Abstract: The study is devoted to methods allowing solving the problem of reconstructing blurry digital images. The authors give a mathematical formulation of the problem of removing blurring from the image. The article presents the Volterra type I equation integral equation. Based on a set of methods that solve this integral equation, the authors propose an automated procedure for solving the problem of reconstructing blurry digital images. The paper discussed in detail the method of Tikhonov regularization. Numerical experiments for different types of digital images are held. The authors give recommendation for choosing the regularization parameter. The research methodology is based on the methods for solving incorrectly posed problems, such as the task of removing the blurring of the digital image. The novelty of the research lies in the uniform approach to solving the problem of removing the blurring of a digital image. This approach has been applied to various kinds of digital images. The results of the selection of the regularization parameter, obtained using numerical experiments are different for different types of images, as expected.

Abstract: In the article the author presents developed procedures of automated automated selection of methods of analysis and digital processing of images, used when creating domain-specific subsystems, in particular for defectoscopy. The relevance of the problem is caused by ever-increasing requirements for technical characteristics of modern equipment used in medicine, space exploration, information technology, etc. And this implies the urgency of the task of creating functions of automated selection of methods for digital image processing and analysis in defectoscopy. The described automated procedures for choosing methods for digital image processing and analysis were developed on the basis of modern methods of digital image processing. The main results of the present research of procedures for automated selection of digital image processing solutions for the problems of defectoscopy is that the use of this procedures, depending on qualification, can significantly improve the quality of digital photos. This will lead to better identification of defects, which in turn will allow to withstand all specified technical requirements for manufactured  products.

Abstract: The subject of study in this paper is developed automated method of selecting of procedures of processing images gathered for the magnetic defectoscopy.  The methods based on the analysis of magnetic fields scattering near the defects after the magnetization of these products are used to detect various defects, such as cracks, in the surface layers of steel parts. In areas where there is a discontinuity, the change of the magnetic flux is present. This effect is the basis of almost all existing methods of magnetic defectoscopy. One of the most known methods of magnetic defectoscopy of method is a magnetic powder: the surface of the magnetized part is covered with magnetic powder (dry method) or magnetic slurry (wet method). When using fluorescent powders and suspensions, the images of the studied details show visible defects significantly better. Therefore, it is possible to automate the processing of images. The paper presents an automated procedure for selecting methods of image processing. The authors give an example of processing image of steel parts for detecting defects using the luminous lines that appeared after applying the magnetic slurry. The study uses the methods of the theory of image processing. These are mainly extraction methods for defining boundaries of objects and morphological image processing. The main result of an automated method is the opportunity to obtain expert information on the basis of which it is possible to make a conclusion about the presence of defects in the test product. In the example given in the article authors show that the lines are continuous and have no sharp change of direction. Therefore, the conclusion about the absence of discontinuities (defects) in the product is made. In addition, authors point out that the binary image can be inverted at the request of the researcher.

Abstract: Nowadays the teachers while lecturing various courses on the ordinary differential equations often use program systems of symbolical mathematics or computer algebra, for example MAPLE well known for its efficiency. In the process of training in computer modeling, teacher often face a problem of designing a mathematical model of the studied process. Because the fundamental laws of nature are formulated as a rule in a language of the differential equations, there is a need to teach the students to design mathematical models. The authors present a solution of the problem of the automated generation of mathematical models on the using a systems of the ordinary differential equations based on Maple system. The paper presents an example of this solution. The given algorithm of generating systems of ordinary differential equations can be easily modified for a specific task. During the course on ordinary differential equations it is necessary to give students the tasks develop the algorithm by themselves. This allows students to develop a culture of logical thinking, which will properly establish cause and effect of physical processes and phenomena from the formal implementation of interdisciplinary connections and practical orientation of training. All of this will undoubtedly contribute to a better knowledge of the disciplines of applied mathematics and other subject areas.