Abstract: The study is devoted to automated procedures of selecting method and relevant parameters for digital image improvement. In this article the authors select filtering method known as Laplace mask to improve images. Since the image is represented by a discrete function, the authors use various discrete representations as an approximation of a continuous formula of two-dimensional Laplace operator. Additionally the paper reviews filters (masks) of Laplace high frequency which are frequently used in digital image processing. The research methodology is based on the computational experiments. Software for these experiments is designed using MATLAB system. The novelty of the research is to indicate the direction which will help reduce the time spent on image optimization while increasing the efficiency and reliability of the software for digital image processing. This is confirmed by the results of numerical experiments that were carried out with the use of the developed automated procedures for selecting and setting parameters Laplace masks for digital image processing.

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: 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.