It is indicated in the article that the study of the electron bunching process in the drift space of a transit klystron is an urgent task that allows one to establish general laws applicable to more complex models. In this connection, the behavior of the pre-modulated electron beam in the drift space of the transit klystron has been investigated. A numerical model has been implemented that takes into account the effect of space charge fields and the interaction of charged particles with elements of an electrodynamic system. A series of numerical experiments with different values ​​of the current and initial velocities of electrons, as well as their comparison with theoretical data, have been carried out. As a result of numerical experiments, data were obtained that characterize the dynamics of the electron flux in the drift space of the transit klystron at different values ​​of the initial velocity (0.5 s, 0.9 s) and cathode current (10 mA, 1A, 10A).

Keywords: flyby klystron, mathematical model, numerical simulation, large particle method, particle-particle method, drift space, convection current distribution, electron flow, multithreaded calculations, system of differential equations

The article considers the dynamics of an ion beam in a laser mass – EMAL-2 spectrometer.a numerical model based on the "large - particle" method is Implemented, taking into account the influence of spatial charge fields and the interaction of charged particles with the field of an electrodynamic system. The software package that implements the mathematical model of ion beam motion consists of two parts. The first part is a program written in C++, in which initial conditions are set, the Coulomb interaction between large particles is calculated using the "particle-particle" method, the system of differential equations (1) is integrated using the fourth-order Runge-Kutta method, and the results are recorded and processed. The second part is a script for the FreeFem++ package, which implements the solution of partial differential equations using the finite element method. A series of numerical experiments and their comparison with the data obtained experimentally are carried out.

Keywords: large particle method, laser mass spectrometer, particle-particle method, electrodynamic system, Runge-Kutta method, laser plasma, magnetic analyzer, ion beam, focusing system, triangulation

The article deals with the dynamics of an ion beam in a tandem laser mass-reflectron. The software package that implements the mathematical model of the ion beam motion is based on the "large - particle" method.it takes into account the influence of the spatial charge field and the interaction of ions with the field of the electrodynamic system. The potential distribution in the device nodes is obtained by numerical solution of the Laplace equation using the mathematical package Freefem++, which implements the solution of partial differential equations by the finite element method. The absence of inhomogeneity of the electric field inside the reflectors is shown. A series of numerical experiments has been carried out, which has shown the convenience of using the finite element method for numerical solution of problems of electrostatics and ion optics, as well as the effectiveness of using numerical modeling to develop and optimize the parameters of mass spectrometers.

Keywords: large particle method, laser mass spectrometer, particle-particle method, electrodynamic system, Runge-Kutta method, laser plasma, ion beam, focusing system, triangulation, gas-forming impurities, time-of-flight mass spectrometer

the article describes a variant of setting sequential algorithms in the form of bipartite graphs by further defining them, which makes it possible to work with algorithms using graph theory methods in the future. Two forms of the task are considered: modular and functional-predicative. The possibility of setting the algorithm in table-predicate form is shown. It is concluded that in addition to the generally accepted methods of setting the algorithm, it can be set in matrix-predicate or table-predicate form, which allows using methods of matrix theory and methods of predicate theory when working with algorithms. setting the algorithm in matrix-predicate form avoids isomorphism when performing algebraic and set-theoretic operations on it.; setting algorithms in matrix-predicate form allows you to perform almost any operations on them

Keywords: graph-algorithm scheme, sequential algorithm, predicative block, functional block, pre-definition, bipartite graph, table-predicative form, graph theory, isomorphism

Finite state machines, being a mathematical abstraction, allow you to perceive information from the control object, process it and give signals to control the object. The disadvantages of the representation of complex production systems by a set of finite state machines include the complexity of carrying out logical and set-theoretic operations on them and the complexity of describing the parallelism that occurs in the operation of complex production systems. When specifying a finite state machine in the matrix–predicate form, due to the information redundancy, it is possible to avoid these difficulties. Matrix–predicate method allows you to uniquely set the finite state machine square matrix, which makes it possible to use the methods of the theory of matrices during the set–theoretic operations on them and it is possible to avoid isomorphism. The paper presents the developed methods of representation of a finite state machine using a multi-place predicate, which greatly simplifies its task.

Keywords: finite state machine, graph, matrix, predicate, algorithm, matrix–predicate method, graph incident, tuple, Cartesian product, complex production systems

At present, modern information technologies are actively used in the design of complex equipment at various industrial enterprises – automated systems for end-to-end CAD/CAM/CAE class design, which provide complex execution of design work with a significant reduction in their execution time while improving the quality of work. When this is achieved the main objective which is the update of the nomenclature of products, reducing costs, improving reliability, efficiency, etc. In view of this, the task of constructing and visualizing solid-state models is relevant today. From the analysis of the literature, it was concluded that today there are not enough methodological techniques for building models, and the existing developments do not contain optimal algorithms for creating 3D models of parts of varying complexity. Therefore, to implement the above problem, an algorithm for constructing a 3D model with a cutout was proposed.

Keywords: CAD/CAM/CAE, graphic packages, projection drawing, computer graphics, construction algorithm, geometric body, solid modeling, software, 3D model, surface toning

The article presents a detailed analysis of the structure of the model of management of the hematopoietic functional system of the body in various physiological situations, which activates the activity of a certain adaptive circuit that characterizes the functional state. The first state and adaptation to the contour of the functional hematopoietic system of the body included in the work are considered in detail. The structural equation of adaptation of the first contour is made. It is concluded that the equation of adaptation compiled for a hypothetical control model adaptation, in the actual state of Affairs raises a number of inconsistencies with the hypothetical implementation-related deviations from the ideal parameters of functioning: autonomic nervous system, internal environment, metabolic state, the processes of transmitting the control actions. All these deviations affect the observed realization of the set of blood form elements (RSBE).

Keywords: physiological model of functional hematopoietic system, the adaptive circuit, the space of external influences, categorical diagram, adaptation processes, gemondo-nuclear level, functino mapping, homomorphic mapping, the equation of adaptation

The article describes the algorithm of recognition of schematic diagrams in the framework of structural design of complex technical objects. It is specified that at statement of a problem of development of the specialized vectorizer it is necessary to define: software subsystems of the simplest tracer; algorithms of the analysis of images; formats of representation of the end result; initial data (formats) for recognition. As a result, it was concluded that for structural and circuit design, during which the vertex of the final portrait of the graph of the projected system is replaced, obtained after optimization by the criterion of the set of the smallest external stability, it is necessary to recognize images of graphic elements. The proposed algorithm allows for adequate recognition of the elements of electronic circuits, which further makes it possible to automatically replenish the database of elements with new elements in a given format.

Keywords: vectorization, concept recognition algorithm, structural design, graphic, element, raster image, electronic circuits, semi-graphical display, block-the functional distribution of the tracer

The article analyzes the adaptation contour, which is an integral level of management of the body's hematopoietic system, aimed at optimal maintenance of the body's metabolism as a whole. It is indicated that for complex measurement problems it is advisable to use the principles of constructing measuring systems, formulated in terms of system functions using the fractal-categorical approach. It is concluded that the functorial and category maps make the analysis of the hematopoiesis process more complete and visual, and the possibility of further decomposition allows the researcher to carry out more detailed research, visually displays the processes of adaptation of the organism under external influences and naturally contributes to the construction of automated measuring systems for which the adaptive The contour is a model of the bioconverter of information on the processes of hematopoiesis included in composition of bioinstrumental measuring system

Keywords: structural and analytical method, information-measuring system, information flows, hematopoietic system, category diagram, functors, adaptation contour, bioinstrumental information-measuring system, control signal, measurements

In the article we have considered the actual problem of determining the error in visualization of generalized control criteria. It is indicated that the most common nonlinear interaction of parameters in technical systems is the multiplicative interaction of measured physical quantities. Based on the fact that the physical elements of the processor measuring channel have linear dynamic characteristics, it is concluded that the application of nonlinear transformations for quantitative estimates of the properties of monitoring systems requires linearization, the errors of which undoubtedly affect the accuracy of the final mathematical model and its magnitude may be is estimated and attributed to the methodological error of visualization. The process of linearization is considered for the example of the multiplicative interaction P of measured physical quantities. As a result of the analysis of the properties of many industrial control objects under the conditions of steady-state technological processes, it was found that they are characterized by small fluctuations with respect to the mathematical expectation (no more than 10%), which makes it possible to apply the obtained mathematical models of errors arising in the process of linearizing the measurement equations for control criteria, for design and research works.

Keywords: control objects, measuring system, programmable logic controllers, visualization error, mathematical expectation, adaptive control, linearized measurement equation, measurement error

The article deals with the question of constructing an analytical model in assessing a person's functional state. It is indicated that for complex measurement problems it is advisable to use the principles of constructing measuring systems, formulated in terms of system functions using the fractal-categorical approach; the technique is applicable in the design and analysis of complex medical complexes, and the resulting system function of a complex medical complex is the basis for further analysis within the selected method; The structural-analytical method for constructing complex systems makes it possible, by analyzing the requirements and constraints of the system, to optimize the functions of transferring control actions, to build blocks, parts of the structure on their basis, and to optimize inter-unit communications. The approach described in the article to the process of hematological research makes it possible to analyze the adaptive response of the body's hematopoietic system to external influences of a different nature and intensity.

Keywords: structural and analytical method, information-measuring system, information flows, hematopoietic system, category diagram, functors, adaptation contour, bioinstrumental information-measuring system, control signal, measurements.

In the article we consider serial hipping-chart of the abstract algorithm and a bipartite graph. Led the detailed algorithm of such a transformation. We gave an example of the ability to specify the algorithms in the matrix-predicate form. In conclusion, we indicated that the resulting matrix-predicate form is completely identical graphic form, however, allows you to work with algorithms much more efficient, since it is possible to ask them in the matrix predicate and partially automate the heuristic methods of their construction.

Keywords: the algorithm graph-diagram, bipartite graph, set, matrix, predicate, logical operator, the circuit

In the article, we considered the actual problem of constructing an algorithm based on the interaction of parallel components. The paper contains elements of the methodology developed by the authors for the parallel functioning of algorithms based on graph theory. It is shown that the construction of an algorithm with parallel functioning of components is impossible without taking into account the time, for which the concept of a time axis was introduced, and the sequential algorithm is represented in the form of a bipartite graph by its additional definition. The methods of parallel algorithms represented in the article, realized as dual graphs or matrix predicate form, make it possible to use them in describing complex control and measuring systems. It is concluded that the advantage of such a representation of the parallel functioning of algorithms lies in the fact that it becomes possible to work with parallel hierarchical structures, tracing the changes in each of them by means of input time axes.

Keywords: algorithm, parallel processing, algorithms, parallel operation of objects posledovatelnostyu algorithms, predicative unit, time axis, of the dual graph, the interaction of parallel algorithms, graph-scheme of algorithm, functional-predicate module