The article is devoted to the actual problem of real-time automated control of the chemically active substances consumption with high accuracy and quickness, which is an important task of modern industries characterized by flexibility and continuity of production, as well as being dangerous to human health and the environment. The importance of this issue is determined by the constantly growing requirements of the global market and international standards regarding product quality, efficiency and safety of production operations. Widely used control and consumption systems are often inefficient or unsuitable for solving a number of the most important tasks of industries that use chemically active liquids. Therefore, the problem of developing our own competitive easily-operated high-precision technological complexes and systems for controlling and determining the flowrate of chemically active liquids with high accuracy, quickness and the possibility of working in automated mode is relevant. In the article, based on a critical analysis of modern research in the chemically active substances flowrates control systems branch, the necessary to develop an automated technological complex for high-precision control of chemically active liquids flowrates, in particular alcohols, is substantiated, and its structural diagram is presented. The proposed technological complex of high-precision control of chemically active liquids flowrates is a multi-level complex system with technical and software automation tools of different composition, working principles and functional capabilities. Its functional set ensures high accuracy and quickness of measurement in automated and real-time mode. In general, the proposed automated technological complex of high-precision control of chemically active liquids flowrates at each level is implemented in the form of four corresponding interconnected subsystems. As a basic element in the lower level of automated technological complex of high-precision control for chemically active liquids flowrates, a developed precision vortex flowmeter is used, which is resistant to the occurrence of parasitic noises when a vortex is formed behind the streamlined body due to the use of a special shaped and designed streamlined body. Furthermore, in accordance with the requirements of the international standard ISO/DIS 3651-2, the protection of the vortex flowmeter contact elements from the aggressive chemical influence of alcohols is ensured. That increases the reliability of the proposed automated technological complex of high-precision flow control of chemically active liquids in general.

Navigation parameters such as vehicle heading, linear speed and latitude and longitude are determined today, as a rule,using satellite navigation systems. However, there is a need for autonomous determination of navigation parameterswhen satellite navigation system signals are unavailable for one reason or another. For example, satellite navigationsystem signals can be jammed by electromagnetic countermeasures.Autonomous systems for determining the vehicle navigation parameters are inertial navigation systems, the basis ofwhich is the double integration of signals from accelerometers, as well as the integration of signals from gyroscopes toform one or another coordinate system, if we are talking about strapdown inertial navigation systems (SINS).Integration of the output signals of accelerometers and gyroscopes, which contain errors, leads to the accumulation ofSINS errors. To increase accuracy, SINS are integrated, for example, with satellite navigation systems. However, suchsystems cease to be completely autonomous.The article uses the method of autonomous determination of vehicle latitude and longitude, which is a new method ininertial navigation. The method is based on the strapdown inertial technology, which, unlike the standard methods usedin SINS, does not use the integration of the output signals of accelerometers and gyroscopes. To determine the angles oflatitude and longitude, the signals of the gyroscopes included in the inertial measurement unite (IMU) are used.As a result of a semi-natural experiment, the efficiency of the method of autonomous determination of latitude andlongitude was verified. Flight data of a small-sized aircraft were used for experimental verification. The data containedinformation about the angles of the heading, pitch, roll of the aircraft, the output signals of three micromechanicalgyroscopes, three micromechanical accelerometers, information about latitude, longitude and altitude measured by thereceiver of the satellite navigation system, as well as information about the horizontal and vertical components of speedand current time. Plots of calculated values of latitude and longitude and values measured using the receiver of thesatellite navigation system are given. From the given plots and tables, it can be seen that from a certain time, thecalculated values coincide with the "reference" ones, which confirms the efficiency of the method of autonomousdetermination of latitude and longitude.

To measure the flowrate of fuel and energy resources, different methods are used, which determine the range of measuring instruments. Instruments based on ultrasonic measurement methods are widely used in measurement practice due to the provision of high accuracy, a wide range of measured flowrates, the absence of additional pressure losses and the design simplicity. Such instruments are easily integrated into automated readout systems for collecting and transmitting information. The asymmetry of the measured medium flow is a significant problem in the use of single-channel ultrasonic meters. This issue is successfully solved by using multi-channel flow transducers.
 The disadvantages of multi-channel ultrasonic flow transducers include a significant complication of the hydraulic channel design, the need to use more complex mathematical algorithms for processing the obtained output signal. This requires the use of high performance electronic elements, first of all microprocessors.
 The use of a transducer with multiple reflection of one measuring beam from the wall of the measuring path acts as an alternative to multi-channel measurement.
 The aim of the work is to create a mathematical model of an ultrasonic flow transducer with a complex measuring path trajectory. For research, a scheme with sounding along three chords was chosen, which implements the time-pulse measurement method, it provides for determining the flow rate by the difference in the time of passage of the measuring path along the flow and against it. In this case, the projections of the chords on the cross section of the measuring section create an equilateral triangle. An analytical expression for the conversion response is obtained for the case of several beam reflections in different planes.
 The authors reproduced the hydraulic part of the investigated flow transducer using simulation modeling implemented on the basis of the finite element method. Transducer’s operation simulation in the range of measured flow rates in the conditions of an ideally formed profile of the gas flow velocity in the transducer inlet cross-section has been carried out. The results obtained confirmed the absence of influence of the measuring circuit elements (beam reflectors) on the flow profile and the measuring beam trajectory.

The article defines the relevance of modeling the parameters of spatial location of an abstract object when performing various functions. Thus, modeling makes it possible to determine object movement trajectories both during industrial application in technological processes and when used to create bionic objects, for example, the action of artificial limbs, correction of the movement trajectory of an object with spatial orientation defects. The main goal of research was to substantiate the analytical models of object movement, taking into account spatial coordinate systems, according to which coordinate transformations are carried out during the functioning of an abstract object of various applications. The creation of a sensory complex to compensate for violations of limb functions based on the justification of analytical models of vector field of main systems of the object, characteristic of its vital activity, can solve the possibility of real actions of an abstract biotechnical object in interaction with other objects of the external environment. It is necessary to compare the idealized parameters of vector fields with the real current characteristics of the object under study and to determine the difference as a differential function that corresponds to diagnostic parameters of state of object's limbs trajectory. Or when applied in industrial conditions, errors in the reproduction of the movement trajectory are taken into account. As a result, the study of nature of this functional dependence of the state violation and its restoration in the automated mode of operation of the integrated tool will allow the creation of a computer-integrated hardware solution for the identification of objects that interact by approaching and touching their surfaces. Thus, determining the positioning of TONTOR step in the space of movement of objects and during their interaction provides the possibility of the functioning of each abstract object when performing various types of work. At the same time, it is necessary to significantly develop the base of physical and mathematical models that determine the vector fields of objects in dynamics over a certain time, taking into account the TONTOR step of the phantom and real spaces of the existence and operation of the object. Thus, hardware implementation of this hypothesis increases the accuracy of identification of objects interactions with a human limb, regardless of its condition, and the accuracy of determining their relative location in space.

The article proposes the use of a walking robot - hexapod for its use to monitor the technical condition of ventilation shafts, technical dry channels, enclosed spaces, etc. The peculiarity of this type of robots is the increased possibility in comparison with tracked or wheeled machines, due to their design and ability to overcome irregularities. Also, in comparison with existing designs, the hexapod can be fully autonomous and does not depend on a stationary power source. In its turn, construction of walking robots requires development of complex algorithms of motion, which are significantly different compared to wheeled or tracked moving devices, because in addition to the control of limbs, which are set in motion by servo drives, the computer core must process information from sensors that provide information both about the position of the robot itself, and about the surrounding objects, which can be: distance sensors, touch sensors, video cameras, accelerometers, gyroscopes, etc. The paper highlights the developments used to date, but analysis of existing algorithms for walking robots showed a lack of such for the use of the robot in narrow and confined spaces, ventilation shafts, dry technical ducts, etc. In this regard, an algorithm was developed that partially closes this gap. The peculiarity of this algorithm is the simplicity of practical implementation, as well as the safety of the construction of work in progress, because it takes into account the need for increased static stability by modifying the matrix of limb position by a third state, which gives the opportunity to consider the initial position, or memorize the limb state, from which, in the future, you can continue the movement from an arbitrary stable position. In addition, the algorithm can be applied not only to robots with six limbs, but also to other kinds of mobile walking platforms, because the proposed variant allows testing and calibration of any type of gait at each iteration of the step. In the future, it is planned to test the proposed algorithm on the developed prototype not only when moving the work on horizontal surfaces, but also on vertical surfaces, which is an important component for the proposed application area.

Currently, the means of measuring and converting information signals from equipment are widely used in industrial processing systems. For the most part, modern systems of mechanical processing of materials use mainly single-channel systems that work on information signals that identify the physical parameters of the technological process. Such a narrow specialization of monitoring one of the parameters usually reduces the reliability of the results obtained and, as a consequence, the reliability of the entire control system. The task of the work is to determine the possibilities of creating the foundations of the automated system on the basis of multi-channel information recording devices from processing equipment and possible approaches to the choice of criteria for the analysis of fluid information. As a result of the given analysis of a condition of branch and its modern transformations, the module of system for data collection on process (from a set of sensors) is offered for development, with a possibility of their further transformation on certain dependence, storage, transfer, and a possibility of signaling of certain events, for example, faults, for use in production automation systems and for equipment not included in the systems. At the same time, the multi-channel device of the sensor system provides opportunities to determine the full amount of information about the process. The basic modern means of control of work of technological processing CNC-equipment applied in the industry are investigated. The most perspective directions of development of multicriteria methods and automated control systems of technological equipment in the part of creation of complex sensors are determined. These sensory complexes register signals that are different in physical phenomena. The main approaches to the creation of control systems provide opportunities to build a theoretical basis given the logic of the system of obtaining specific information data in the automation of technological processes. Promising research at creating algorithms for such complex systems of quality control and diagnostics of technological processes can be aimed.

Introduction. Preliminary consideration of the problem of the spread of viruses in space, studied by the authors [1], proves that the nature of their movement depends on the shape of these objects, and therefore the main aspects of the geometric dimensions of object’s presence area in interaction with other objects projects, including at the field level. Since the research was conducted under the assumption of formalizing the ideal structure of presence zone of (distribution) of material particles, the relevance of further research by the requirements for the need to determine the actual size of the flows is confirmed.Research results. The main purpose of this study was to continue to create a model for the spread of viruses as material particles in the surrounding space. As a result of analytical modeling of the nature of the spread of the body of the virus in the environment, it is shown that the virus as a physical object is under the constant action of various forces on the way from source to consumer. At the last stage, it is inhibited in the near-surface layer, although it is hardly possible to call it a full-fledged inhibition, because at a constant pulse the free path length is reduced. In the near-surface layer, the flow of the medium has a turbulent flow around the surface. Based on the study, it was determined that the geometric shape, or rather its phantom, play a major role in its movement in the environment. Thus, simulation of particle motion in space has shown that, as a physical object, a virus cannot form a rigid impact situation because it has a fairly large pandanus zone of receptors. The pandanus zone of the virus has a number of rarefied receptors that significantly soften the impact.Conclusions. Thus, the peculiarities of the spread of the flow of viruses in the environment under the presence of certain conditions of interaction of objects are considered. The analytical model of the propagation of fluxes of viral objects as streams of material particles in space-time coordinates is substantiated and the main features of such motion in the near-surface environments of the object and at a distance from it are determined.In further research, the phantom model of the propagation of streams of viral objects in space requires modeling of motion and touching the surface of the object at the level of different types of touching, depending on the state of their interaction.

Introduction. The article deals with the study of the propagation of material particles, like viruses, in space, the definition of their dimensional features. Modern medicine faces the problem of diagnosing infectious diseases, as well as determining the place of origin and nature of the formation of viruses, their structure and the nature of interaction with living organisms. These problems of avoiding a pandemic are paramount. The relevance of the study is confirmed by the necessary requirements to improve the accuracy of determining the actual size of the flows.Research results. Based on the problems described, the main purpose of this study was to create a model of the spread of viruses as material objects in space, ie the geometric parameters of their zones of presence. Versions of hypotheses concerning their origin are considered. Such hypotheses are regressive, cellular origin and coevolution. Each of them has its supporters and opponents, and therefore has no reason to focus on this topic. For now, abstracting this object, we will perceive it as a ball from the surface of which comes a stream of viruses. The mass of viruses that leaves the mother's body creates a flow in the form of a collection of individual particles. The general dependence of the number of viruses that can diffuse into the surrounding space has been determined. In addition, a model for determining conservative fields that have the property of force acting that coincides with the direction of the vector field is created. At the same time, the field structures of the mother body can be distorted when interacting with the fields of other mother bodies and objects. Therefore, the size of the zone of presence of viruses in the space around the mother's body is determined, ie the ability to determine the magnitude of the radius that outlines the outer contour of the zone of viral presence.Conclusions. Thus, the peculiarities of the spread of the flow of viruses in the surrounding space under ideal conditions are considered. It is very clear that we get an infected space in the form of a sphere, and the concentration of viruses varies exponentially from the center to the periphery. Thus, the analytical phantom model of the propagation of the flow of material particles as abstract objects is substantiated. It is proposed to investigate aspects of the formation and behavior of viral flows in spatio-temporal coordinates

Процеси прикладних задач досить часто моделюються диференціальними, інтегральними та інтегро-диференціальними рівняннями, нерівностями і включеннями з відповідними початковими і граничними умовами, визначеними середовищем.
\nФункціональні моделі, де невідома функція і/або її похідні мають нелінійні залежності, часто адекватно описують процеси досліджуваних об'єктів.
\nРізноманітність математичних моделей нелінійної залежності вимагає особливого наукового підходу до їх дослідження і методів знаходження вирішення завдань. У додатках для адекватного перебігу процесу виникає необхідність враховувати реальні обставини по суті різновидів нелінійної залежності.
\nДосліджені питання, пов’язані з розв’язанням квазілінійних диференціальних рівнянь. Припущено, що відповідне лінійне однорідне рівняння відносно заданого квазілінійного рівняння не має ненульових розв’язків, що задовольняють початково-граничним умовам. При цьому застосуванням функції Гріна знаходження розв’язку квазілінійного рівняння приводиться до розв’язку інтегрального або інтегро-диференціального рівняння.
\nУ статті доведено теорему про достатню умову застосовності принципу стискаючого відображення у просторі Lp [a,b], p > 1, з приведенням до нелінійного інтегрального рівняння з використанням функції Гріна для пошуку розв’язку задачі з початковою та/або граничною умовами квазілінійного звичайного диференціального рівняння. Способом, наведеним у доведенні теореми, за початковою умовою u(a) = u0 визначається u1(x), далі у аналогічному порядку відшукується послідовність функцій u3(x), u4(x), …, um(x), що надає можливість наближення до розв’язку задачі з бажаною точністю. Доведена теорема та інші супутні результати можуть застосовуватись для дослідження і пошуку розв’язків практичних задач. Це дозволяє отримувати досить широке застосування теореми, наприклад, при підвищенні точності роботи автоматичних контрольно-вимірювальних приладів.

Вступ. У даній статті розглянуто найпоширеніші сфери застосування тепловізорів, що розміщені на безпілотних літальних апаратах. Авторами розглянуто відмінності у конструкціях крил та спричинені цим переваги і недоліки безпілотних літальних апаратів. Мета. Як головну мету роботи автори визначають проблему поліпшення вихідних параметрів тепловізійних камер. Основна частина. Особлива увага приділена типу конструкції крил безпілотного літального апарата, значенню місця розташування камери на корпусі, проблемі усунення нестабільності зображення, що може бути спричинена вібрацією від двигуна. Наведено конструктивні і цифрові можливості для підвищення стабільності зображення. Окрім цього, автор акцентує увагу на шляхах підвищення ефективності вимірювань тепловізором внаслідок узгодження характеристик приймача випромінювання з параметрами об’єктива. Наголошується, що використання спеціального набору матеріалів дозволяє підвищити якість виготовлення неохолоджуваних мікроболометрів. Наведено порівняльну характеристику основних готових рішень тепловізійних модулів, що можуть використовуватися на безпілотному літальному апаратові, а також метод оцінки якості зображення за допомогою розрахунку мінімальної ефективної різниці температур. Висновки. Розглянуті аналоги модулів тепловізорів дають підстави вважати, що окрім узгодження параметрів мікроболометричної матриці та об’єктива велику роль грає програмне забезпечення, а саме алгоритми обробки потоку кадрів для стабілізації зображення. Авторами отримали фізико-математичну модель тепловізора, що розташований на безпілотному літальному апаратові, та шляхи контролю найбільш важливих вихідних параметрів тепловізорів: просторової та температурної роздільної здатності, мінімальної роздільної різниці температур.