The article analyzes the concept of process management in an industrial enterprise, which provides functional stability of technological processes using information systems of various types and allows to increase productivity of all production centers while reducing the number of people employed in production and the impact of various destabilizing factors. The research of existing mathematical models of functionally stable complex technical systems and formalization of the main types of procedures of the process of functioning of the intellectual information system of the enterprise is carried out. The method of ensuring the properties of functional stability of the intelligent information system of the enterprise is improved by presenting the functioning of the system in the form of a formalized process, in which the main types of procedures are accumulation of tests, analysis of test links, diagnosing a failed module and restoring the system. This technique allows to ensure the property of functional stability of the information system of the enterprise.

Ensuring the security of digital operations, especially in the areas of e-commerce and financial transactions, remains increasingly relevant. Therefore, the subject of research is the development of a specialized software library. This library aims to improve the security of web applications. The purpose of this study is to develop a software library that uses artificial intelligence and machine learning methods to analyze and improve the level of security of financial transactions. The use of these advanced technologies helps automate the detection of potentially fraudulent or risky transactions, thereby providing a higher level of user protection. The following tasks are solved in the article: analysis of modern methods of processing financial transactions and identification of possible security threats; development of a UML diagram of library classes for processing and analyzing financial transactions; testing and validation of the developed artificial intelligence model for assessing the security of financial transactions on real financial data. Machine learning methods were defined and applied using the scikit-learn library in Python, the algorithms of which are capable of analyzing large volumes of data and identifying potential risks with high accuracy. This ensures effective integration of artificial intelligence technologies. The following results were obtained in the work: the criteria for assessing the riskiness of financial transactions for the identification of potential risks are defined; the program operation algorithm is described, which includes procedures for determining and classifying transaction risks; pseudocode is presented, which illustrates the structure of classes and methods of the model, opening opportunities for its adaptation and scaling; methods of generating test data reproducing realistic scenarios of financial transactions have been developed; an analysis of the results was carried out to assess the effectiveness of the developed model. In conclusion, the results of research and testing allow us to evaluate the model's response to various data and its effectiveness in real conditions, as the work presents examples of processing various types of transactions. In addition, the study presents not only the development and validation of the developed model, but also the prospects of its use on a larger scale, integration with existing web applications.

В роботi дослiджується проблематика формування практико- i професiйно-орiєнтованих умiнь засобами загальноосвiтнiх предметних областей в умовах постiйної модернiзацiї освiтнiх стандартiв вищої професiйної освiти i реалiзацiї концепцiї розвитку математичної освiти. Вивчається задача зближення в навчальному процесi теоретичної i прикладної математики, яка, власне, вирiшується засобами ефективного використання iдей i методiв математичного моделювання. Видiляється наскрiзна змiстовно-методична лiнiя математичних моделей, в реалiзацiї якої закладається найбiльший потенцiал для зростання мотивацiї студентiв до математичної дiяльностi. Показується, що такий пiдхiд є носiєм iнновацiйностi, новизни в змiстi математичних курсiв i методики їх викладання та практико-орiєнтованої спрямованостi. Розкривається нерозривний зв’язок методологiї пiзнання та методологiї практичної цiльностi вивчення прикладних задач природознавства, якi вивчаються в рiзних математичних курсах ЗВО для подальшого формування фахових компетенцiй в курсi математичного моделювання.

Electrochemical devices based on nickel hydroxide electrodes are used in different areas. The main ones are chemical current sources, variable transparency “smart” windows, devices for carrying out electrocatalytic reactions, sensors for determining various substances. In this regard, methods of nickel hydroxide synthesis are of great interest, especially those that allow forming nickel hydroxide directly on the surface of electrodes. One of these methods is electrochemical deposition with cathodic current polarization. The available information on nickel hydroxide synthesis from nickel solutions was considered. It was shown that the available data mainly covered information on dilute solutions from 0.01 to 0.25 mol/L Ni(NO3)2. In addition, no comparison was found in the literature for the efficiency of the cathodic formation of Ni(OH)2 at different concentrations of nickel nitrate. To eliminate the lack of information, the dependence of the current efficiency on the concentration of nickel nitrate in the electrodeposition solution was determined at a constant cathode current density of 0.625 mA/cm2. The resulting dependence decreased nonlinearly with increasing concentration. The nickel hydroxide deposit formed in this case had an X-ray amorphous structure, and it depended little on the Ni(NO3)2 concentration. In addition, the current efficiency reached zero at concentrations of 1.5 mol/L Ni(NO3)2 and higher. However, with polyvinyl alcohol in the solution and at Ni(NO3)2 concentrations of 1.5 and 2 mol/L, electrochemically and electrochromically active Ni(OH)2 films were deposited. The current efficiency calculated indirectly for 1.5 and 2 mol/L Ni(NO3)2 solutions was 3.2 and 2.3 %, respectively. Thus, it was concluded that polyvinyl alcohol affected the mechanism of nickel hydroxide electrodeposition from aqueous solutions of nickel nitrate.

We obtain order estimates for Bernstein-Nikol'skii-type inequalities for trigonometric polynomials with an arbitrary choice of harmonics. It is established that in the case q = infinity, 1 < p <= 2 these inequalities for trigonometric polynomials with arbitrary choice of harmonics and for ordinary trigonometric polynomials has different order of estimates.