The allowance for various defects including cracks represents a critical issue related to structural risk analysis. The complexity and the ambiguity involved with such allowance for the amount and growth of defects (cracks) is demonstrated on the real structure of a metallurgical overhead crane. The problem of distribution function conversion must be solved to allow for any variations in defects starting from the point of time when the initial (technological) defectiveness is determined and ending with the estimated time of risk analysis. Due to the lack of data on cyclic resistance to cracking for Вст3сп5 steel, it does not yet seem possible to construct the distribution functions and to determine the estimated theoretical average and dispersion of crack sizes. However, by using the previously obtained calculated data on active stresses and strains, it is now possible to simulate growth of cracks based on Weibull distribution. Different engineering solutions can be accepted at various stages of operating large structures, according to the obtained results.

A series of elements of order 4 in the symplectic cobordism ring is constructed.

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Development of modern test materials using the LaTeX package for the organization of students' independent work in the study of higher mathematics The article presents a study on the problem of creating and using modern interactive tests that meet the requirements of the modern educational paradigm and are designed to activate students' independent learning and cognitive activity. The purpose of this article is to justify the need to use interactive test materials, to show examples of interactive tests developed and tested in the process of studying mathematics. The article provides examples of interactive math tests created by the authors, describes the types of tasks used in them, and presents a way to make online tests interactive by using the acrotex library, part of the LaTeX package. The article also describes how to use test materials to organize independent work of students. The authors are engaged in the creation of original electronic educational-methodical tools, which consist of formative tests. Students study the topic with their help, achieving the necessary level of education due to regular stimulation of their academic work. And the teacher can apply an individual approach in the educational process, to observe the students training and carry out monitoring quickly and objectively.

Abstract. The recent reforms in education have given rise to distant training due to the sharp increase in the percentage of time allowed for individual work. It causes the necessity of working out new teaching resources that would contribute to the revitalization of the students' individual work. Until recently, the creation of electronic training tools has been viewed as creation of lecture materials or tests, given in PDF format. Since Adobe Acrobat Reader has been supporting integrated JavaScript [2], there is an opportunity to implement interactive content into the documents in PDF format.At the moment we are working at the project of creating a series of interactive electronic educational resources in mathematics with the use of Acrotex package for the first year technical students. The package is written by a Professor of Mathematics in the