We propose a protocol for probing mechanically induced stochastic phase-matching fluctuations in spontaneous parametric downconversion (SPDC) by Hong–Ou–Mandel (HOM) interferometry. The analysis is formulated for collinear type-II SPDC in β-barium borate (BBO). We distinguish the ideal white-jerk limit from the experimentally relevant finite-bandwidth regime. In the ideal limit, the incremental phase variance generated during a photon transit scales as L5; however, for a 5-mm BBO crystal, the transit time is only about 29 ps, so a piezoelectric mechanical drive is quasi-static on this time scale and the L5 law is not assumed as a direct experimental signature. Instead, the measured acceleration power spectral density and the mechanical transfer function are used to calculate the finite-bandwidth phase fluctuations. The connection to HOM visibility is derived through the biphoton joint spectral amplitude: stochastic phase mismatch modifies the phase-matching function, and the ensemble-averaged spectral-exchange overlap determines the coincidence dip. A frequency-independent common phase cancels from this overlap and therefore does not reduce HOM visibility. The resulting formulation provides a directly testable route for phase-stability metrology without requiring the experimentally inaccessible white-noise approximation.
The article presents the актуal issue of using AI technologies in teaching English speaking within the framework of distance education. The main principles of teaching speaking skills to university students are highlighted. Digital resources and AI platforms aimed at developing various aspects of oral foreign-language speech are presented. It is argued that the comprehensive application of AI technologies can help achieve significant results in improving English speaking skills.
The article reveals ways to prepare a parent's homeroom teacher to organize joint leisure time with children by reading books dedicated to the Great Patriotic War and the post-war period, in order to develop their own meanings, assessments that take into account family traditions and socio-cultural realities. As part of the search for ways to help parents that an educational organization can provide in the implementation of family education in a civil-patriotic direction, training is offered according to the Kolb model of the technology "War and Peace", developed in the spring of the Year of Defender of the Fatherland.
Статья посвящена применению компетентностного подхода в преподавании линейной алгебры и математического анализа в высшей школе. Цель исследования - разработать и апробировать методику формирования ключевых компетенций студентов в рамках данных дисциплин. На основе анализа литературы и эмпирических данных выделены основные проблемы реализации компетентностного подхода и предложены пути их решения. Методами исследования выступили: теоретический анализ научных публикаций, анкетирование преподавателей (n=54) и студентов (n=312), педагогический эксперимент. Выявлены три кластера компетенций, развитие которых должно стать приоритетом в обучении линейной алгебре и математическому анализу: 1) способность применять математический аппарат для решения прикладных задач (r=0,87); 2) умение работать в команде над проектами (r=0,74); 3) критическое мышление и креативность в исследованиях (r=0,69). Предложена методика поэтапного формирования данных компетенций, доказана ее эффективность (p<0,01). Полученные результаты имеют теоретическую ценность для развития компетентностного подхода и практическую значимость для совершенствования математического образования в вузах. Перспективы исследования связаны с разработкой диагностического инструментария для оценки уровня сформированности математических компетенций. The article is devoted to the application of the competence approach in teaching linear algebra and mathematical analysis in higher education. The purpose of the research is to develop and test a methodology for the formation of students' key competencies in these disciplines. Based on the analysis of literature and empirical data, the main problems of implementing the competence approach are identified and ways to solve them are proposed. The research methods were: theoretical analysis of scientific publications, a survey of teachers (n=54) and students (n=312), a pedagogical experiment. Three clusters of competencies have been identified, the development of which should be a priority in teaching linear algebra and mathematical analysis.: 1) the ability to apply mathematical apparatus to solve applied problems (r=0.87); 2) the ability to work in a team on projects (r=0.74); 3) critical thinking and creativity in research (r=0.69). A method of step-by-step formation of these competencies is proposed, and its effectiveness is proven (p<0.01). The results obtained have theoretical value for the development of a competence-based approach and practical significance for improving mathematical education in higher education institutions. The prospects of the research are related to the development of diagnostic tools for assessing the level of mathematical competence formation.
