Foundations of abstract probability theory

Using the ideas of abstract algebra, we introduce the basic concepts of abstract probability theory that generalize the Kolmogorov's probability theory, possibility theory and other theories that deal with uncertainty. Based on abstract addition and multiplication, we define an abstract measure and abstract Lebesgue integral. System of Kolmogorov's axioms is criticized, after which we introduce an abstract probability measure and abstract conditional probability, show that they have recognizable probability properties. In addition, we define an abstract expected value operator as the abstract Lebesgue integral and prove its properties.Comment: 12 page

The impact of macroeconomic factors on collateral value within the framework of expected credit loss calculation

The study examines the impact of macroeconomic factors on the expected credit losses of a financial instrument related to changes in the value of collateral. The author has developed a method of calculating this impact on the basis of econometric models, as well as simulated the effect on expected credit losses and reserves on a financial instrument. Based on the proposed approach, appropriate models have been constructed based on the data of the US and Ukrainian economies for the maximum period available, taking into account the adequacy of the data. In particular, it has been shown that applying the methodology of adjusting collateral value to macroeconomic factors can lead to a reduction of the reserve according to the requirements of the regulator, i.e. from the financial institution's point of view it is possible to release some of the funds additionally

Revealing changes in the technical parameters of the teat cup liners of milking machines during testing and production conditions

To implement effective cow milking, it is necessary to take into account the peculiarities of the milk flow process, the milking machine's adaptability to perform the given technological functions. The aim of research is to establish changes in the design and technological parameters and physical and mechanical properties of teat cup liner of milking machines during its testing and in production conditions. The results obtained will make it possible to make a rational choice of rubber, ensure an efficient milking process during its service life. It is found that the tensile strength of silicone teat cup liner at the beginning of operation was 1.6 times higher than that of a rubber compound, and after 6 months. operation – 1.7 times. With respect to the relative elongation, this difference was 1.4 times, and after operating time – 1.3 times. Studies have proven that rubber during operation changes its physical and mechanical properties: the length of the active part increased by 3.1 mm; wall thickness – 0.2 mm. It is found that the most intensively elastic properties of teat cup liner changed during the first 10–20 days. After 10 days, the closing vacuum increased by 16.6 % compared to the initial one, and after 20 days by 23.3 %, which amounted to 8.57 and 9.06 kPa, respectively. Up to 420 hours of operation, the clamping vacuum reached 11.3 kPa, which is 5.8 % lower than the requirements for toughening teat cup liner for rejection. In general, over the period of experiments, the average value of the vacuum of closing the opposite walls of teat cup liner increased from 7.35 to 12.43 kPa, which is 3.6 % higher than the norm (12 kPa). As a result of experimental studies, the regularity of the rubber tension force depending on the operating time in the form of a fourth degree polynomial is obtained. It is found that after 150 hours of operation, the tensile force of teat cup liner decreased by 21 

Specifics of the Surface Structure of Steel Products After Various Laser Alloying Methodics

In modern conditions, volumetric alloying of steels is becoming an increasingly less economically viable process. However, the level of performance properties of unalloyed steels cannot cover the current industry needs. One of the ways to solve this problem – usage of various surface alloying methods of steels, makes it possible to obtain the required properties of the working surface of the alloyed part with minimal consumption of expensive alloying elements. Over the course of the study, combined method of laser-plasma alloying of steel surfaces was analyzed, its technological capabilities were determined, and the structural-phase state of surface layers, formed during laser and hybrid laser-plasma processing was compared. During comparative studies of samples obtained by both methods of surface alloying, it was found that in the case of laser-plasma alloying, the observed structure and carbide phases are smaller in size, with a low density and uniform distribution of dislocations in the metal of the alloyed layer. After various analysis, it was established that during both laser and laser-plasma methods of surface alloying, the crack formation tendencies was mostly attributed to various structural and concentration changes associated with the redistribution of elements, leading to the formation of sharp grain-boundary concentration gradients. An increase in the number of cracks is observed in regimes with higher heating temperatures, increased duration of exposure to high temperatures and reduced cooling rates

Remote sensing techniques in the study of structural and geotectonic features of Iturup Island (the Kuril Islands)

The article presents structural and geotectonic features of Iturup Island, the largest island in the Greater Kuril Ridge, a unique natural site, which can be considered as a geological reference. The structural and geotectonic analysis carried out on the basis of a comprehensive study of the new Earth remote sensing data, maps of anomalous geophysical geophysical fields, and other geological and geophysical materials using modern modelling methods made it possible for the first time to identify or clarify the location of previously discovered discontinuous faults, typify them and determine the kinematics, as well as to establish a more reliable spatial relationship of the identified structures with magmatism with the stages of the geological development of the region. The constructed diagram of the density distribution of the zones with increased tectonic fracturing shows a significant correlation between the distribution of minerals and weakened areas of  the Earth's crust and can be used as an alternative method for predicting minerals in the study region, especially in remote and hard-to-reach areas. The presented approach can be extended to the other islands of the Greater Kuril Ridge, thereby bringing research geologists closer to obtaining the answers to questions about the features of the geotectonic structure and evolution of the island arc. The use of customized software products significantly speeds up the process of interpreting a large array of geological and geophysical data

About Scientometric Performance Indicators Scientist

Наведено найпопулярніші наукометричні показники, які демонструють деякі грані продуктивності роботи науковця. Описано різні способи розрахування індексу Хірша та продемонстровано один із способів на конкретному прикладі. Відмічено переваги і недоліки наукометричних показників при оцінці наукової діяльності ученого.It is presented the popular scientometric performance indicators that show some facets productivity scientist. It is describes various methods for calculating the Hirsch index and demonstrated one way of a specific example. It is indicated the advantages and disadvantages of the scientometric performance indicators in the evaluation of the scientific activity of the scientist

Virtual Laboratory as a Part of Modern Experiment

У статті коротко проаналізовано підходи у тлумаченні терміну «віртуальна лабораторія», на підставі чого у контексті сучасних тенденцій в інформатизації освіти зроблено висновок про необхідність використання майбутніми вчителями природничо-математичних дисциплін віртуальних лабораторій. Наведено приклад системи віртуальних лабораторних робіт. Зазначені переваги використання віртуальних лабораторій у навчальному процесі. Зазначені напрямки віртуального лабораторного практикуму, таких як віртуальні симулятори або тренажери та дистанційно виконувані віртуальні лабораторні роботи.The article analyzes approaches to the interpretation ofthe term "virtual laboratory" ofvarious scientists on the basis ofwhat in the context ofcontemporary trends in Informatization ofeducation concluded on the need for future teachers naturally-mathematical disciplines virtual laboratories. Under the virtual laboratory is a complete replacement ofthe laboratory setup – when the whole process ofmeasurement and processing ofdata involved the computer, but the hand ofthe researcher is only needed for proper confiuration ofcomputer equipment. The use of virtual laboratories allows not only to observe a kind ofexperiment, but also directly participate in it, and this in turn contributes to learning in a more conscious and deeper level. LabVIEW (Laboratory Virtual Instrumentation Engineering Workbench) ofNational Instruments allows to create measuring systems and automation systems based on virtual devices is shown ofa system ofvirtual laboratory works

To the Issue of Digital Identifiers of Scientists

У статті проаналізовано поняття унікального цифрового ідентифікатора науковця, його основні характеристики та можливості використання. Однією із основних систем ідентифікації науковців розглянуто Open Researcher and Contributor ID.The article analyzes the concept of a unique digital identifier of a scientist, his main characteristics and possibilities of use. One of the main systems for the identification of researchers is Open Researcher and Contributor ID

Analysis of the Competence Orientation of the Content of Geometry Learningin the Example of Studying the Topic "Triangles"

У педагогічній теорії немає одностайного підходу до розуміння компетентнісного підходу і шляхів його впровадження в освітню діяльність, тому ця проблема є предметом дискусій і досліджень, у т.ч. в контексті методики навчання математики. Формування математичної компетентності в учнів основної школи на уроках геометрії передбачає різною мірою формування процедурної, логічної, технологічної, дослідницької і методологічної її складових. Тому мета статті: привести результати аналізу компетентнісної орієнтації змісту навчання геометрії на прикладі вивчення теми «Трикутники». Для досягнення мети використовуються такі теоретичні методи дослідження як: аналіз наукової та навчально-методичної літератури з проблеми дослідження, аналіз змісту навчальних планів, програм та підручників, узагальнення досвіду роботи вчителів математики. Нами проаналізовано завдання з теми «Трикутники» у підручниках сьомих класів та наведено порівняльні таблиці кількості завдань, які спрямовані на розвиток тієї чи іншої компоненти математичної компетентності. Зроблено висновок, що найбільшу частку завдань становлять завдання, спрямовані на формування процедурної компетентності, найменшу – методологічної компетентності. А от завдань спрямованих на формування технологічної компетентності не представлено в жодному з підручників. За аналізом підручників з п’ятого по дев’ятий класи закладів загальної середньої освіти та закладів з поглибленим вивченням математики виявлено, що всі автори намагаються спрямувати кожне зі своїх завдань на розвиток певного компоненту математичної компетентності. Однак кількість таких завдань, відповідно до класифікації компонентів, відрізняється. А кількість завдань з кожного компонента математичної компетентності визначається ще й віковими особливостями учня.In pedagogical theory, there is no unanimous approach to understanding the competence approach and the ways of its implementation in educational activity, therefore this problem is the subject of discussions and research, including in the context of mathematics teaching methods. The formation of mathematical competence in elementary school students in geometry lessons involves the formation of its procedural, logical, technological, research, and methodological components to varying degrees. Therefore, the purpose of the article is to present the results of the analysis of the competence orientation of the content of geometry education on the example of studying the topic "Triangles". To achieve the goal, such theoretical research methods are used as an analysis of scientific and educational, and methodological literature on the research problem, analysis of the content of curricula, programs, and textbooks, and generalization of the work experience of mathematics teachers. We have analyzed the tasks on the topic "Triangles" in seventh-grade textbooks and provided comparative tables of the number of tasks aimed at developing one or another component of mathematical competence. It was concluded that the largest share of tasks is tasks aimed at the formation of procedural competence, and the smallest - is methodological competence. But tasks aimed at forming technological competence are not presented in any of the textbooks. Based on the analysis of textbooks from the fifth to the ninth grades of general secondary education institutions and institutions with in-depth study of mathematics, it was found that all authors try to direct each of their tasks to the development of a certain component of mathematical competence. However, the number of such tasks, which characterizes the components of math competence, differs. There are showing, that the number of tasks for the development of each component of mathematical competence and the age characteristics of the student have a connection

Registration in Scientometric on Google Scholar ICT Competence as a Scientist

Обґрунтовано необхідність представлення результатів сучасних науковців у віртуальному науковому середовищі, що характеризує у тому числі їх ІКТ-компетентність. Зазначено про важливість кількісних наукових показників для оцінки продуктивності науковців і доцільність реєстрації їх у світових наукометричних базах. Описано процес створення профілю у науковій пошуковій системі Google Академія.It is substantiated the necessity of presenting the results of work of modern scientific researchers as also a feature of their ICT competence. It is indicated the importance of using quantitative indicators to evaluate the scientific performance of researchers, and the expedience of registration in scientometric databases around the world. It is showed the process of the creating a profile in the scientific search system Google Scholar