Formation of multi-group trains is aimed at arranging their cars in a given order and is one of the mass operations performed at railway. In this regard, the reduction of the duration of shunting operations for the formation of multi-group trains is an urgent task for railway transport. In this paper, for a discrete deterministic-controlled system that simulates the operation of the flat yard, a mathematical statement of the problem of choosing the optimal order of multigroup train formation is obtained. The set of possible states of the system under study and the transitions between them are presented in the form of directed graph, which made it possible to reduce the problem of choosing the order of train formation to the problem of searching the shortest paths on the graph. An algorithm of searching the optimal order of train formation is proposed.

The peculiarity of the transit freight transportation by rail in international traffic is the fact that while performing transportation, the railway administrations are in competition among themselves. At the same time, the routes of cargo traffic volumes significantly depend on the conditions of transportation by railways of individual states. The mathematical model for the distribution of transit freight traffic volumes on the railway network, based on the methods of graph theory and game theory, was proposed in this article. The developed model enables the evaluation of the possibilities of attracting transit freight traffic volumes by individual railway administrations by changing the tariff value and transportation conditions. 110

Objective. The article is aimed to improve the understanding of university communities (teachers, students, librarians) concerning the development of distance learning, open educational resources, and the new role of university libraries in these processes. Methods. The main data on the development of distance learning, OER, and increasing the role of university libraries in these processes were obtained due to the analysis of professional publications in periodicals and on the university websites of around the world, the application of methods of method of participant and non-participant observation, a description of the authors’ own experience (the director of the scientific library, the associate professor of IT disciplines and the heads of the scientific library departments) who work at the Ukrainian State University of Science and Technology (Dnipro, Ukraine). Results. It has been established that the implementation of distance learning systems, the use and availability of open (preferably free) information sources on open access platforms or open educational resources (OER), exchange of scientific research in the digital scientific space, etc. – these components are closely interconnected and used among teachers, scientists, students. Distance education requires inclusion in the processes of both teachers – authors of open educational resources, and employees of certain services providing information and IT support for both teachers and the resources created by them. Such structures are university libraries, which were among the first to support the philosophy of openness and to join the processes of supporting open access, open science, and open education based on intellectual information systems and technologies. The experience of the scientific library of USUST is considered – a structure that enables online access to text and non-text OER as a necessary element while ensuring limited personal interaction between a teacher and a student. Conclusions. Today, during the crisis caused by the Covid-19 pandemic and the war in Ukraine, the foundations are being actively laid to make the provision of educational services at universities, in particular distance education, dynamic and multidimensional. It is necessary to integrate electronic library resources with distance learning platforms to ensure unhindered access for students and teachers.

Purpose. The purpose of this paper is the construction of methods and models for the graphical representation process of sorting station, using the unified modeling language (UML). Methodology. Methods of graph theory, finite automata and the representation theory of queuing systems were used as the methods of investigation. A graphical representation of the process was implemented with using the Unified Modeling Language UML. The sorting station process representation is implemented as a state diagram and actions through a set of IBM Rational Rose. Graphs can show parallel operation of sorting station, the parallel existence and influence of objects process and the transition from one state to another. The IBM Rational Rose complex allows developing a diagram of work sequence of varying degrees of detailing. Findings. The study has developed a graphical representation method of the process of sorting station of different kind of complexity. All graphical representations are made using the UML. They are represented as a directed graph with the states. It is clear enough in the study of the subject area. Applying the methodology of the representation process, it allows becoming friendly with the work of any automation object very fast, and exploring the process during algorithms construction of sorting stations and other railway facilities. This model is implemented with using the Unified Modeling Language (UML) using a combination of IBM Rational Rose. Originality. The representation process of sorting station was developed by means of the Unified Modeling Language (UML) use. Methodology of representation process allows creating the directed graphs based on the order of execution of the works chain, objects and performers of these works. The UML allows visualizing, specifying, constructing and documenting, formalizing the representation process of sorting station and developing sequence diagrams of works of varying degrees of detail. Practical value. The usage of the Unified Modeling Language (UML) based on software package IBM Rational Rose and allows to create processes of varying degrees of detail, reduce the time expenditure for the process research of sorting station and get a clear graphical representation, as well as to reduce the human costs at the construction and improvement of existing technological processes.

Purpose. Nowadays, it is difficult to imagine a person who would not use a smartphone. The main direction in creating many applications are such operating systems as iOS and Android. One of the essential stages of the life cycle of cross-platform applications for iOS and Android is building architecture. It is important not only to be able to build an architecture using well-known «tools», but also to understand to which extent this should be implemented and what impact it will have on the software product in the future. The aim of the work is to analyze approaches to development with excessive or insufficient use of design principles and templates, as well as analysis of the results of the final product, cross-platform software for iOS and Android operating systems. Methodology. To improve the existing software, a static analyzer has been designed and implemented, which is focused on the development of architecture in software of different sizes and types. Only the necessary templates and design approaches which allowed implementing the necessary functionality without complicating the system and guarantee easy support, testing and extension of functionality if it is needed, were used to create the software product. Findings. During the experiments, it was found that when designing cross-platform software for iOS and Android operating systems, not only neglect of patterns and common design approaches, but also their excessive use complicates the development, expansion, maintenance and testing of software. Originality. The extent and consequences of using the design templates, the benefits and examples of using the patterns and approaches in the design of cross-platform applications were determined. For the first time, the necessary degree of use of design templates for mobile applications of different sizes and purposes was analyzed. Practical value. The results of the work will allow the programmer to better understand the principles of designing the applications for iOS and Android operating systems, as well as the conditions of use of the known design templates. The information obtained can be used by teachers of higher education institutions as a means of providing practical examples and demonstrations for higher education students in performing practical work and programmers on real commercial projects.