Heterogeneity is an important factor controlling fracture initiation, accumulation, and propagation within rock destruction. Traditionally, rock reaction instability within rock destruction is associated with rock non-homogeneity or considered self-excited, but no clear relations between rock structure options and reaction force oscillation were proposes. This work hypothesizes the idea rock structure options are one of the factors of drill bit whirling. The authors innovated the Wojtanowicz and Kuru’s force static balance model to numerically simulate 3-cutter movement in a rock space, assuming a crack propagates by rock grains getting around. Instability of deviation between directions of cutting force and crack propagation causes rock reaction instability. Novelty of this work is to consider the mutual influence of rock granulomentric composition options (sizes, shape and distribution of grains) and drill bit design options (cutter diameter, distance between adjacent cutters, etc.) on rock reaction force oscillation. The follow tendencies were observed: rock grain dimension increasing and grain concentration increasing were accompanied with rock reaction force magnitude decreasing; random grain placing and/or grain random dimensions caused increasing of rock reaction force scattering; random grain sizes are more essential for rock reaction forces (and their projections) scattering than random grain distribution.

The paper aims to develop a model for measuring economic system management efficiency of the Black Sea region of Ukraine through the context of sustainable development. The model includes the rates of social and economic efficiency, productivity, and performance. The proposed approach calculates the region’s economic system management efficiency. The respective evaluation criteria are systematized: economic and social efficiency of the region’s economic activity, productivity of the use of resources, and performance of the management system. The system of evaluation indicators by each criterion and mathematical apparatus to calculate them are suggested. The paper suggests methodical approaches to evaluate the economic system management efficiency in the region under transformation. They help determine the current level against similar indicators achieved within the country and the tendencies influenced by regional factors, form the “economic system management profile”, and identify the strengths and bottlenecks.

Trading is the most sensitive sector of the economy, directly and indirectly responding to innovative challenges. High competition, political risks and planetary scales have made it susceptible to any globalization fluctuations. Effective management is seen as the most important opportunity to gain competitive advantage. This explains the increased interest in the system of indicators of management system evaluation in the business processes in the supply chains. The aim of this paper is to develop and substantiate analytical approaches to the study of the status of transnational trade economic relationships with the identification of significant impact indicators and vulnerability indicators. The globalization aspect of the existing trend of world trade (export-import) among differentiated groups of countries is justified, distinguishing the forecast component. A two-tier model of business process “reliability management” has been constructed, taking into account the results of linear regression models based on the profiles of Australia and New Zealand.

The objective of this paper is to determine the basic features of the use of mathematical modeling of the system to forecast cryptocurrency exchange rate. The study determines that cryptocurrency is the simplest investment asset being and, at the same time, the riskiest one. Advantages and disadvantages of cryptocurrency use are specified. Advantages include: code openness, anonymity, decentralization, emission, and reliability. Disadvantages include lack of guarantees, instability, risk of prohibition and possible loss. A model to forecast bitcoin cryptocurrency exchange rate is proposed and substantiated mathematically. The observations are the basis to develop a hypothesis: the faster the cryptocurrency (e.g. bitcoin) is mined, the more difficult it is to forecast bitcoin cryptocurrency exchange rate. Certain factors emphasize which may affect the cryptocurrency exchange rate: trade wars of the USA with other export-oriented world economies (China); advent of IEO as the alternative for ICO and new drivers connected with the interest in cryptocurrency; FATF recommendations for market control, the entry of world giants (e.g. Facebook) into the crypto-market and the development of the stablecoin market.

Readily available tetrachloro-2-aza-1,3-butadienes enter into directed cyclocondensation reaction with N-phenyl-1,2-cyclopentanediamine which leads to regioselective cyclopentane annulation by the 1,3,5-triazepine. The formation of the 1,3,5-triazepine derivatives was confirmed proved by 1H- and 13C-NMR spectral study, elemental analysis and, in one case, single-crystal x-ray crystallographic study.

In the context of globalization and fierce competition in world markets, the high level of investment activity in the country is a key to economic and innovative development. The high level of wear and tear of fixed assets in developing countries gives special relevance to solving the problem of attracting investments for production development. Hence, for the investment management system choosing an optimal variant among several available investment projects is one of the most responsible stages of ensuring the stable operation and sustainable development of an enterprise. In this regard, the aim of the article is to develop a comprehensive multi-criteria approach to choose the best investment option. The article analyzes the existing methodological approaches to assess the economic efficiency of the investment projects, identifies their advantages and disadvantages. A multi-criteria method of investment project evaluation is proposed, which is characterized by the absence of restrictions on the number of individual evaluation indicators and the possibility for the investor to determine the significance of every indicator using weights independently. The use of the proposed methodology by enterprises will improve the quality of management decisions at the stage of choosing the optimal investment option.

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

The quantum-chemical modeling mechanism of the [4+2]-cycloaddition reaction of 2,3 dimethylbuta-1,3-diene and methyl acrylate was conducted. Its qualitative aspects were analyzed at the molecular level by the program MOPAC2012 and semiempirical method RM1. The potential energy surfaces of 2,3 dimethylbuta-1,3-diene and methyl acrylate [4+2] cycloaddition possible reaction pathways were constructed by restricted and unrestricted Hartree-Fock approximation. It has been established that the molecule of the final product methyl-3,4-dimethylcyclohex-3-encarboxylate has the half-chair shape, wherein the carboalkoxyl group is in the exo-orientation. Interaction between molecules of 2,3 dimethylbuta-1,3-diene and methyl acrylate occurs by a two-step mechanism more likely than one-step, since the activation parameters of this interaction maximum coincide with the experimental data.

Ensuring household food security should be a priority goal of state policy. The level of ensuring household food security reflects the state of the country's economic development and the effectiveness of agricultural policy. Household food security is achieved by ensuring a high level of purchasing power of households, which is possible by increasing income. Savings are the “safety cushion” for households during the financial and economic crisis caused by the coronavirus pandemic. The level of household savings is important both for the households themselves and for the country's economy, since savings, on the one hand, help to avoid hunger during crises, and, on the other hand, are an important investment resource for the country's economy. That is why assessing the level of household savings and identifying factors affecting savings are important aspects of building an effective government policy in the field of food security.

The global process of society information has covered almost all countries of the world and is currently the core of scientific, technical and socio-economic development. The effectiveness of the power exercise in any state depends on its information support. Indeed, without information, successful political structure, the development of mass political consciousness as well as the interaction of the subject and the object of government are impossible. That is why this research aims to improve the methodics of evaluation of informational security through theoretical-methodological substantiation, forming and calculation of integral indexes of its competitiveness of a country. Global economic crisis had consequences for almost every country and cannot be ignored by any conditions, that is why the methodic of informational security calculations should be adapted to modern economic conditions. Cardinal changes in political, economic and social conditions in Ukraine causes inaccessibility of approaches to information security level calculations and particularly in the national security system. In modern scientific schools the questions of effective informational security have not been sufficiently studied. The aim of this article is to analyze active methods of state informational safety level calculations in order to adapt their indexes to actual global circumstances in Ukraine and in the world. Integral informational security have been composed of such components (indicators): income of the broadband Internet access market, dynamics of broadband Internet subscribers (connections), penetration rate of fixed broadband access (number of subscribers per 100 people), dynamics of Internet penetration (percentage of Internet users to the total population of the country), Network Readiness Index of the country, ICT Development Index of the state, Global Innovation Index, capital investments in intangible assets of Ukraine (that is, in software and databases). Every component of informational safety has factors of relevance and indispensability of reinforcement of national competitiveness on security foundations are substantiated. A taxonomic indicator is used to measure the level of informational safety. The paper proves that each of the components of the state informational security has almost equal input in forming its integral index.

Two potential energy surfaces 1 ²A1 and 1 ²B1 for linear geometry of F-H-Br system have been computed with aug-cc-pVQZ basis set using dynamically weighted state averaged MCSCF followed by MRCI-F12 method. State 1 ²A1 has smaller barrier height (3.49 kcal/mol) than 1 ²B1. (13.6 kcal/mol). The latter has deep van der Waals well in Br-HF valley (2.12 kcal/mol).