• Journal of Astronomy and Space Sciences
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• v.36 no.1
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• pp.21-33
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• 2019

This paper focuses on the interpretation of radiation fluxes from active galactic nuclei. The advantage of positron annihilation spectroscopy over other methods of spectral diagnostics of active galactic nuclei (therefore AGN) is demonstrated. A relationship between regular and random components in both bolometric and spectral composition of fluxes of quanta and particles generated in AGN is found. We consider their diffuse component separately and also detect radiative feedback after the passage of high-velocity cosmic rays and hard quanta through gas-and-dust aggregates surrounding massive black holes in AGN. The motion of relativistic positrons and electrons in such complex systems produces secondary radiation throughout the whole investigated region of active galactic nuclei in form of cylinder with radius R= 400-1000 pc and height H=200-400 pc, thus causing their visible luminescence across all spectral bands. We obtain radiation and electron energy distribution functions depending on the spatial distribution of the investigated bulk of matter in AGN. Radiation luminescence of the non-central part of AGN is a response to the effects of particles and quanta falling from its center created by atoms, molecules and dust of its diffuse component. The cross-sections for the single-photon annihilation of positrons of different energies with atoms in these active galactic nuclei are determined. For the first time we use the data on the change in chemical composition due to spallation reactions induced by high-energy particles. We establish or define more accurately how the energies of the incident positron, emitted ${\gamma}-quantum$ and recoiling nucleus correlate with the atomic number and weight of the target nucleus. For light elements, we provide detailed tables of all indicated parameters. A new criterion is proposed, based on the use of the ratio of the fluxes of ${\gamma}-quanta$ formed in one- and two-photon annihilation of positrons in a diffuse medium. It is concluded that, as is the case in young supernova remnants, the two-photon annihilation tends to occur in solid-state grains as a result of active loss of kinetic energy of positrons due to ionisation down to thermal energy of free electrons. The single-photon annihilation of positrons manifests itself in the gas component of active galactic nuclei. Such annihilation occurs as interaction between positrons and K-shell electrons; hence, it is suitable for identification of the chemical state of substances comprising the gas component of the investigated media. Specific physical media producing high fluxes of positrons are discussed; it allowed a significant reduction in the number of reaction channels generating positrons. We estimate the brightness distribution in the ${\gamma}-ray$ spectra of the gas-and-dust media through which positron fluxes travel with the energy range similar to that recorded by the Payload for Antimatter Matter Exploration and Light-nuclei Astrophysics (PAMELA) research module. Based on the results of our calculations, we analyse the reasons for such a high power of positrons to penetrate through gas-and-dust aggregates. The energy loss of positrons by ionisation is compared to the production of secondary positrons by high-energy cosmic rays in order to determine the depth of their penetration into gas-and-dust aggregations clustered in active galactic nuclei. The relationship between the energy of ${\gamma}-quanta$ emitted upon the single-photon annihilation and the energy of incident electrons is established. The obtained cross sections for positron interactions with bound electrons of the diffuse component of the non-central, peripheral AGN regions allowed us to obtain new spectroscopic characteristics of the atoms involved in single-photon annihilation.

• Communications of Mathematical Education
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• v.35 no.2
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• pp.173-191
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• 2021

This study noted that a survey of teachers in a leading study conducted in Korea during the Pandemics period pointed out that the "real-time interactive" classes account for a significantly small portion of the remote class format. Contentually, the study reported cases of developing and applying "real-time interactive" class materials based on "planar decision requirements" of high school mathematics subject geometry. The teacher who participated in the development was a math teacher who worked at a Seoul-based high school with 28 years of high school teaching experience, and a teacher who was in charge of geometry in the math department in 2020. The development teacher decided to develop real-time interactive classes. In particular, the materials were developed by organizing the class guidance plan in four stages: 'Meeting and Class Guidance', 'Giving motivation', 'Suggesting tasks', 'Individual Investigative Activities and Teacher Feedback' and 'Reflection and Evaluation' which were selected through the process of selecting the class contents and selecting online class tools. At this time, the development teacher produced and presented about five minutes of video material using the videooscribe, a whiteboard animation program. And in case of task number 8, it consisted of recording the students' free thoughts after class, which served as a role of assessment by students themselves and providing feedback to their teachers. This study is a case study that introduces a series of courses in which field teachers develop class materials, and in addition to presenting class materials that can be applied directly to classes, is a result of a study that focuses on the role of presenting samples for future class data development. The materials developed were verified as class materials based on the opinions of the students who participated in the class and the results of the evaluation commissioned by the three math teachers.