Purpose. Determining the structural elements of savings and clarifying the characteristics of their transformation into real and financial investment as well as studying the role of banks, pension funds, insurance companies and collective investment institutions in these processes in modern Ukrainian realities. Methodology. Structural and functional analysis of components of using savings and general principles of macroeconomic modelling has been applied. Finding. It has been proved that equality of savings and investment are only a necessary but not sufficient condition for achieving equilibrium. Three areas of savings use have been selected: for completion of financial and non-financial assets, as well as increasing cash reserves. It was found that part of the savings is eliminated from the process of their transformation into investment through sedimentation as cash reserves or through replenishment involved in speculative operations in the financial markets. The loss must be compensated at the expense of the money multiplier, creating a threat of building a macroeconomic pyramid and it is one of the causes of the financial and economic crisis. Funds mobilized by pension funds, insurance companies and collective investment institutions tend to remain in circulation in the financial market and do not turn into real investment. The balance of savings and investments under these conditions can be achieved only when new bank loans exceed the loans to be returned at this time. This cannot last continuously. That is why government regulation of saving processes is necessary. Originality. The macroeconomic equilibrium model considering the different possibilities of individual parts to transform savings into investment has been improved. Practical value. The ways of state influence on the structure of using savings, the implementation of which will improve the macro-economic, balance have been substantiated.

Purpose. Development of a methodology for identifying leaders of modern world development based on the ranking of applicants by key indicators that reflect the status and trends of their development. Methodology. The development of a methodology for identifying world leaders is based on four criteria: the country's economic potential; opportunities to influence other countries and the development of the world economy as a whole; efficiency of available potential use; the country's innovation. The calculation of the Global Leadership Index is based on comparing the corresponding indicator for each country with the best indicator in the world and adjusting it by the weight factor. The sum of the results will be shown by the Global Leadership Index. Finding. Based on the analysis, it is revealed that the undisputed economic leaders of the modern world are the US and the EU, which have virtually the same value of the Global Leadership Index. However, due to the monolithic character the United States position is more preferable. The role of leaders can also be claimed by China and Germany. Although China is still inferior to the US and the EU, the dynamics of its economic development and the magnitude of its impact on the world give reason to predict its approach to leaders. On the contrary, Russia and India can still only claim to be regional leaders, not world leaders. Originality. The original methodology for calculating the Global Leadership Index, based on the country's ranking of GDP, exports of goods and FDI in global indicators, as well as GDP per capita and Global Index, has been proposed. Practical value. The results of the study can be used to identify trends in world leaders' changes and to predict possible directions for exacerbation of contradictions on this basis.

Purpose. To classify the models of assets and liabilities of the Visegrad Group and compare them with similar indicators of Ukraine's international investment position. Methodology. The separation of models is carried out by three criteria: the formation of the structure, the degree of risk and the activity of the state. The asset model of Ukraine's international investment position is defined as dynamic, with low risk and moderate government intervention. The liability model is also dynamic, but with high risk and increased government activity. Ukrainian economic models are not similar to any of the studied European models and are irrational by most criteria. Finding. Based on the comparison of the models of assets and liabilities formed in Ukraine with similar indicators of the Visegrad Group countries, a number of hypotheses about the strategy of improving the international investment position of Ukraine have been expressed. The basis for solving these problems should be activities aimed primarily at solving the internal problems of Ukraine, which can improve the mechanisms of direct and portfolio investment. Originality. An original methodology for classifying the models of assets and liabilities of the country's international investment position has been developed. Its approbation by the example of Visegrad countries and Ukraine allowed finding the strengths and threats of different models and predict future scenarios of changes in the international investment position. Practical value. The developed methods for assessing the models of international investment position of the country can be used in other studies, which will allow developing countries to choose a certain international model to develop their own strategy for managing international financial flows.

Основна мета статті - розробка тривимірної CFD-моделі для моделювання процесу біологічного очищення стічних вод в аеротенку. Для математичного моделювання процесу біологічного очищення стічних вод у реакторі, з урахуванням гідродинаміки потоку, геометричної форми аеротенка, конвективно-дифузійного переносу субстрату та активного мулу, побудовано тривимірну CFD-модель. В основу моделі покладено тривимірне рівняння руху ідеальної рідини тарівняння збереження маси для субстрату й активного мулу. Поле швидкості потоку стічних вод в аеротенку розраховано на базі рівняння для потенціалу швидкості. Процес біологічного перетворення субстрату розраховано на базі моделі Monod. Для чисельного інтегрування рівнянь конвективно-дифузійного переносу активного мулу та субстрату використано схему розщеплення. Розщеплення здійснено так, щоб на кожному кроці враховувався перенос субстрату (активного мулу) лише в одному напрямку. Розрахунок невідомої величини концентрації субстрату (активного мулу) виконано за явною схемою. Під час чисельного інтегрування тривимірного рівняння для потенціалу швидкості використано метод Річардсона, розрахунок невідомого значення потенціалу швидкості здійснено за явною формулою. Для чисельного інтегрування рівнянь, що описують процес трансформації субстрату та зміну концентрації активного мулу (модель Monod), використано метод Ейлера. Здійснено програмну реалізацію побудованої тривимірної CFD-моделі. Описано структуру розробленого пакету програм. Подано результати проведеного комп'ютерного експерименту з дослідження процесу очищення стічних вод в аеротенку з додатковими елементами. Розроблено нову багатофакторну тривимірну CFD-модель, що дозволяє швидко оцінити ефективність біологічного очищення стічних вод в аеротенку. Побудована CFD-модель може бути використана для аналізу ефективності роботи аеротенку за різних умов експлуатації та на етапі ескізного проектування систем очищення стічних вод.

The object of this study is the process that forms conceptual foundations for managing the impact of virtual water deficiency risks on the global food crisis. The main idea of the study focuses on determining the consequences of the global food crisis in the world under the influence of a significant reduction in virtual water exports from Ukraine to agri-food markets. It is determined that most likely, in the context of the replacement of Ukrainian exports of grain and agricultural products as a result of Russian aggression in Ukraine, the countries of the world will resort to new ways of obtaining effective imports of virtual water from other countries. The study proved that rapid structural changes in the economies of the countries of the world and the reorientation of their national economies towards the development of the agricultural sector under modern conditions of global uncertainty would inevitably lead to certain consequences. Namely, either to the fall in the growth rate of national economies, or to the state of the "bifurcation explosion" with the subsequent dispersion of possible states of development. The proposed scientific and methodological approach to assessing the sustainability of the systemic development of the territory over time for water-intensive regions makes it possible to take calculated decisions at the national level regarding the scale and prospects for the development of economic activities in the state. The described theoretical and methodological foundations of the interdependence of water and food security and the developed fundamental provisions of the economies of countries under the conditions of the global food crisis and the risk of a shortage of virtual water will create the following opportunities. Specifically, they enable state authorities to assess the depth of the specified crisis in the world and its consequences for all countries in 2022 - 2023. Such an understanding creates the conditions for making effective decisions on the volume of import of virtual water in a particular country.