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ВЕРОЯТНОСТЬ НЕЗАВИСИМОСТИ (сюжет для исследовательских проектов школьников)
Математика в школе. 2024. № 4. С. 34–40.
Simple examples are given to show that
the independence of two random events is a very
rare circumstance. It is shown how to estimate its
frequency. Open questions are posed
A. V. Pereskokov, Journal of Mathematical Sciences 2026 Vol. 302 No. 4 P. 531–545
We consider the Zeeman effect problem for the hydrogen atom in a magnetic field using
irreducible representations of the Karasev–Novikova algebra with quadratic commutation
relations. We find the asymptotics of a series of eigenvalues and the corresponding
asymptotic eigenfunctions near the upper boundaries of spectral clusters. ...
Added: October 1, 2026
Yakovlev K., Puchkin N., Journal of Complexity 2026 Vol. 97
We present a theory for simultaneous approximation of the score function and its derivatives, enabling the handling of data distributions with low-dimensional structure and unbounded support. Our approximation error bounds match those in the literature while relying on assumptions that relax the usual bounded support requirement. Crucially, our bounds are free from the curse of ...
Added: September 30, 2026
Zlotnik A., Mathematical notes 2026 Vol. 120 No. 6 P. 1005–1009
Numerical methods for solving systems of gas dynamic equations are the subject of a vast literature. A special family of spatially symmetric conservative difference methods based on preliminary kinetic, or quasi-gasdynamic (QGD), regularization of these equations was constructed and successfully tested. A pressing issue is the construction of numerical methods that are not only conservative ...
Added: September 30, 2026
Dvoinin A., Развитие личности 2025 № Спецвыпуск С. 17–20
The article outlines A.M. Dvoinin’s personal reminiscences of his teacher, the prominent psychologist Valeria Sergeevna Mukhina ...
Added: September 30, 2026
Beldiev I., Тимашёв Д. А., Алгебра и анализ 2026 Т. 38 № 5 С. 1–10
An algebraic variety X is called a homogeneous space if there exists a transitive regular action of an algebraic group on X. We prove inequalities between the dimension of a homogeneous space of a linear algebraic group and its Picard number. ...
Added: September 30, 2026
Patarakin Y., Kutuzov A., Искусственные общества 2026 Т. 21 № 3 Статья 10
This paper presents STiMUS (Stigmergy and Mutualism in Socio-Technical Systems), an agent-based model implemented in NetLogo 7.0. The model formalises two complementary coordination mechanisms in digital project teams. The first is stigmergy: contributor agents select shared artefacts to work on by following traces left by previous editors, without explicit communication. The second is mutualism: artefacts ...
Added: September 30, 2026
Planche L., Ilina A., Jay F. et al., Molecular Biology and Evolution 2026 Article 235
Admixture between populations is a common feature of human history. Admixture events introduce new genetic variation that can fuel evolution. Characterizing the significance of admixture events on the evolution of populations across various species is of great interest to evolutionary geneticists. Local Ancestry Inference (LAI) methods infer genetic ancestry of an individual at a particular ...
Added: September 30, 2026
Glutsyuk A., Ilyashenko Y., Izvestiya. Mathematics 2026 Vol. 90 No. 1 P. 73–89
We show that a completely non-degenerate B-group is uniquely determined by its factor: two such groups with conformally equivalent factors are Möbius conjugate. A similar property is inherent to the quasi-Fuchsian groups but not to degenerate B-groups. We also study the factor of a B-group as a triple: the main factor, the marked characteristic complex, and a homotopy class of ...
Added: September 30, 2026
Akhmedjanova D., М.: Издательский дом НИУ ВШЭ, 2026.
Восемнадцатый выпуск серии учебно-методических пособий «Подготовка профессионалов для нового образования» посвящен преподаванию курса по метакогнитивной регуляции обучения на магистерской программе «Педагогическое образование» Института образования НИУ ВШЭ. Пособие систематизирует современные знания о природе, диагностике и развитии саморегуляции в образовании и призвано восполнить дефицит качественных русскоязычных публикаций, интегрирующих достижения отечественной научной школы и передовые международные исследования. Пособие ...
Added: September 29, 2026
Tuzhilin M., Автоматика и телемеханика 2026 № 11 С. 84–97
Предлагается обобщение двух известных инвариантов реальных сетей: степени и кси-центральности. Строится серия центральностей, основанная на матрице Лапласа сети и параметризованная параметром j со следующими свойствами: во-первых, при j = 0, 1 эти центральности совпадают со степенью и ксицентральностью; во-вторых, их распределение хорошо приближается распределением Вейбулла; в-третьих, для реальных сетей они имеют правостороннюю асимметрию, а для ...
Added: September 29, 2026
Melnikov I., Pelinovsky E., Доклады Российской академии наук. Физика, технические науки (ранее - Доклады Академии Наук. Физика) 2026 Т. 529 С. 29–36
Conditions for the emergence of pyramidal solitary waves (solitary waves possessing more than two inflection points) are presented for a family of generalized Korteweg – de Vries (KdV) equations. For the generalized Gardner equation, it is shown that pyramidal solitons are unstable. The decay of initial perturbations close to pyramidal solitary waves is demonstrated numerically. ...
Added: September 29, 2026
Merkulov S., Journal of Pure and Applied Algebra 2026 Vol. 230 P. 1–19
We study the dual cyclic Hochschild complex $Cyc(A,\K)$ of a
(possibly, infinite-dimensional) $A_\infty$-algebra $(A,\mu)$ and prove
that any pre-Calabi-Yau extension $\pi$ of the given $A_\infty$ structure $\mu$ in $A$
induces on the cyclic cohomology of $(A,\mu)$ a representation of a new dg properad of {\em oriented}\, ribbon graphs. We compute the cohomology of that properad in terms of ...
Added: September 29, 2026
Хрыстик М. А., European Journal of Combinatorics 2026 Vol. 136 P. 104393–104393
Let 𝑓𝑊(𝑛) be the number of different factors of length 𝑛 appearing in a word 𝑊. In a classical result by Morse and Hedlund, a characterization is given for infinite words satisfying the condition 𝑓𝑊(𝑛)≤𝑛 for some 𝑛∈ℕ. In this paper, we describe the form of finite words that satisfy the condition 𝑓𝑊(𝑛)≤𝑛. We study ...
Added: September 28, 2026
Teregulov T., Loubenets E. R., / Series Quantum Physics "arXiv". 2026. No. 2609.31472.
We develop a new three-party quantum secret-sharing (QSS) protocol based on a three-qubit W state. This protocol encodes the secret-sequence bits using X gates and employs randomly selected Hadamard operations and measurement bases to generate information and security-test rounds. We evaluate the efficiency of the proposed protocol and analyze its security against an internal adversary ...
Added: September 28, 2026
Ostapenko E., Ivanov I., JOURNAL OF EDUCATION AND LEARNING 2026 Vol. 20 No. 4 P. 2288–2295
In the Russian educational context, where structured extracurricular activities are widely promoted and institutionalized by the state, the role of unstructured after-school practices in shaping socioeconomic inequalities in academic achievement remains unexplored. This study examines how unstructured after-school activities are associated with students’ academic achievement, with a particular focus on whether these associations vary across ...
Added: September 27, 2026
Guterman A., Jonoska N., Kreines E. et al., Proceedings of the Edinburgh Mathematical Society 2026 Vol. 69 No. 3 P. 1041–1057
We provide four equivalent combinatorial conditions for a simple assembly graph (rigid vertex graph where all vertices are of degree 1 or 4) to have the largest number of Hamiltonian sets of polygonal paths relative to its size. These conditions serve to prove the conjecture that such a maximum, which is equal to 𝐹_(2𝑛+1) −1, ...
Added: September 27, 2026
Sergei L. Semakov, , in: Proceedings of the 2026 12th International Conference on Control, Decision and Information Technologies (CoDIT) (Italy, Bari, July 13–16, 2026).: IEEE, 2026. P. 153–156.
The problem of the first achievement of a given level by a random process is considered. The previously obtained general results are specified for a smooth Gaussian process. ...
Added: August 24, 2026
Семаков С. Л., Автоматика и телемеханика 2025 № 12 С. 104–118
This paper considers the problem of estimating the probability of the following event: a continuous random process will first reach a given level at some time from a given variation interval of the independent variable. The general results obtained previously are specified for a smooth Gaussian process. The estimates are calculated for different values of ...
Added: February 23, 2026
Semakov S., Semakov A., Semakov I., , in: 62nd IEEE Conference on Decision and Control (CDC), Singapore, Singapore, 2023.: IEEE, 2023. P. 3820–3825.
We estimate the probability that the first achievement of a given level by the component y_1(x) of n-dimensional continuous process y(x)={y_1(x),…,y_n(x)} occurs at some moment x* from a given interval (x′,x′′) and, at this moment x*, the condition (y_2(x*),…,y_n(x*))∈D holds, where D is a given domain of (n−1)-dimensional Euclidean space R^(n−1). The need to calculate the abovementioned probability arises in the problems of aircraft control during landing. ...
Added: August 9, 2025
Семаков С. Л., Семакова М. В., Автоматика и телемеханика 2023 № 3 С. 126–138
This paper considers aircraft landing on a carrier. We propose two schemes for calculating, first, the probability of a go-around due to disengaging the arresting gear and, second, the maximum descent of the aircraft’s trajectory with respect to the deck level immediately after leaving the deck. The instant to increase the aircraft’s thrust before touching ...
Added: August 8, 2025
Семаков С. Л., М.: Физматлит, 2011.
Излагаются элементы теории вероятностей и случайных процессов. Много внимания уделяется решению задач, которые занимают большую часть пособия. Рекомендовано Учебно-методическим объединением высших учебных заведений РФ по образованию в области прикладных математики и физики в качестве учебного пособия для студентов высших учебных заведений по направлению "Прикладные математика и физика". ...
Added: August 5, 2025
Семаков С. Л., М.: Наука, 2005.
В могографии излагается взгляд на теорию случайных процессов как инструмент математического моделирования. В первой главе рассматриваются основные классы и характеристики случайных процессов; вторая посвящена выбросам случайных процессов: задачам о пересечениях и касаниях фиксированного уровня, экстремумах, первом достижении границ заданной области; третья - приложениям математических результатов в авиации. Ядром второй и третьей глав работы являются результаты ...
Added: August 5, 2025
Sergei L. Semakov, IEEE Transactions on Information Theory 2024 Vol. 70 No. 10 P. 7162–7178
We propose a scheme for finding the probabilities of events related to crossings of a level by a random process. Using this scheme, we estimate the probability that the first achievement of a given level by the component y_1(x) of an n-dimensional continuous process y(x)={y_1(x),…,y_n(x)} occurs at some moment x* from a given interval (x′,x′′) and, at this moment x* , the other components y_2(x*),…,y_n(x*) satisfy given ...
Added: August 3, 2025
Sergei Semakov, International Journal of Dynamics and Control 2025 Vol. 13 No. 5 Article 201
We consider the problem of the exit of a diffusion Markov process to the boundary of a given domain. We concentrate on the one-dimensional case and solve the problem of finding the probability that the first exit of the process beyond the established corridor will occur at a given time. We apply the obtained results ...
Added: August 2, 2025