Abstract: The subject of the study is the sensitivity of the experimentally observed characteristics of the particle and radiation flow to variations in the parameters of the model of interaction of particles with the medium. The object of study is the diffusion flow of particles propagating in an unlimited medium. The author considers the variations in particle flux due to changes in the diffusion coefficient both over time and at different points in space. It is emphasized that the expressions obtained in this work can be considered as a statement of the inverse problem in the form of integral equations of the first kind. The research method is variational analysis and numerical experiment. The justification of the method is based on a comparison of the results of calculations by the proposed method and those obtained by the numerical diffusion equation by the difference method. The main conclusions of the study are the expressions for the function of the sensitivity of the diffusion flux to functional variations of the diffusion coefficient. The novelty of the study lies in the formulation of the inverse problem of determining the functional form of the coefficients of the diffusion equation (thermal conductivity) through the function of the sensitivity of the particle flux to variations of the desired parameters.

Abstract: The subject of the research is numerical algorithms for solving fractional partial differential equations. The object of the study is the stability of several algorithms for the numerical solution of the anomalous diffusion equation. Algorithms based on the difference representation of the fractional Riemann-Liuville derivative and the Caputo derivative for various orders of accuracy are considered. A comparison is made of the results of numerical calculations using the analyzed algorithms for a model problem with the exact solution of the anomalous diffusion equation for various orders of the fractional derivative with respect to the spatial coordinate. The results of the work were obtained on the basis of the analysis of the constructed difference schemes for stability, the conducted numerical experiments and a comparative analysis of the data obtained. The main conclusions of the study are the advantage of using the approximation of the fractional Caputo derivative compared to using the difference scheme for the fractional Riemann-Liouville derivative in the numerical solution of the anomalous diffusion equation. The paper also indicates the importance of choosing the method of difference approximation of the second derivative, which is a derivative of the Caputo.

Abstract: The object of this research is the assessment methods of the formation of students’ competencies. The subject of this research is the correlation between the results of intermediate and final certification of students. The author examines the existing assessment techniques of the level of students’ competences in the process of mastering the curriculum. Based on the example of 200 students in the field “Law Enforcement Activity”, the author meticulously analyzes the correlation between the certification results in certain disciplines and final grades received by the students for state examinations and graduation thesis. The research method is the application of systemic and comparative statistical analysis of the results of intermediate and final certification of students throughout the entire period in the educational facility. The conclusion is made on strong correlation between the majority of assessments of the level of students’ competencies, acquired based on the results of intermediate certification using the traditional competency matrices, which decreases the information value comparing to the results of terminal examinations. It is suggested assessing the level of students’ competencies based on the term papers and state final examination.

Abstract: The subject of this research is the assessment of formation of competencies of a student as a component of the portfolio provided in digital information educational environment of the educational organization. The article discusses the methods of assessment of the level of formation of competencies of a student based on the results of interim attestation and creative output of a student throughout the entire period of education. The authors examine the use of the matrix of competencies of the main curriculum in evaluation of the level of formation of single competencies of a student. The application of information resources in organization of the educational for automation of building a portfolio is being discussed. The main conclusion of the conducted research lies on the thesis that for consideration of the results of interim attestation on the main curriculum disciplines in assessment of the level of formation of competencies, it is necessary to introduce the new weighted coefficients into the matrix of competencies. The three-level evaluation of competencies of a student suggests considering the results of creative works and participation in the competitive examination only for making changes between the second and third levels.

Abstract: The subject of this research is the process of assessment of the level of formedness of knowledge of the practical disciplines students with implementation of the active forms of education. The object of this research is the ways of automation of the knowledge testing process, as well as the pattern of test tasks, applied for the interval final academic assessment of the students. The authors examine the traditional methods of knowledge testing with grade system and using the computer testing. Special attention is given to application of the multimedia means as a tool of control over the students’ knowledge. In addition to the multimedia means, it is suggested to use computer simulators and training programs. The results of the work have been acquired based on the use of systemic analysis of the problems emerging in assessment of competencies of the educational organizations. The authors propose using the computer simulators for assessment of knowledge in work with the complex valuable equipment, as well as for composition of the test tasks, using the multimedia materials.