Purpose. Study of the plasma flow interaction with the borehole surface in the process of its thermal reaming for determination of transient temperature distribution along the borehole surface and the average coefficient of heat transfer from the plasma flow to the borehole surface. Methods.Experimental study of the plasma flow interaction with the flange union with internal lateral surface simulating the rock surface in a borehole has been carried out. The essence of the experimental study is in measuring temperature of the flange union external side while the plasma flowing inside the flange union. To measure temperature on the external surface of the flange union, a chromel-alumel thermocouple with thermoelectrodes of 1.2 mm in diameter was used. In experimental research, plasma flows out through a nozzle directly to the flange union made of copper. The parameters of the flange union and the nozzle of plasmatron are geometrically similar.Findings. Experimental data are processed as a relationship between the temperature of the copper flange union lateral surface, i.e. borehole surface, and the time of the copper flange union heating by the heat carrier. Experimental data are processed as a dependence of temperature of the tin pipe side surface, i.e. surface of the borehole, on the location of temperature measurement point along the tin pipe and the time of the tin pipe heating by the heat carrier.Originality. Physical simulation modeling of the heat carrier (low temperature plasma) flow interaction with the borehole surface simulated by the copper flange union and the tin pipe in a certain range of geometrical parameters of the copper flange union, tin pipe and the plasmatron nozzle as well as thermophysical properties of the heat carrier assumed in accordance with geometrical similarity to the technological and design parameters of the plasmatron and borehole diameter before the beginning of thermal reaming process.Practical implications. Methodology of experimental research of the heat carrier (low temperature plasma) flow interaction with the borehole surface that was simulated by the copper flange union of the tin pipe is developed. The results of the influence by high-temperature heat carrier jets on the processes of fragile rock destruction are rather useful in the borehole drilling processes.

МАТЕМАТИЧНЕ МОДЕЛЮВАННЯ В ЗАДАЧАХ ОЧИСТКИ СТІЧНИХ ВОД В даній роботі описано побудову чисельних моделей для оцінки ефективності роботи горизонтальних відстійників, що використовуються в системах очистки стічних вод. Особливістю запропонованих чисельних моделей є можливість моделювання поля швидкості та процесу переносу домішки з урахуванням геометричної форми горизонтальних відстійників та можливістю використання в них додаткових елементів типу пластин. Процес масопереносу домішки у горизонтальних відстійниках розраховується на базі двовимірного рівняння розповсюдження домішки. Це рівняння враховує конвективний перенос домішки та перенос домішки за рахунок дифузії. Нерівномірне поле швидкості розраховується на базі двох гідродинамічних моделей. Перша гідродинамічна модель-це система рівнянь вихрових течій ідеальної рідини. Друга гідродинамічна модельце система рівнянь Нав'є-Стокса, що записані у змінних «вихор-функція току». Для чисельного інтегрування моделюючого рівняння масопереносу використовується різницеві схеми розщеплення. Базове рівняння масопереносу попередньо розщеплюється на рівняння, що враховує лише конвективний перенос домішки у відстійнику, та на рівняння, що враховує перенос домішки за рахунок дифузії. Для чисельного інтегрування моделюючих рівнянь гідродинаміки використовуються неявні різницеві схеми розчеплення. Чисельний розрахунок здійснюється на прямокутній різницевій сітці. Час розрахунку одного варіанту завдання складає декілька секунд. Видаються результати проведеного обчислювального експерименту. Ключові слова: математичне моделювання, очисні споруди, горизонтальний відстійник.

Objectives: Modern production activity of railway transport of Ukraine (RTU) is characterized by high the level of complexity of processes and a wide range of conditions of uncertainty. The article is devoted to the tasks of development of unified automated intelligent analysis and control technologies indeterminate RTU processes in case of uncertainty. Methods / Approach: To achieve the goal a new model of the concept of formation of automated intellectual technologies of RTU is offered, implementation of which is based on a modular platform of unified analytical services designed for effective solution of certain typical tasks (diagnosis, classification, forecasting, management, etc.). The concept as a system includes stages of research of properties of processes, theoretical and methodological basis and methods of modeling and automated control, scenarios and intelligent acceptance procedures decisions in case of uncertainty. Results:As examples of application of the concept to the formation of unified technologies RTU presented intelligent services for diagnosing processes with several categories of uncertainty, as well as analysis and forecasting the parameters of anti-resistance processes. The analysis procedures developed in the article differ using the scheme of fuzzy control method Takagi-Sugeno adapted for diagnostic tasks with the uncertainty of different types (statistical, fuzzy, etc.) , which is provided by the use integrated indicatorthe reliability index, as well as the formal capabilities of the individual accounting for the importance of controlled variables of the process model together for all rules of diagnosis, and for each rule separately. By aggregating the levels of time series of non-deterministic RTU processes developed and researched correct mathematical models and algorithms designed for unified procedures classification and research of properties of anti-persistent processes of railway transport. Conclusions:In order to develop unified intelligent automated technologies RTU developed a concept analysis and management of non-deterministic RTU processes in case of uncertainty based on the platform analytical services. In work at formation of the specified services of the automated intellectual The technology has developed advanced diagnostic procedures that use Takagi-Sugeno-type models for several categories of uncertainty, as well as methods for classifying anti-persistence processes, algorithms interpolation of levels within aggregation ranges, analysis models and short-term forecasting processes designed to develop the theoretical basis and means of improving automated systems RTU.

Purpose. The aim of the article is to develop complex constructive mathematical models of ordering processes for multi-sequences of elements with fuzzy parameters. At the same time, the following requirements for fuzzy ordering of multi-sequences with complexity evaluation (FOMSCE) were established: accounting fuzzy estimates of the formation operations complexity, the need to define fuzzy classes for ordering the initial elements, as well as building individual fuzzy models for the processes of receiving orders from different sources. Methodology. To solve the problems of optimal planning of non-deterministic processes of clinical monitoring of the patients’ treatment, the formation of complex constructive mathematical models of the processes of ordering multi-sequences of elements with fuzzy FMLCPM parameters was applied. For forming models of FOMSCE tasks, a methodology is used to create models with multilayer structures. To implement fuzzy problems, methods and procedures for discretizing a system of fuzzy quantities using sets of α-levels are applied. Findings. The article proposes an approach to solving the problems of analysis and optimal planning of the processes of clinical monitoring of the patients’ treatment, represented as flow control in service systems under uncertainty. For its formalization and implementation, complex multilayer constructive-production models for ordering multi-sequences with fuzzy parameters have been developed. Originality. The work has developed constructive-production methods for modeling complex systems, presented in the form of a multilayer model FMLCPM, which are designed for the processes of ordering multi-sequences of elements with fuzzy parameters. In FMLCPM, layer models are proposed that provide accounting for fuzzy estimates of the complexity of ordering operations, classification of fuzzy parameters of output elements, the formation and analysis of individual fuzzy models of the processes of receipt of orders in service systems. Practical value. The practical value of the results obtained lies in the spectrum development of applications of the problems of optimal planning of the processes in the service systems, presented as an ordering of multi-sequences with fuzzy parameters. The complex models of FOMSCE processes developed in the article are suitable and effective for formalizing the tasks of analysis and optimal planning of clinical monitoring processes, as well as a wide range of other tasks for monitoring non-deterministic transport processes, logistics and service systems.

The article presents the investigation results of the models and the algorithms for the formation of a wide range of transport and logistics real time processes, which create sorted structures of the mass orders. Operators of the different complexity, «weight» are used in this process. Different issues related to the creation of the formal models of the input data sets are resolved. They provide an effective implementation of the technological and the logistic processes. The purpose of the models is to improve the procedures for optimal ordering and classification of the sequences of analysing elements and orders. We have proposed new specialized models (graph models, binary trees) for the input (primary) sets of the elements, as well as algorithms for their processing, which ensure an efficiency increase of the ordering process components. In addition, graph models and algorithms allow solving classification tasks for the data of various types, and they are also suitable for organizing multi-sequencial orders. The high computational efficiency of the proposed new algorithms for arranging and classifying data has been established using comparative analysis. The article provides meaningful examples and notes the peculiarities of the tasks used for real time ordering and classification of the multi-sequencial orders. Namely, this is the task of disassembling and forming railway trains and the task of «mass order delivery to address». Examples of real time creation and transformation of the data flows binary graph models are provided to demonstrate the models and the algorithms. The formed models have been also applied to the tasks of effective sorting and classification with interval uncertainty of the data. We have investigated the possibilities of fuzzy arrangement structure creation and classification of numerical data received online.