Cherkasy National University

This paper introduces a unified theoretical perspective that views deep generative models as probability transformation functions. Despite the apparent differences in architecture and training methodologies among various types of generative models - autoencoders, autoregressive models, generative adversarial networks, normalizing flows, diffusion models, and flow matching - we demonstrate that they all fundamentally operate by transforming simple predefined distributions into complex target data distributions. This unifying perspective facilitates the transfer of methodological improvements between model architectures and provides a foundation for developing universal theoretical approaches, potentially leading to more efficient and effective generative modeling techniques.

Coarsening of BCC precipitates in the B2-ordered phase of the AlCoCrFeNiTi0.2 compositionally complex alloy is investigated at temperatures between 1023 and 1273 K. The temporal evolutions of the morphology, size, distribution, and composition of these coherent precipitates are examined and evaluated. These BCC precipitates, formed through spinodal-like decomposition and appeared to be uniformly distributed in the B2 matrix, first grow as long strips and then transform to cuboidal-like particles before coarsening further. The coarsening kinetics of the precipitates is analyzed using the Philippe-Voorhees model, and this kinetics is correlated with the diffusion rates measured by the radiotracer diffusion technique. It is shown that accounting for both, the first- and second-neighbor interactions in a surrogate binary B2 structure, a simple model can be formulated which features A2 disordering, B2 ordering, and spinodal-like decomposition stages for an off-stoichiometric binary AB alloy as the temperature is decreasing.

The purpose of scientific research is to establish cause-and-effect relationships between technical progress , technological improvement , the acceleration of the digitalisation of entrepreneurship. It also involves searching for reserves for the digitalisation of business projects that affect production efficiency and the effectiveness of the country's economy. The object of scientific research is the field of knowledge and technology, existing patents and utility models, and scientific and technical articles, analysed in the context of groups of countries by income level. This analysis includes an evaluation of rating indicators and the GII, as well as the expansion of digital opportunities for entrepreneurship, based on existing human capital. The implementation of inventions, utility models and ideas produced by this capital is one of the key drivers of innovative and digital economic development. Methodology. Using dialectical and systemic methods, the impact of technical and technological progress on the movement of the production function curve in digital enterprises was investigated. This revealed a promising reserve of existing innovation with positive dynamics, highlighting the need for a strategic approach to the digitalisation of entrepreneurship. The concretisation method was employed to develop the author's proposals for innovation and the digitalisation of the country's economy. R & iecy;sults. The factors that determine the quality and efficiency of a digital enterprise are presented, including harmonisation of costs associated with developing innovative products and digital services, network effects, the growing importance of big data and analytics, resource availability, digital infrastructure, consumption dynamics and working with clients. Analysed statistical data showed that, for post- industrial countries with an innovative approach and a digital strategy, "healthy" competition stimulates digital development as businesses strive to provide higher-quality innovative products and digital services. The findings of the research conducted allowed the assertion to be made that digital entrepreneurship is both the result and the source of continuous scientific and technical achievements, inventions and ideas. Furthermore, the digital changes taking place in its work are based on new technologies that are constantly produced by the scientific world. Practical implications. The dissemination of practical advice has been undertaken, with the objective of maintaining positive dynamics in terms of accelerating innovation and digitalisation of national economies at both the macro and micro levels. Measures to promote the digitisation of traditional entrepreneurship are outlined, including the establishment of scientific, production, research and experimental digital ecosystems based on the country's leading industry-focused universities, and the development and implementation of youth scientific support programmes lasting three, five and seven years, under the names "Youth in Research", "Innovations and Young Researchers", and "Youth. Inventions. Progress". Hold events in leading scientific and technical laboratories under the names "Week of Innovations , Inventions", "Week of Science and Technology" and "Week of the Researcher, Innovator and Inventor". Every science needs individual researchers, inventors and innovators. In the innovation-digital process, the innovator who produces the invention is therefore a valuable "player" and a key link. Value/Originality. After conducting a thorough analysis of the Global Innovation Index ratings by country group and income level, the authors found that China leads the group of countries with above-average incomes in terms of the number of patents and utility models. The leaders of the "Labour and Technology Results" index in terms of knowledge creation remain the three high-income countries of Sweden, Switzerland and the USA. Analysis of the available data revealed that the level of development of intangible assets can accelerate the formation and development of digital entrepreneurship and facilitate business mobility. Technical and technological progress is proposed to be understood through the prism of the formation of Industry 5.0, which is a consistent process of improving and perfecting production and industrial business processes with the aim of producing new products and services while focusing on the quality of existing goods and services. It has been determined that changes in technology and technologies are indicative of transformations occurring in terms of digitalisation in production business processes. Alternatively, enterprises have the capacity to develop and utilise new or improved innovative products and digital services. The overall socio-economic effect of digital entrepreneurship is predicated on the interrelation of technical and technological changes, capital utilisation , enhanced productivity per employee. It is hypothesised that, in terms of the genesis of Industry 5.0, this will signify the evolution of digital business, enhanced remuneration for proficient workers who possess digital competencies, and an enhancement in the quality and standard of living of the population.

This article examines the fundamental transformation of Civilian Telecommunications Infrastructure (CTI), which by 2026 has evolved from a service industry into a critical cyber-physical macrosystem. The author analyzes the burgeoning divergence between the pace of technological innovation (5G-Advanced, 6G, SDN/NFV, Edge Computing) and the inertia of traditional regulatory institutions. Based on systems analysis and the case study method (Orange, Starlink, Rakuten Mobile), the research substantiates the necessity of transitioning from rigid state administration (government) to flexible models of multi-level governance (governance). The work proposes a concept of hybrid governance that integrates Zero Trust Architecture (ZRA), dynamic compliance mechanisms and digital twins as proactive oversight tools. Particular emphasis is placed on issues of cyber resilience in the context of the quantum threat (Q-day), algorithmic transparency (XAI) and the implementation of ecological imperatives (Green ICT). As a result of a comparative analysis of approaches in the EU, USA and Asian countries, universal principles of effective regulation have been identified, ensuring a balance between technological sovereignty and global network connectivity. The article establishes a scientifically substantiated basis for the creation of adaptive regulatory frameworks capable of serving as a catalyst for long-term progress in an era of global digital uncertainty.

The article examines the results and current challenges of the reform of local self-government and territorial organization of power in Ukraine in the context of national resilience, post-war recovery, and European integration. It is substantiated that decentralization has contributed to the formation of institutionally and financially capable territorial communities, the expansion of their administrative autonomy, and the strengthening of the principles of subsidiarity and responsibility. The key outcomes of the reform are identified, including the strengthening of the financial capacity of territorial communities, the formation of a new territorial framework for local self-government, and the development of digital public services. It is established that, under the conditions of the full-scale war, territorial communities have demonstrated their ability to maintain critical infrastructure, provide essential public services, and respond promptly to security and humanitarian challenges, confirming the important role of decentralization in ensuring national resilience. The strategic importance of local self-government for post-war recovery based on the build back better principle is substantiated, combining reconstruction with energy efficiency, inclusiveness, digitalization, investment attraction, and local economic development. The main challenges to the further implementation of the reform are identified: the incomplete institutional and regulatory framework, financial disparities among territorial communities, shortages of qualified personnel, and the risks of excessive supervisory pressure. Priority areas for the further development of decentralization are proposed, including strengthening the financial and human resource capacity of territorial communities, improving state supervision mechanisms, advancing digital governance, and developing partnerships between the state, territorial communities, businesses, and international partners. It is demonstrated that strengthening local self-government is an important prerequisite for effective post-war recovery, the economic resilience of territories, and Ukraine’s further European integration. Keywords: decentralization, local self-government (LSG), territorial communities (TCs), resilience (Resilience), recovery (Recovery), European integration, personal income tax (PIT), Institution of Prefects, personnel shortages, pressure on LSG.