Abstract: The subject of study in algebra is a ternary (three-dimensional) hypercomplex numbers (triplexes). Since the time of Hamilton (1983) algebras of hypercomplex numbers attracted the attention of researchers. The largest number of papers in this area is dedicated to quaternion algebra and bicomplex numbers, as well as its applications to the solution of various problems of science and technology. Algebra of ternary (three-dimensional) hypercomplex numbers is less studied. However, it is undoubtedly promising in solving problems related to processing of point objects and fields in three-dimensional Euclidean space. The main objective of the article is forming a basis of idempotent algebra of three-hypercomplex numbers. Idempotent bases are typical for commutative multiplicative algebras without division. Such bases provide a simple definition and way of studying mathematical constructions of hypercomplex numbers as well as a significant increase in computational efficiency. The paper presents all possible unit vectors of potential idempotent bases of triplex numbers. The authors highlight two idempotent bases providing not excessive presentation of triplexes. The main attention is given the study of one of these bases with complex unit vectors. The paper shows, that idempotent triplexes basis allows formulating the definition of arithmetic operations and triplex argument functions in terms of the well-studied algebra of real and complex numbers. At the same time mentioned basis provides a high computational efficiency for calculating values of these operations and functions.

Keywords: hypercomplex numbers, commutative hypercomplex algebra, zero divisor, idempotent basis, triplex, Algebra without division, triplex algebra, conjugation, triplex function of the argument, triplex ring

Abstract: The article describes an approach to the development and implementation of a software system for the design, testing and implementation of trading algorithms. The author shows methods of obtaining and transmitting data from a medium to the terminal and vice versa. The article presents a review of similar software and highlights the main advantages of this approach to design. The author uses a prototype-based programming approach to software implementation. As a method of research the author uses observation. The object of research is the algorithm. The subject of the study is a data set for analysis of the algorithm. The main novelty of the proposed approach is to use prototype-based programming approach to algorithm design and implementation used as an object-oriented model. The article suggests a scheme of data exchange with third-party applications using functions of native dynamic libraries of a terminal. The study gives an algorithm for the application.

Keywords: data analysis, software, lua, programming, development, stock market, testing, optimization, .NET, C #

Abstract: The subjects of the research are techniques for combining sensory and synthesized video information in appliance to the aviation system of combined vision. The use of such systems allows controlling manned and unmanned aerial vehicles under conditions of low visibility by combining video information from on-board camera with video data synthesized by a priori given virtual model of a terrain. It is known that on-board navigation system measuring the position and orientation of the aircraft has accuracy errors because of which the angle of the synthesized image on a virtual model of the area does not match the foreshortening of shooting onboard cameras. This is why a procedure for combining sensory and synthesized video information in the aviation system of combined vision is needed. The study was conducted with the use of mathematical and computer modeling of combined vision systems using both synthesized and real images of an underlying terrain. The novelty of these results lies in the universality of the developed algorithm. This algorithm allows combining video content with an arbitrary data along with the possibility of its practical implementation and high quality combining. Developed algorithm for combining sensory and synthesized video information on the basis of typological binding and Kalman filtering provides a sufficiently precise and reliable combining that meets the minimum requirements for the aircraft systems combined vision. The algorithm is universal, has low demands to the scene recorded images, has low computational complexity and can be implemented in hardware and software based on modern avionics. When testing the algorithm the authors used precision characteristics at the level of consumer navigation devices which significantly inferior in accuracy compared to modern air navigation systems. This indicates the possibility of using the algorithm in inexpensive and compact user systems, as well as in mobile robots.

Keywords: algorithms, vision systems, a virtual reality, combining images, virtual model of the terrain, man-machine interfaces, aviation systems, airborne avionics, combined vision systems, synthesized vision system

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.

Keywords: Image processing, Image Enhancement, Image Smoothing, Filtering of images, Laplace mask, CAD, The automated procedure, MATLAB, The selection procedure, Laplace operator

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.

Keywords: blur images, convolution, blind deconvolution, eliminate blurring, image enhancement, image processing, picture, discrepancy, Tikhonov regularization method, The automated procedure

Abstract: The article studies methods of constructing sets of elements required for the existence and functioning of developed mathematical model of information-measuring system for electric current and the magnetic field control. The authors research numerical methods for constructing a model of an information-measuring system. On the basis of system analysis the authors review specifications of information-measuring system for electric current and the magnetic field control, ways of constructing its mathematical model using numerical methods, the accuracy of which will reduce the accuracy of measured values. The study is based on the use of system analysis, statistical theory of optics, systems theory, and transformation of electromagnetic field theory, numerical methods. For the majority of tasks a full implementation of mathematical models of a information-measuring system is difficult because of the complicated structure of system components as well as the presence of the factors affecting the operation of the system. In this connection the authors attempt to determine the relationship between the characteristics and parameters of the process of transformation of the measuring system component of the input signal, taking into account all factors.

Keywords: information-measuring system, mathematical model, fiber optic transmitter, numerical method, accuracy, error, Faraday effect, systems analysis, fiber-optic system, technical specifications

Abstract: The object of the research is a study of the possibility of using the micro-controller kits during the "Fundamentals of the control theory" course. The author describes existing situation in this field and discusses some of the solutions on the issue. The author in detail reviews the procedure and content of the practical works on discipline-based education-enforcement robot kit "Amperka." The article gives recommendations on the preparation and use of certain elements of the microprocessor kits and software for various kinds of tasks for the study of control theory. As a research method author uses testing preposition approach for practical training. The main conclusions of the study are the undisputed usefulness of robot constructors in forming skills on the subject during the courses studied by students under the direction of computer technology and programming. The quality and effectiveness of education depends on a variety of things, and primarily on the qualifications of the instructor. However, if the other conditions are equal, the students are more likely to learn the theory, when they can apply it to the practical problems.

Keywords: microcontroller, management theory, robotics, educational kit, Arduino, Amperka, regulator, PID controller, practical work, processing