Розроблено методи обчислення рекурентних діаграм в просторі зі скалярним добутком, які дозволяють вивчати властивості і особливості вектора станів різних за складністю динамічних систем природної та соціальної сфери. Новий науковий результат полягає в розробці науково-методичного апарату для обчислення рекурентних діаграм векторів станів систем у розширених на основі скалярного добутку метричних просторах. Запропоновані два методи обчислення рекурентних діаграм для векторів станів складних динамічних систем, які мають високу інформативність, помірну складність і універсальність щодо розмірності досліджуваного простору станів. На практиці запропоновані методи можуть використовуватися для обчислення і порівняння рекурентних діаграм станів досліджуваних систем в метричних просторах різної розмірності без додаткової нормування. Перевірка працездатності запропонованих методів проведена на основі експериментальних спостережень концентрацій формальдегіду, аміаку та оксиду вуглецю в атмосфері промислового міста. Встановлено, що при значеннях кутового розміру області 10° і 30° запропонований метод обчислення рекурентних діаграм має підвищену інформативність, меншу складність та інваріантність до розмірності простору станів. Показано, що методи обчислення рекурентних діаграм в просторі зі скалярним добутком дозволяють використовувати їх при наявності короткочасних інтервалів відсутності спостережень. Експериментально встановлено, що в окремих випадках параметрів результати обчислення рекурентних діаграм на основі розроблених методів збігаються з результатами відомих методів. Це свідчить про більш загальний характер запропонованих методів Ключові слова: рекурентні діаграми, вектор станів, забруднення атмосфери, складні динамічні системи UDC 004.

Photovoltaic cells with a base layer of cadmium telluride with a decrease in its thickness are studied. It is known that the widespread use of photovoltaic converters is constrained by their high price in the case of highly efficient instrument structures, or low efficiency. The creation of tandem and two-sided sensitive photoelectric converters will reduce their cost while increasing their efficiency. However, to create tandem and two-sided sensitive photoelectric converters, the necessary conditions are the use of transparent contacts and a decrease in the thickness of the base layer for efficient absorption of incident radiation by the converter, which is lower. In the research process, it was found that reducing the thickness of the base layer to 1 μm allows to increase the efficiency of the photoelectric transducer during irradiation from the back. An increase in the efficiency of the photoelectric converter occurs due to a decrease in the distance from the generation region of nonequilibrium charge carriers in the region of separation. If the thickness of the base layer is less than 1 μm, then regardless of which side of the irradiation is carried out, a decrease in the efficiency of the instrument structure is observed. Increase in the efficiency of photoconverters is associated with an increase in the negative influence of recombination processes on the back contact, a decrease in the number of charge carriers generated due to incomplete absorption of incident radiation, and a decrease in the volume of the built-in field of the separating barrier when it overlaps with the depletion region of the back contact. ITO/CdS/CdTe/Cu/ITO SCs with a base layer thickness of 1 μm demonstrates degradation stability. The highest value of efficiency in the case of illumination from the front side 8.1 % and with illumination from the back side 3.8 % received after a year of operation of the photovoltaic converter.

The dispersed oxide fillers of different chemical composition were investigated: rutile (TiO2), alumina (Al2O3), calcite (CaO) and hematite (Fe2O3). The mineral composition, surface morphology, particle size and specific surface of the fillers were investigated using modern physicochemical methods. It has been established that the acid-alkaline properties of the active surface centers (ASC) and hydroxyl-hydrate layer (HHL) depend on the chemical and mineral nature of the fillers. It is established that with decreasing acidity of the oxide, the desire for its surface to adsorb water molecules from the air increases. As the alkalinity of the oxide increases, the thickness of both the hydroxyl and hydrate surface layers increases in proportion. It is shown that the acid-alkaline properties of the surface correlate with the acid-alkaline properties of the oxides included in the fillers.

Researched quartz disperses materials (Ukraine): mineral - quartzite of the Ovruch deposit and quartz sand of the Novovodolazsky deposit and products of processing of quartz minerals - dinas and marshalite. The mineral composition, surface morphology, dispersion and specific surface area were experimentally studied. The structure of the hydroxyl-hydrate surface layer was studied by thermogravimetric (TG) analysis and differential thermal analysis (DTA). The number and acid-base characteristics of surfaces active centers were investigated by the methods of pK-metric and pH-metric. It is established that the mechanisms of physical and chemical adsorption of water molecules on the surface of all quartz dispersed materials are identical and do not depend on the mineral nature of impurities. It is shown that the thickness of the surface hydroxyl-hydrate layer of quartz dispersed materials is determined by the amount of chemically adsorbed water, i.e. the thickness of the hydroxyl layer and depends on the nature of the associated minerals. It is established that the acid-base surface characteristic of quartz materials significantly depends on the chemical nature of the accompanying minerals and does not depend on the thickness of the surface hydroxyl-hydrate layer.

A significant number of emergencies that occur in the chemical, processing and transport industries begin with an accidental spill and ignition of a flammable liquid. In this case, the spread of fire to neighboring objects is of particular danger. When developing fire protection measures in areas where flammable liquids are stored, as a rule, heat transfer from a fire only by radiation is taken into account. But in some cases, the convection component of the heat flow can make a significant contribution to the overall heat transfer. Ignoring it can lead to an erroneous assessment of the safety of an industrial facility. In the paper, a model of the distribution of velocity and temperature in the upward flow, rising above the spill of a burning liquid, is constructed. The model is based on the system of Navier-Stokes equations, which, by means of simplifications, is reduced to a non-linear second-order differential equation of the parabolic type. The properties of the combustion site determine the boundary conditions of the first kind. In this case, the spill of a flammable liquid can have any shape. The presence of wind is taken into account by introducing a stable horizontal component of the flow velocity. For the numerical solution of the equation, the method of completed differences is used. The dependence of the kinematic viscosity on the flow temperature is taken into account. An empirical formula is used as the relationship between temperature and speed. It is shown that the presence of wind leads to an inclination of the ascending flow. The angle of inclination is not constant and increases with distance from the combustion source due to a decrease in speed and cooling of the flow. An estimate of the coefficient of convection heat transfer convection of the tank wall with ascending flows over the combustion source is constructed. It is shown that the coefficient of convection heat transfer increases with increasing wind speed