In the realm of modern education, the integration of technology has emerged as a powerful catalyst for transforming traditional classrooms into dynamic and engaging learning environments. This paper provides a concise overview of the multifaceted ways in which technology contributes to enhanced classroom engagement.

The properties of the beta batteries are compared, which are made on the basis of the different β-isotopes with beta decay. Tritium and Ni-63 make it possible to make β-sources of high activity, without harmful associated emissions, with low self-absorption, emitting high-energy β-electrons that penetrate deep into the semiconductor and generate a large number of electron-hole pairs. The efficiency of beta batteries needs to be analyzed based on the real energy distribution of β-electrons. It makes possible to obtain the real value of the energy absorbed inside the β-source, correctly estimate the amount of self-absorption of the β-electrons and part of the β-electronsthere is a penetrate into the semiconductor, the number of electrons and holes that are generated in the semiconductor, and the magnitude of the idling voltage. Formulas for these quantities are calculated in this paper.

This systematic literature review examines the convergence of entrepreneurship and information technology between 2005 and 2024. It investigates how the emergence of information technologies such as social networks, smart devices, big data, and cloud computing have transformed business operations and entrepreneurial approaches. The study use technologies such as Bibliometrix to analyze academic literature and identify research trends, knowledge structures, and their evolutionary routes. During the specified time frame, a grand total of 292 articles were published by 777 writers. These publications have played a key role in redirecting academic focus from traditional entrepreneurship to the field of digital entrepreneurship and the applications of information technology. A thematic analysis uncovers a shift from theoretical investigation to practical implementations and multidisciplinary research, while a co-citation analysis highlights important contributors and influential works. This study emphasizes the crucial importance of information technology in influencing entrepreneurial behaviors and strategic business decisions. It also offers valuable insights for future research and entrepreneurial practice in the information age.

The article is devoted to formulation of theoretical principles and practical recommendations regarding organization and planning of the investigation of criminal offenses in the field of economic activity, which are committed with the participation (assistance) of law enforcement officers. The methodology for the article is chosen taking into account the purpose and tasks, object and subject matter of the study. The research results were obtained with the help of the following methods: dialectical; formal and logical; formal and legal; comparative and legal; historical and legal, complex analysis; analysis and synthesis; axiomatic; system and structural method. The obtained results of the study indicated that organization and planning of the investigation of criminal acts under consideration is a purposeful activity of the authorized bodies, which is carried out under the guidance of the investigator, detective of the pre-trial investigation body. These activities require systematic, comprehensive approach and must take into account a wide range of circumstances that can affect the process and results of the investigation: the nature of the criminal offense, access to the necessary financial, human and technical resources; the competence of the investigator, the detective; terms and deadlines for investigation and presenting materials to the court, establishing effective cooperation between competent authorities. The study highlights the peculiarities of the organization and planning of the investigation of criminal offenses in economic activities, when law enforcement officers are involved, and suggests directions for improving the effectiveness of their implementation.

The effective drainage radius of coal seam is an important basis for the spacing of pre-drainage gas boreholes. To quickly and accurately determine the effective drainage radius, a new method was proposed. For the coal face where the desorbable gas content before mining has met the standard, the compliance of mine gas drainage rate was used as the basis to determine the effective drainage radius. The fluid-structure interaction model was constructed, numerical simulation of coal seam gas drainage was carried out by using COMSOL software, and the model was validated by combining the field test results. The results show that the new method has the advantage of short cycle. With the extension of drainage time, the increase of effective drainage radius gradually decreases, and finally reaches a relatively stable limit value, which conforms to the Langmuir function. The average error between numerical simulation and field test values of effective drainage radius is 4.9%, which proves that the model is reliable. This model can accurately predict the effective drainage radius under different coal seam gas contents and drainage times. The research results provide a new mean for determining the effective drainage radius of coal seam and the layout of gas drainage boreholes.

In this paper, an improved mathematical model for flashover behavior of polluted insulators is proposed based on experimental tests. In order to determine the flashover model of polluted insulators, the relationship between conductivity and salinity of solution pollution layer of the insulator is measured. Then, the leakage of current amplitude of four common insulators versus axial, thermal conductivity and arc constants temperature was determined. The experimental tests show that top leakage distance (TLd) to bottom leakage distance (BLd) ratio of insulators has a significant effect on critical voltage and current. Therefore, critical voltage and current were modeled by TLd to BLd ratio Index (M). Also, salinity of solution pollution layer of the insulators has been applied to this model by resistance pollution parameter. On the other hand, arc constants of each insulator in new model have been identified based on experimental results. Finally, a mathematical model is intended for critical voltage against salinity of solution pollution layer of different insulators. This model depends on insulator profile. There is a good agreement between the experimental tests of pollution insulators obtained in the laboratory and values calculated from the mathematical models developed in the present study.