of their application for the formation of state and regional programs for the reconstruction of the housing sector, the integration of social protection policy with employment policy, Thus, the results obtained contribute to the adaptation of best European practices to Ukrainian realities. The proposed approaches are capable of not only meeting the basic needs of the population, but also contributing to the sustainable economic development of Ukraine in the long term
Problems and prospects of assessing the information security of enterprises under dynamic economic
No full textСтаття присвячена дослідженню проблем, потенційних можливостей оцінювання інформаційної безпеки підприємств за динамічних умов господарювання. На основі проведеного огляду наукових досліджень за тематикою можна виокремлено ключові проблеми оцінювання інформаційної безпеки. Запропоновано агреговану економіко-математичної моделі, яка включає розширений набір індикаторів, методику їх нормалізування, агрегування, формули для даних розрахунків, рекомендації щодо валідування і практичного впровадження/використання.The article is devoted to the study of problems and potential opportunities for assessing the information security of enterprises in dynamic economic conditions. The research uses methods of analysis and synthesis. Based on a review of scientific research on the subject, key problems in assessing information security can be identified. An aggregated economic-mathematical model is proposed, which includes an extended set of indicators, methods for their normalisation and aggregation, formulas for these calculations, recommendations for validation and practical implementation/use.
The purpose of the proposed model is to obtain an integrated quantitative assessment of the level of information security of an enterprise (with an indication of the scale of this assessment, as a generally accepted option: from «0» to «100»), which will take into account technical, organisational, legal, human, operational (resilience) components and will be suitable for comparisons, monitoring and prioritisation of measures.
Assessing the information security of enterprises (at the enterprise level) in dynamic (and sometimes even highly dynamic) economic conditions requires a departure from traditional formal approaches and a gradual transition to comprehensive, adaptive, risk-oriented methodologies. An important task is to develop integrated indicators that reflect the level of security not only from a technical point of view, but also from an organisational, legal, personnel and other points of view. A promising area of research is the creation of a unified assessment methodology that will enable the comparison of different enterprises and the integration of information security assessment (the assessment process) into the overall economic security system. The implementation of these approaches will enable enterprises not only to identify and neutralise threats in a timely manner, but also to ensure long-term stability and competitiveness.
The expected results of implementation will be as follows: increased business resilience to external information threats, reduced risk of confidential information loss, protection of business reputation and customer bases, and increased trust among consumers, partners, investors and other stakeholders
Discrete Lagrangian Multiforms for ABS Equations II: Tetrahedron and Octahedron Equations
No full textWe present four types of discrete Lagrangian 2-form associated with the integrable quad equations of the ABS list. These include the triangle Lagrangian that has traditionally been used in the Lagrangian multiform description of ABS equations, the trident Lagrangian that was central to Part I of this paper, and two Lagrangians that have not been studied in the multiform setting. Two of the Lagrangian 2-forms have the quad equations, or a system equivalent to the quad equations, as their Euler-Lagrange equations, and one produces the tetrahedron equations. This is in contrast to the triangle Lagrangian 2-form, which produces equations that are weaker than the quad equations (they are equivalent to two octahedron equations). We use relations between the Lagrangian 2-forms to prove that the system of quad equations is equivalent to the combined system of tetrahedron and octahedron equations. Furthermore, for each of the Lagrangian 2-forms, we study the double zero property of the exterior derivative. In particular, this gives a possible variational interpretation to the octahedron equations.The authors are grateful to Professor Frank Nijhoff and Dr. Vincent Caudrelier for their continued support over many years, and to the organisers and supporters of the BIRS-IASM workshop on Lagrangian Multiform Theory and Pluri-Lagrangian Systems in October 2023, where this work was started. We thank the anonymous referees for their constructive criticism on the initial version of this paper, which inspired much of the work presented in Part I. JR acknowledges funding from the Engineering and Physical Sciences Research Council DTP, Crowther Endowment, and School of Mathematics at the University of Leeds. MV is supported by the Engineering and Physical Sciences Research Council [EP/Y006712/1]
Mathematical modeling of impulse excitation of a layer weakened by a through hole (skew-symmetric case)
No full textУ статті представлено нову математичну модель розв’язання динамічної (ударної) кососиметричної крайової задачі для шару, що послаблений наскрізним отвором, при ковзному защемленні торців.This paper presents a new mathematical model for solving a dynamic (impact) skew-symmetric boundary value problem for a layer weakened by a through hole, with sliding clamping of the edges