Introduction. The article is concerned with the use of special electronic teaching tools to increase the students’ understanding of the subject and adaptation to the professional language environment of the host country, taking into account the mathematical education. Our purpose is to develop a methodology of multilingual support of mathematical courses in the host country to improve the effectiveness of students’ academic mobility using e-learning tools. Materials and Methods. The basis of the research was methods of system analysis and descriptive and analytical methods, primarily experimental. To identify advantages of the proposed approach the methods of empirical research were used (observation and comparison). To prove the efficiency, classical methods of measurement were used. Results. We analyzed the existing electronic learning environments and defined an e-learning environment Math-Bridge that allows for creating mathematical courses in several languages in parallel. For example, the e-training course “Optimization Methods” was developed in three languages for training Russian-speaking Master programme students. The comparative analysis of the target and control student’s groups showed that 100 % of the students in the target group achieved an excellent level of mastering competencies, while the control group has only 75 %. For the control group, the degree of motivation to mathematical studying has not virtually changed (increase by 0,86 %). In the target group the level of student interest to the mathematics increased from 0,9 % to 8,9 % (mean 2.21 %). Discussion and Conclusion. The results described in the article will be useful for the staff of international departments, administrations and deans, as well as teachers of those universities that participate in the students’ international academic mobility programmes.

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Models that describe the trace element status formation in the human organism are essential for a correction of micromineral (trace elements) deficiency. A direct trace element retention assessment in the body is difficult due to the many internal mechanisms. The trace element retention is determined by the amount and the ratio of incoming and excreted substance. So, the concentration of trace elements in drinking water characterizes the intake, whereas the element concentration in urine characterizes the excretion. This system can be interpreted as three interrelated elements that are in equilibrium. Since many relationships in the system are not known, the use of standard mathematical models is difficult. The artificial neural network use is suitable for constructing a model in the best way because it can take into account all dependencies in the system implicitly and process inaccurate and incomplete data. We created several neural network models to describe the retentions of trace elements in the human body. On the model basis, we can calculate the microelement levels in the body, knowing the trace element levels in drinking water and urine. These results can be used in health care to provide the population with safe drinking water.

The regulation of the anthropogenic load on waterbodies is carried out based on water quality standards that are determined using the threshold values of hydrochemical indicators. These applied standards should be defined both geographically and differentially, taking into account the regional specifics of the formation of surface water compositions. However, there is currently no unified approach to defining these regional standards. It is, therefore. appropriate to develop regional water quality standards utilizing modern technologies for the mathematical purpose of methods analysis using both experimental data sources and information system technologies. As suggested by the use of sets of chemical analysis and neural network cluster analysis, both methods of analysis and an expert assessment could identify surface water types as well as define the official regional threshold values of hydrochemical system indicators, to improve the adequacy of assessments and ensure the mathematical justification of developed standards. The process for testing the proposed approach was carried out, using the surface water resource objects in the territory of the Republic of Tatarstan as our example, in addition to using the results of long-term systematic measurements of informative hydrochemical indicators. In the first stage, typing was performed on surface waters using the neural network clustering method. Clustering was performed based on sets of determined hydrochemical parameters in Kohonen’s self-organizing neural network. To assess the uniformity of data, groups in each of the selected clusters were represented by specialists in this subject area’s region. To determine the regional threshold values of hydrochemical indicators, statistical data for the corresponding clusters were calculated, and the ranges of these values were used. The results of testing this proposed approach allowed us to recommend it for identifying surface water types, as well as to define the threshold values of hydrochemical indicators in the territory of any region with different surface water compositions.

The article describes a method for automatically recognizing the target points of the trajectories of unmanned vehicles moving underwater, such as autonomous submarines and flying underwater vehicles of aircraft-like structures. The coordinate of the center of an object with radial symmetry properties is considered a terminal control point. A method for constructing a multiscale weighted image model based on the developed fast radial symmetry transformation and the Hough method is proposed, which ensures noise stability and high speed of calculating the coordinates of the desired point. When the object of interest has a contour of a specific color, a model is based on our proposed chromatic and weight components. As an example of detection, we have given an algorithm for detecting a base underwater station with light markers as a signal luminous ring.