graphical method
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Abstract. The article discusses the developed graphical method of calculating the size rolls diameter and the radius of their contact with the jaws.

The research aims to examine the theoretical aspects of administrative and territorial reform as well as to identify the attitudes of Latgale region residents to implementing the new administrative and territorial reform. The following research methods were employed: qualitative content analysis; analysis of legislative enactments and legal documents; a sociological research method – a survey was conducted to identify the opinions and assessments of Latgale residents about the new administrative and territorial reform; descriptive statistics and the graphical method. The research examined theoretical aspects regarding the division of territory into administrative units as well as the concept and definitions of a municipality as an administrative unit. The research analysed the results of the survey of Latgale region residents and identified the respondents’ assessments of implementing the new administrative and territorial reform.

The problem of the study is that Latvian citizens often express dissatisfaction with vehicle registration prices, speculating that these services are available at lower prices in the neighbouring countries – Lithuania and Estonia. The aim of the research: to compare and analyse vehicle registration services in the Baltic States in order to provide suggestions for the improvement of the services. The research uses general scientific research methods: the monographic and descriptive methods, the document analysis method, the comparative analysis method, the horizontal analysis, the ranking method, the logical construction method and the graphical method. Based on the cases analysed, the authors conclude that vehicle registration costs are the lowest in Lithuania, yet these costs may depend on factors such as vehicle age and technical parameters, so not always the cheapest price is reported in Lithuania. Vehicle registration costs in Estonia, regardless of any parameters, for all light vehicles are the same at 192,00 euro. The authors compared and analysed vehicle registration services in the Baltic States, evaluated the price of services and the elements included in them. The study shows that when receiving vehicle registration services in the Baltic States, the conditions and price for receiving them differ. It is mainly influenced by the tax policies and pricing strategies of each country.

The paper revisits some pioneering work of Sir Thomas Havelock on wave patterns with particular attention focussed on his graphical method of analysis. Motivated by a desire to explore this method further using numerical methods, it is extended in a simple manner to give three-dimensional illustrations of the wave patterns of a point disturbance in deep and shallow water. All results are confined to the sub- and trans-critical regimes with some obtained very close to the critical Depth Froude Number. Some conclusions are drawn on the wave types produced when operating close to the critical speed and their decay with distance off.

Abstract The article presents the results of studies of the process of obtaining NPK fertilizer from low-grade phosphate raw materials with P2O5 of about 18%. Phosphate raw materials were leached with a mixture of nitric-phosphoric acids with the addition of potassium carbonate, which serves as a source of potassium in the final product. The main parameters determined were the content of the main nutrients P2O5:N:K2O, temperature and time of the leaching process. According to the graphical method, the “apparent” activation energy of the heterogeneous process is found, which is equal to 3.8 kJ/mol indicates the intradiffusion nature of the process. Methods of chemical analysis, scanning electron microscopy and XRD analysis were used for a comprehensive study of raw materials and final products.

AbstractComparing the differences in outcomes (that is, in “dependent variables”) between two subpopulations is often most informative when comparing outcomes only for individuals from the subpopulations who are similar according to “independent variables.” The independent variables are generally known as “scores,” as in propensity scores for matching or as in the probabilities predicted by statistical or machine-learned models, for example. If the outcomes are discrete, then some averaging is necessary to reduce the noise arising from the outcomes varying randomly over those discrete values in the observed data. The traditional method of averaging is to bin the data according to the scores and plot the average outcome in each bin against the average score in the bin. However, such binning can be rather arbitrary and yet greatly impacts the interpretation of displayed deviation between the subpopulations and assessment of its statistical significance. Fortunately, such binning is entirely unnecessary in plots of cumulative differences and in the associated scalar summary metrics that are analogous to the workhorse statistics of comparing probability distributions—those due to Kolmogorov and Smirnov and their refinements due to Kuiper. The present paper develops such cumulative methods for the common case in which no score of any member of the subpopulations being compared is exactly equal to the score of any other member of either subpopulation.

Information system of motor transport enterprise is one of the most important components of its activity. The perfection of this system strongly affects the efficiency of the enterprise. The purpose of the article is to develop proposals for improving the existing information system taking into account the characteristics of the enterprise. To achieve the objectives of the article, the following methods were used: information on approaches to defining the concept of information system was analyzed and synthesized, the existing approaches to the design of information systems were sassessed. Using a logical approach, the components of the information-logical model of the “Travel Letter” database were identified. The study also widely used the methods of comparative analysis, graphical method and the method of operagrams to study the document flow of the enterprise. In the article the information system of the motor transport enterprise which, unlike existing ones, takes into account current condition of the information flows, which provide effective management of the enterprise and optimizes the routes of document movement was further developed. The proposed improvements will allow MTE to achieve their goals more systematically, increase the speed of information flows, ensure their quality and efficiency. The obtained results, which include the development of an improved information system of the enterprise, allow to carry out further research on the document flow of all divisions and services of MTE and to develop their improved information systems on the basis of research results.

The graphical progression method can obtain grand coordinated schemes with minimal computational complexity. However, there is no standardized solution for this method, and only a few related studies have been found thus far. Therefore, based on the in-depth discussion of the graphical optimization theory mechanism, a process-oriented and high-efficiency graphical method for symmetrical bidirectional corridor progression is proposed in this study. A two-round rotation transformation optimization process of the progression trajectory characteristic lines (PTC lines) is innovatively proposed. By establishing the updated judgment criteria for coordinated mode, the first round of PTC line rotation transformation realizes the optimization of coordinated modes and initial offsets. Giving the conditions for stopping rotation transformation and determining rotation points, rotation directions, and rotation angles, the second round of PTC line rotation transformation achieves the final optimization of the common signal cycle and offsets. The case study shows that the proposed graphical method can obtain the optimal progression effect through regular graphing and solving, although it can also be solved by highly efficient programming.

The aim of the study is to analyze and forecast the use of payment cards for making non-cash payments through national payment systems in Kazakhstan. Based on this goal, a hypothesis was put forward that in Kazakhstan, there is a relationship between the number of payment cards and the volume of non-cash payments. This hypothesis was confirmed because of the study. The information base of the study was the data on payment cards, which were taken from the Statistical Bulletin of the National Bank of the Republic of Kazakhstan. Hypothesis testing was carried out using correlation analysis for three periods: 2009, 2016, 2020. The method of finding Pearson’s correlation in the SPSS program was used. The results showed a downward change in the relationship between the selected indicators and the amount of funds transferred over time. Also, in this study, a forecast was made for 2021-2023 for the indicators under consideration. To make a forecast for the indicators under consideration, a graphical method (polynomial trend line) was used. The resulting forecast shows the growth of cardholders and, consequently, the spread of the number of payment cards among the population in 2021-2023. The practical significance of this study is that the proposed methodology can help predict the dynamics of payment cards in any country in the world. Recommendations are also given for further improving the financial system, since increasing the transparency of monetary circulation in small-and-medium sized businesses will lead to a positive result in the implementation of the program for universal declaration of income in 2025.