This work presents a stress-strain state analytical estimation of restored tooth hard tissues with consideration of their contact interactions with a monolithic filling or a dental onlay. The tooth with a defect is simulated as a continuous isotropic cylindrical body with a non-through hole, and the filling or onlay is simulated as an elastic deformable cylinder. The contact between the tooth and the fillings (onlay) is simulated as the ideal contact. The final strength estimation of the restored tooth is carried out according to the energy criterion. The authors suggest a linear index of tooth damage for practical application of the obtained results. This index can be easily obtained by direct measurement. The differential approach is developed to select a restoring method of the tooth with the defect to provide a reliable restoration of the anatomical crown of the tooth.

This paper substantiates that increasing the capacity of the consumer market is an important direction of the life quality improvement policy. Its implementation is the major strategic priority of all reforms in Ukraine. Based on the methods of economic and mathematical modeling, namely constructing the linear multiple regression equation, the level of impact of stimulating and destimulating factors on the consumer capacity of the oblasts of the Carpathian region is determined.

The influence of military-political instability at the state security has special consequences and cannot be ignored. That is why the methods of economic security calculations should be adapted to modern conditions. Significant changes in economic, political, social conditions in Ukraine because of the influence of military events cause the necessity of developing approaches to calculations of economic security level. The article aims at analyzing active methods of calculations of economic security level to adapt their indicators to actual economic circumstances in Ukraine and the world. Indicators of the economic security have been composed of budget, money-credit, foreign exchange, debt, known banking financial market security, banking security. Every component of economic security has factors of war influence, which, as a result, correlates with the integral indicator of economic security. The relevance and indispensability of reinforcement of the economy’s competitiveness on security foundations are substantiated. The authors’ methods of calculation of an integral indicator of economic security have been suggested. A taxonomic indicator is used to measure the level of security. Conclusions regarding the preconditions, capacity, and availability of tendencies of economic security in regions of the country have been made. Strategic priorities of the state policy for reinforcement of economic security have been substantiated.

The reaction of lithiation of 2-bromo-4-(1,3-dioxolan-2-yl)-1,3-thiazole with in position 5 of the thiazole ring and double lithiation with t-butyllithium (t-BuLi) in positions 2 and 5 lithium diisopropylamide (LDA) are investigated. When lithiated and dilithiated thiazoles were treated with different electrophiles, a number of trifunctional 1,3-thiazoles were obtained with high yields.

The agricultural production, due to the specificity of the functioning of the agricultural industry, is influenced by factors that have significant impacts on agricultural enterprises and determine the importance of state support. The unpredictable factors of agrarian production such as weather, natural disaster, and epidemics increase the risks of agricultural business. That is why farmers need to attract investments. But some farmers do not attract investment because of government subsidies. Besides, using government subsidies could have a negative impact on agrarian business. So, it is necessary to establish the effectiveness of governance for agricultural production and food security in general.

Recently, there has been explosive growth in the development of the digital industry concept. One of the most important elements of this concept is the application of mathematical modeling methods and data mining to create models of production processes and final products, with the aim of making decisions under stochastic uncertainty. In this paper, a method of diversifying the investment portfolio in the formation of a digital twin is proposed, which is aimed at reducing the total risk by distributing existing assets (resources, investments, etc.) between the analog and digital enterprises. Three types of scenario are proposed: pessimistic - when an enterprise - a pessimist - does not show risk exposure under this scenario when forming a digital counterpart; neutral - when an enterprise shows a neutral attitude to risk (indifference); optimistic - enterprise - optimist is exposed to risk, in particular the risk of untapped opportunities. The result is a set of optimal portfolios, each reflecting a particular position of the enterprise on the risks of untapped opportunities and a certain scenario of forming a portfolio structure, taking into account the relationship between the individual components of the risks of untapped opportunities. Highlighted the advantages of technology "digital twins" for business. Digital counterparts use the data obtained from sensors installed on production lines or on the basis of the final product to predict equipment malfunctions, optimize product quality and reduce the negative impact of production processes on the environment.

In a market economy, entrepreneurship requires large-scale innovations to maintain competitiveness and high rates of economic growth, and large investments are needed to implement innovations. However, in the process of their activities, investors face increased investment risk and therefore need reliable methods of investment evaluation and investment modeling of innovations in industrial enterprises. In this regard, the purpose of this study is to develop a conceptual model for assessing the investment attractiveness of innovative projects. The article builds a graphical model of investment in an innovative product at different stages of its life cycle. A conceptual structural and mathematical model for assessing the investment attractiveness of innovative projects of industrial enterprises has been developed, which reflected the stages of risk management, phases of the life cycle of the innovation project and the stages of the innovation process. The main idea of the proposed model is to manage investment in innovation based on the impact on the level of specific innovation risks.

This paper was retracted based on the authors' request due to errors in the computations.

In connection with the global financial and economic crisis, the leading countries have made adjustments to the economic strategies and policies to stabilize the post-crisis economy. The goal of transnationalization is, on the one hand, to reduce quickly the technological gap between domestic producers and their Western competitors, and on the other hand, to win more dynamic demand at lower costs. Ownership structure and market positioning have become two factors that determine the strategic motivation of Transnational corporations (TNCs) and the ways of their expansion. The aim of the study is to analytically generalize the globalization trends of TNCs in the field of production, taking into account industry definitions and point determination of factors influencing the effectiveness of its adaptation in industry. The profiles of adaptation of transnationalization in the sphere of production of Germany, France and the Netherlands were singled out in separate analytical sets, which allowed to reveal heterogeneity of economic practices and branch changes in the sphere of production and to determine the degree of influence of array of variables (factors): Production value and Gross operating surplus profitability of multinational companies, in the sectoral context (domestic production, ISIC Rev 4, 21 industry), as a “basket” of reserve instruments to increase the profitability of production in TNCs.

The complexity and ambiguity of the contribution of foreign direct investment (FDI) to economic growth necessitates the development of recommendations for the analysis and management of foreign investment flows to maximize their positive impact on the economy and prevent negative consequences. In this regard, the aim of the study is to propose an economic and mathematical modeling of the foreign direct investment impact on economic growth and their interaction with domestic direct investment. The article proposes a classification of factors that determine the inflow of foreign direct investment to developed countries and developing countries. By introducing the external effect of foreign direct investment (capital repatriation), the authors modified the model with foreign direct investment in the form of accumulated foreign capital reserves. An analytical expression is obtained to relate the rate of economic growth to the amount of repatriation depending on the effects of supplementing and substituting foreign direct investment for foreign direct investment.

This paper was retracted based on the authors' request due to errors in the computations.

The research is devoted to the adaptation of theoretical and applied organizational grounds of favorable investment climate based on the establishment of an efficient mechanism of investment capacity increase in Ukraine. The main aim of the paper is to substantiate the mechanism of forming a favorable investment climate as the basis of investment capacity increase in Ukraine. The paper verifies the authors’ hypothesis on the adequacy of the substantiation of the mechanism of favorable investment climate forming as the basis of investment capacity increase leading to the substantial improvement of Ukrainian positions in international rankings. The dependence of Ukraine’s investment climate on the formed mechanism of its development is confirmed, and the necessity of its improvement is emphasized. The paper proves that forming of the favorable investment climate as the main precondition of boosted development, reproduction, and efficient use of investment climate at all levels is one of the most important strategic tasks that Ukraine faces. Economic, institutional-legal, and organizational-administrative mechanisms and implementation tools directed at improvement of the investment climate in Ukraine and the creation of conditions for investment capacity growth and its efficient transformation into an investment product are systematized.