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Study of Synergy between Different Components of Resource Potential: the Impact of Human Resources and Technological Innovations on the Efficiency of Using the Region's Resource Potential
No full textУ статті досліджується взаємозв’язок між людськими ресурсами та технологічними інноваціями як ключовими компонентами ефективного використання ресурсного потенціалу регіону. Аналіз синергії між цими елементами дозволяє виявити механізми оптимізації процесів видобутку, обробки та повторного використання ресурсів із мінімальним впливом на довкілля. Особлива увага приділяється ролі кваліфікованих кадрів у впровадженні інноваційних рішень і адаптації до змін у зовнішньому середовищі, передусім, у сфері природокористування. Розкрито значення технологічного прогресу для зниження витрат і забезпечення екологічної стійкості. У підсумку наголошується, що інвестиції в розвиток людського капіталу та інновацій є необхідною умовою забезпечення сталого розвитку економіки та збереження ресурсного потенціалу регіону для майбутніх поколінь.The article explores the interrelation between human resources and technological innovations as key components for the efficient use of natural resources. The analysis of synergy between these elements reveals mechanisms for optimizing extraction, processing, and reuse processes of resources with minimal environmental impact. Special attention is given to the role of qualified personnel in implementing innovative solutions and adapting to changes in natural resource management. The significance of technological progress in reducing costs and ensuring ecological sustainability is highlighted. The study concludes that investments in the development of human capital and innovation are essential for sustainable economic development and the preservation of resource potential
Quantum technologies in Ukraine: development and application (transcript of scientific report at the meeting of the Presidium of NAS of Ukraine, July 2, 2025)
No full textДоповідь присвячено проблемам розвитку квантових технологій в Україні. Квантові обчислення, квантове моделювання, квантові комунікації, сенсорика і метрологія є одними з ключових напрямів розвитку глобальної інноваційної економіки. Потенційний вплив таких технологій на всі сфери людської діяльності настільки значний, що його нерідко називають другою квантовою революцією. Технологічні прориви в галузі квантових технологій неможливі без ґрунтовних фундаментальних досліджень.The report is devoted to the problems of development of quantum technologies in Ukraine. Quantum computing, quantum modeling, quantum communications, quantum sensors and metrology are some of the key development areas of the global innovation economy. The potential impact of such t echnologies on all spheres of human activity is so significant that it is oft en referred to as the second quantum revolution. Technological breakthrough in the field of quantum technologies is impossible without thorough fundamental research
Ecologization of the Logistics Strategy of Aviation Enterprises' Supply Chain
No full textУ статті розглянуто актуальні питання екологічного впливу авіаційної логістики на довкілля, зокрема викиди парникових газів, забруднення повітря, шумове навантаження та вплив на біорізноманіття. Проаналізовано основні джерела негативного впливу на різних етапах життєвого циклу повітряних суден – від проєктування та виробництва до експлуатації та утилізації. Визначено ключові фактори, що зумовлюють екологічний слід авіації, а також інноваційні підходи до зменшення впливу: використання композитних матеріалів, сталого авіаційного пального, оптимізації маршрутів, рециклінгу та програми компенсації викидів. Особливу увагу приділено формуванню екологоорієнтованої стратегії ланцюга постачань, що передбачає моніторинг, оцінку ризиків, інтеграцію екологічних цілей у загальну стратегію підприємства та постійний контроль ефективності.The article examines current issues of the effect of aviation logistics on the environment, particularly greenhouse gas emissions, air pollution, noise pollution, and impacts on biodiversity. The main sources of negative impact at different stages of the aircraft life cycle-from design and production to operation and disposal – were analyzed. Key factors determining aviation's ecological footprint are identified, along with innovative approaches to reducing impact: use of composite materials, sustainable aviation fuel, route optimization, recycling, and emissions compensation programs. Special attention is paid to the formation of an ecologically oriented supply chain strategy, which includes monitoring, risk assessment, integration of environmental goals into the overall enterprise strategy, and continuous performance control
90th anniversary of Corresponding Member of NAS of Ukraine V.M. Klymenko
No full text7 серпня виповнюється 90 років відомому вченому в галузі теплофізики і теплоенергетики головному науковому співробітнику відділу теплофізичних проблем систем теплопостачання Інституту технічної теплофізики НАН України, лауреату Державної премії України в галузі науки і техніки, доктору технічних наук, члену-кореспонденту НАН України Віктору Миколайовичу Клименку
Prolongation of (8, 15)-Distribution of Type ₄ by Singular Curves
No full textCartan gives the model of (8, 15)-distribution with the exceptional simple Lie algebra ₄ as its symmetry algebra in his paper (1893), which was published one year before his thesis. In the present paper, we study abnormal extremals (singular curves) of Cartan's model from the viewpoints of sub-Riemannian geometry and geometric control theory. Then we construct the prolongation of Cartan's model based on the data related to its singular curves, and obtain the nilpotent graded Lie algebra which is isomorphic to the negative part of the graded Lie algebra ₄.The authors would like to thank anonymous referees for their valuable and helpful comments to improve the paper. The first author is partially supported by JSPS KAKENHI Grant Number 24K06700, by JST CREST Geometrical Understanding of Spatial Orientation, and by the Research Institute for Mathematical Sciences in Kyoto University
Integrable Dynamics in Projective Geometry via Dimers and Triple Crossing Diagram Maps on the Cylinder
No full textWe introduce twisted triple crossing diagram maps, collections of points in projective space associated to bipartite graphs on the cylinder, and use them to provide geometric realizations of the cluster integrable systems of Goncharov and Kenyon constructed from toric dimer models. Using this notion, we provide geometric proofs that the pentagram map and the cross-ratio dynamics integrable systems are cluster integrable systems. We show that in appropriate coordinates, cross-ratio dynamics is described by geometric -matrices, which solves the open question of finding a cluster algebra structure describing cross-ratio dynamics.TG thanks Nick Ovenhouse for discussions about networks in a cylinder. SR thanks Ivan Izmestiev for discussions on cross-ratio dynamics during a visit to TU Wien, Anton Izosimov for comments on Newton polygons in the first version of this paper, and Rei Inoue for exchanges on the geometric R-matrix. NA was supported by the Deutsche Forschungsgemeinschaft (DFG) Collaborative Research Center TRR 109 “Discretization in Geometry and Dynamics” and by the ENS-MHI chair funded by MHI. NA and SR were partially supported by the Agence Nationale de la Recherche, Grant Number ANR-18-CE40-0033 (ANR DIMERS). SR was also partially supported by the CNRS grant Tremplin@INP, which funded a visit of NA to Paris-Saclay
Isomonodromy and Painlevé Type Equations, Case Studies
No full textThere is an abundance of equations of Painlevé type besides the classical Painlevé equations. Classifications have been computed by the Japanese school. Here we consider Painlevé-type equations induced by isomonodromic families of linear ODE's having at most = 0 and = ∞ as singularities. Requiring that the formal data at the singularities produce isomonodromic families parametrized by a single variable leads to a small list of hierarchies of cases. The study of these cases involves Stokes matricesand moduli for linear ODE's on the projective line. Case studies reveal interesting families of linear ODE's and Painlevé-type equations. However, rather often the complexity (especially of the Lax pair) is too high for either the computations or the output. Apart from classical Painlevé equations, one rediscovers the work of Harnad, Noumi, and Yamada. A hierarchy, probably new, related to the classical ₃(₈), is discovered. Finally, an amusing ''companion'' of ₁ is presented.We thank the referees for their work and suggestions, resulting in a considerable revision of an earlier version of this text. We especially thank Anton Dzhamay for his successful effort to identify two of the Painlevé-type equations obtained in this paper
Discrete Lagrangian Multiforms for ABS Equations I: Quad Equations
No full textDiscrete Lagrangian multiform theory is a variational perspective on lattice equations that are integrable in the sense of multidimensional consistency. The Lagrangian multiforms for the equations of the ABS classification formed the start of this theory, but the Lagrangian multiforms that are usually considered in this context produce equations that are slightly weaker than the ABS equations. In this work, we present alternative Lagrangian multiforms that have Euler-Lagrange equations equivalent to the ABS equations. In addition, the treatment of the ABS Lagrangian multiforms in the existing literature fails to acknowledge that the complex functions in their definitions have branch cuts. The choice of branch affects both the existence of an additive three-leg form for the ABS equations and the closure property of the Lagrangian multiforms. We give counterexamples for both these properties, but we recover them by including integer-valued fields, related to the branch choices, in the action sums.The impetus for this work was provided by the critical questions asked by an anonymous referee of the paper that has now become Part II of the present work [17]. We are grateful for their detailed feedback and constructive criticism. We would like to thank Prof Frank Nijhoff and Dr. Vincent Caudrelier for helpful discussions on the topic of this work and many related subjects. 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]
1D Landau-Ginzburg Superpotential of Big Quantum Cohomology of ℂℙ²
No full textUsing the inverse period map of the Gauss-Manin connection associated with *(ℂℙ²) and the Dubrovin construction of Landau-Ginzburg superpotential for Dubrovin-Frobenius manifolds, we construct a one-dimensional Landau-Ginzburg superpotential for the quantum cohomology of ℂℙ². In the case of small quantum cohomology, the Landau-Ginzburg superpotential is expressed in terms of the cubic root of the -invariant function. For big quantum cohomology, the one-dimensional Landau-Ginzburg superpotential is given by Taylor series expansions whose coefficients are expressed in terms of quasi-modular forms. Furthermore, we express the Landau-Ginzburg superpotential for both small and big quantum cohomology of *(ℂℙ²) in closed form as the composition of the Weierstrass ℘-function and the universal coverings of ℂ∖(ℤ⊕eπⁱᐟ³ℤ) and ℂ∖(ℤ⊕ℤ), respectively.I am grateful to Professor Hertling for his remarkable advice, guidance, and for proofreading this manuscript. Furthermore, I would also like to thank Professors Doran and Milanov for helpful discussions. I am also thankful to the anonymous referees for their valuable comments and suggestions. This work was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – 494849004. The work was carried out while I was at the University of Mannheim, and I now work at the Max Planck Institute of Molecular Cell Biology and Genetics, Dresden
Stolz Positive Scalar Curvature Structure Groups, Proper Actions and Equivariant 2-Types
No full textIn this note, we study equivariant versions of Stolz's -groups, the positive scalar curvature structure groups ˢᵖⁱⁿₙ()ᴳ, for proper actions of discrete groups . We define the concept of a fundamental groupoid functor for a -space, encapsulating all the fundamental group information of all the fixed point sets and their relations. We construct classifying spaces for fundamental groupoid functors. As a geometric result, we show that Stolz's equivariant -group ˢᵖⁱⁿₙ()ᴳ depends only on the fundamental groupoid functor of the reference space . The proof covers, at the same time, in a concise and clear way, the classical non-equivariant case.The authors thank the referees for the careful reading of the paper, improving the presentation, and helping to avoid inaccuracies