Continuous education today is a major feature of modern society. In order to ensure the competitiveness of future professionals who obtain higher education within the walls of the Institutions of Higher Education, the education process should be aimed at ensuring a high level of professional knowledge as well as the formation of graduates' adaptability to changeable modern production. Since for a future engineer knowledge of higher mathematics is the basis for solving complex problems of a production nature, it can be argued that they are part of professional mobility. The implementation of technologies for the formation of professional mobility in higher mathematics has made it possible to note that the readiness to change activities can be considered not only in the context of changing professional activity, but also in the process of students’ educational activity. And this, in turn, made it possible to determine the «mathematical mobility». The purpose of the article is to theoretically substantiate and practically test the methods of forming mathematical mobility of future engineers in higher mathematics classes. The experiment used competency-oriented tasks, test tasks in higher mathematics, built on the basis of Bloom's taxonomy, developed interactive methods for conducting practical classes in the process of studying higher mathematics. The results of the experiment showed the effectiveness of the proposed innovative technologies in the process of fundamental training of future engineers.
The paper examines the features of segmentation of the upper respiratory tract to determine nasal air conduction. 2D and 3D illustrations of the segmentation process and the obtained results are given. When forming an analytical model of the aerodynamics of the nasal cavity, the main indicator that characterizes the configuration of the nasal canal is the equivalent diameter, which is determined at each intersection of the nasal cavity. It is calculated based on the area and perimeter of the corresponding section of the nasal canal. When segmenting the nasal cavity, it is first necessary to eliminate air structures that do not affect the aerodynamics of the upper respiratory tract - these are, first of all, intact spaces of the paranasal sinuses, in which diffuse air exchange prevails. In the automatic mode, this is possible by performing the elimination of unconnected isolated areas and finding the difference coefficients of the areas connected by confluences with the nasal canal in the next step. High coefficients of difference of sections between intersections will indicate the presence of separated areas and contribute to their elimination. The complex configuration and high individual variability of the structures of the nasal cavity does not allow segmentation to be fully automated, but this approach contributes to the absence of interactive correction in 80% of tomographic datasets. The proposed method, which takes into account the intensity of the image elements close to the contour ones, allows to reduce the averaging error from tomographic reconstruction up to 2 times due to artificial sub-resolution. The perspective of the work is the development of methods for fully automatic segmentation of the structures of the nasal cavity, taking into account the individual anatomical variability of the upper respiratory tract.
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