International Scientific Journals
of Scientific Technical Union of Mechanical Engineering "Industry 4.0"

The paper deals with some aspects of the presentation and application of periodic time-dependent functions in the Fourier analysis. Different approaches for defining and utilising periodic functions are considered. The case when one has only a discrete set of values obtained from measurement and the function itself is not known is also included. In general, the type and the shape of the corresponding frequency distribution is a point of interest and discussion.
The paper presents numerous examples which illustrate the proposed ideas.

Obtaining source functions in Fourier transform (FT) on the base of some knowing frequency distributions are presented. The proposed approach allows to study the properties of the obtained results. This technique is used for calculation of some improper integrals as well.

Paper focuses on the use of renewable energy sources and in particular the use of water energy. A hydro power plant is a complex of facilities and equipment for converting the energy of the water flow into electrical energy. The advantages of hydro power plants are obvious – a supply of energy constantly renewed by nature itself, simplicity of operation, absence of environmental pollution. Taking into account the growing role of small and medium-sized enterprises in the economic development, both of an individual country and on a global scale, as well as the widespread orientation towards the use of renewable energy sources in the production of electricity, the main goal of the current development is the analysis of the operation of the electrical part of a specific hydro power plant with small power. Statistical processing of operational data on the change of certain variables was carried out. In conclusion, it is summarized that the hydro power plant under consideration has good operational indicators.

The paper is devoted to distance exams, as in that the focus is on mathematical disciplines. Some advantages are standing out, as well as significant disadvantages have been discussed. Current modern tools are considered, which are applied both in the preparation of students and in distance exams.

Paper deals with low power photovoltaic system implemented by means of flexible module. Flexible modules powered by sunlight are really a very interesting and promising novelty, being one of the newer alternative energy sources. A selected technical solution with specific characteristics of the individual components is presented. Measurements with digital measuring equipment were performed and experimental results were presented. In conclusion, it is summarized that the tested flexible module gives good results.

This paper is devoted to some up-to-date computational tools, which are on-line available and appropriate to remote learning as well as to scientific research implementation relevant to mathematics and their applications.
The following aspects are concerned and discussed: some of the opportunities and benefits afforded by the software tools which are taken into consideration; necessary requirements which have to be met in order to use these tools; some disadvantages and drawbacks which may arise.
Comparison of fees and prices for different mathematical software tools is done.
For purpose of illustration realistic examples are also given.