Khmelnytskyi National University

The identification of the real level of economic development of the region is an important condition to design effective regional development policy. Economic development is characterized by a large number of indicators. This study provides an approach for assessing the level of economic development based on the use of a comprehensive index, which is a convolution of initial indicators. The model involves the use of both a group of absolute indicators and a group of relative measures of dynamics. Each of the groups of indicators has its special data normalization procedure and its special method of convolution into a partial comprehensive index. The outcome of the evaluation is obtained by weighted multiplicative convolution of partial comprehensive indexes. In this study, the level of economic development of regions of Ukraine according to the data of 2017 has evaluated. As a result, Ukraine’s regions were allocated into three groups: with the level of economic development above average, with the average level of economic development and with the level of development below average. The article suggests a way to determine the boundary values of the comprehensive index for grouping. Comparison of the obtained results of grouping with the results of clustering of the Ukraine’s regions by the k-means method with the same data showed their identity. The article shows that Ukraine’s regions can be allocated by the level of economic development into other number of groups.

We present two realizations of the 𝔰𝔩2-action of a complex Lie algebra 𝔰𝔩2 on the algebra of symmetric polynomials Λn via differential operators. For each realization, we determine its action on Schur polynomials and obtain a decomposition of Λn into irreducible representations. By using an 𝔰𝔩2-isomorphism between Λn and the vector space of Young diagrams ℚYn with at most n rows, we transfer these representations to ℚYn.

We present a complete algebraic description of the field of first-order joint projective invariants for configurations of n points in the plane, under the natural diagonal action of the projective group PGL(3,R). For n>1, we construct an explicit minimal generating set for the field of absolute invariants and prove its algebraic independence. We further determine the structure of the full field of invariants as a simple algebraic extension of field of absolute invariants, generated by a single primitive relative invariant of weight -1, for which we provide a closed-form expression valid for all n>1.

The enterprise as an economic system at the micro level is characterized by uncertainty in situations when making decisions, a large number of input indicators, as well as the presence of a decision maker of information that is poorly formalized and cannot be taken into account when applying only quantitative methods. The uncertainty of the system leads to an increased risk of ineffective decisions, which may result in negative economic, technical and social consequences. The research considers the main structural elements of the strategy of developing the foreign economic potential of microeconomic systems. On the basis of calculations, the clear meaning of the indicators that are included in the groups defining the basic elements of the external economic potential is obtained. The algorithm of forming the strategy of development of the foreign economic potential of the enterprise is presented in the framework of the general approach to the organization of the process of increasing the foreign economic potential of microeconomic systems on the basis of a unified information system. As a result of the formation of a mechanism for increasing the foreign economic potential of microeconomic systems, a strategy was developed that was based on substantiation of the direction of development of foreign economic potential in accordance with the level of influence of external factors, using the method of fuzzy modeling and modeling the process of organizational interaction.

Subject of the Study. The subject of the study is the theoretical, methodological, and applied foundations of the formation and implementation of product innovation policy in the system of international exchange trade under conditions of digitalization, globalization, and transformation of global commodity markets. Purpose of the Study. The purpose of the article is to investigate the conceptual foundations of product innovation policy in the system of international exchange trade and to substantiate directions for enhancing the competitiveness of goods in the context of globalization, digitalization, and the transformation of global markets. Research Methods. The methodological basis of the study consists of general scientific and specialized research methods that ensured a comprehensive analysis of the conceptual foundations of product innovation policy in the system of international exchange trade. The methods of analysis and synthesis were applied to generalize theoretical approaches to the formation of product innovation policy; the systems approach was used to examine the interrelationships among innovative, digital, institutional, and market factors influencing the development of international exchange trade; and the comparative method was employed to assess global trends in digitalization, ESG transformation, and the development of exchange markets. Theoretical generalization, logical, and institutional methods made it possible to substantiate directions for improving product innovation policy, digitalizing exchange processes, and enhancing the competitiveness of goods in the global economic environment. Research Results. The study established that product innovation policy in the system of international exchange trade serves as an important instrument for ensuring product competitiveness under conditions of globalization, digital transformation, and increasing international competition. It was substantiated that the formation of modern product policy should be based on a combination of innovative product development, digitalization of trading processes, international standardization, ESG-oriented management, and mechanisms for adapting to changes in the global market environment. It was determined that the technological level of products, their environmental responsibility, digital traceability, and compliance with international quality standards are becoming key factors in creating competitive advantages in global exchange markets. The research proved that the digitalization of international exchange trade significantly increases the efficiency of commodity market functioning through the implementation of electronic trading platforms, blockchain technologies, smart contracts, digital certification systems, and Big Data analytics. It was established that the use of modern digital tools ensures greater transparency of exchange transactions, reduces transaction costs, accelerates the processing of trade agreements, and improves control over commodity flows. It was substantiated that the integration of digital technologies into the system of international exchange trade contributes to the formation of effective market monitoring mechanisms and increases the accessibility of international trading platforms for market participants. The study revealed that the further development of international exchange trade requires improvements in the institutional environment, harmonization of regulatory requirements, development of ESG-oriented trading mechanisms, and broader access of enterprises to digital exchange infrastructure. The expediency of implementing integrated digital platforms, developing electronic product certification, applying risk-oriented market monitoring systems, and supporting innovative commodity clusters was substantiated. The implementation of these measures will contribute to enhancing product competitiveness, integrating enterprises into global value chains, and strengthening Ukraine’s position in international commodity markets.