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Чем пятиугольники лучше шестиугольников?
Математика в школе. 2026. № 1. С. 13–17.
It has been shown that the area of any convex pentagon is at least 4/3 times greater than the area of the polygon formed by the segments connecting the midpoints of adjacent sides; the constant 4/3 is unimprovable, and for hexagons no similar estimate with k > 1 exists.
Tyukin I., Tyukina T., van Helden D. P. et al., Information Sciences 2024 Vol. 678 Article 120856
AI errors pose a significant challenge, hindering real-world applications. This work introduces a novel approach to cope with AI errors using weakly supervised error correctors that guarantee a specific level of error reduction. Our correctors have low computational cost and can be used to decide whether to abstain from making an unsafe classification. We provide ...
Added: May 23, 2026
Zaikin A., Sviridov I., Sosedka A. et al., Technologies 2026 Vol. 14 No. 2 Article 84
High-dimensional tabular data are common in biomedical and clinical research, yet conventional machine learning methods often struggle in such settings due to data scarcity, feature redundancy, and limited generalization. In this study, we systematically evaluate Synolitic Graph Neural Networks (SGNNs), a framework that transforms high-dimensional samples into sample-specific graphs by training ensembles of low-dimensional pairwise ...
Added: May 23, 2026
Kibkalo Vladislav, Chertopolokhov V., Mukhamedov A. et al., IEEE Access 2026 Vol. 14 P. 14369–14392
This study presents on-the-fly identification and multi-step prediction of nonlinear systems with delayed inputs using a dynamic neural network combined with a smooth projection onto ellipsoids. The projection enforces parameter constraints that guarantee stability, while a Lyapunov–Krasovskii analysis yields computable ultimate error bounds. Riccati-type matrix inequalities are derived, providing an efficient vectorization–projection–devectorization implementation suitable for ...
Added: May 22, 2026
Морозов С. В., Calcolo 2026 Vol. 63 No. 2 Article 23
The approximation of tensors in a low-para metric format is a crucial component in many mathematical modelling and data analysis tasks. Among the widely used low-parametric representations, the canonical polyadic (CP) decomposition is known to be very efficient. Nowadays, most algorithms for CP approximation aim to construct the approximation in the Frobenius norm; however, some ...
Added: May 22, 2026
Селянин Ф. И., Journal of Dynamical and Control Systems 2026 Vol. 32 No. 2 P. 1–16
A B-facet is a lattice -dimensional polytope in the positive octant with a positive normal covector, such that every -dimensional simplex with vertices in it is a B-simplex (i.e., a pyramid of height one with base on a coordinate hyperplane). B-facets were introduced in [2] in the context of the monodromy conjecture. In this paper, we complete the ...
Added: May 21, 2026
Ausubel L., Baranov O., Journal of Economic Theory 2026 Vol. 235 No. 106192
The Vickrey-Clarke-Groves (VCG) mechanism is one of the most compelling constructs in mechanism design, but the presence of complementary goods creates the possibility of non-core and even zero-revenue outcomes. In this article, we show that joint feasibility constraints on allocations offer a second pathway to ill-behaved outcomes in the VCG mechanism, even when all bidders ...
Added: May 20, 2026
Denis Seliutskii, Russian Journal of Mathematical Physics 2025 Vol. 32 No. 2 P. 399–407
In this paper, we find an upper bound for the first Steklov eigenvalue for a surface of revolution with boundary consisting of two spheres of different radii. Moreover, we prove that, in some cases, this boundary is sharp. ...
Added: May 19, 2026
Жакупов О. Б., European Journal of Mathematics 2025 Vol. 11 Article 84
We provide examples of smooth three-dimensional Fano complete intersections of degree 2, 4, 6, and 8 that have absolute coregularity 0. Considering the main theorem of Avilov, Loginov, and Przyjalkowski (CNTP 18:506–577, 2024) on the remaining 101 families of smooth Fano threefolds, our result implies that each family of smooth Fano threefolds has an element of absolute ...
Added: May 18, 2026
Zamkovaya M., Педагогика и психология образования 2026 № 1 С. 57–67
В статье рассматривается процесс становления системы билингвального образования в Республике Сербия с акцентом на его цели, достижения и существующие вызовы. Отмечается, что несмотря на положительные результаты, образовательные учреждения сталкиваются с рядом проблем, среди которых недостаточное финансирование, нехватка квалифицированных специалистов и отсутствие четкой нормативно-правовой базы, регламентирующей процесс билингвального обучения. В статье также анализируются результаты эмпирических исследований, ...
Added: May 18, 2026
Андреева О. С., Просвещение, 2023.
Эта книга о том, как воспитать финансово грамотных детей. Не так важно, какой уровень дохода в вашей семье: умение зарабатывать, сберегать и тратить поможет вашим детям достичь благополучия в будущем. Все необходимые навыки для реальной сложной и порой трудной жизни вы должны вложить в детей сами.
Эта книга – пособие, которое поможет родителям понятно, последовательно и ...
Added: May 18, 2026
Андреева О. С., Росмэн-Пресс, 2026.
«Деньги. Энциклопедия российского школьника» кратко и емко расскажет:
· Чем в древности платили за товары
· Как выглядели первые деньги, из чего их делали и где хранили
· Как найти клад и можно ли выиграть в лотерею
· Как работает банк
· Как дети и подростки могут зарабатывать и распоряжаться личным бюджетом
· И еще сотни интересных научно-обоснованных фактов
Книга поможет мальчикам ...
Added: May 18, 2026
Андреева О. С., Просвещение, 2024.
В книге собраны рекомендации и практические советы приёмным родителям, с помощью которых можно сформировать у детей правильное отношение к денежным средствам, рассказывается, какими словами объяснять понятные взрослым истины относительно личных и семейных финансов ребёнку любого возраста. Одной из задач книги стала необходимость объяснения этого феномена — потребительского отношения приёмных детей к труду замещающих родителей, к ...
Added: May 18, 2026
Pavliuk D., Higher Education 2026
The literature on doctoral students’ experience rarely examines the importance of thesis topic characteristics, even though this is one of the central decisions both at the start and throughout the doctoral journey. Although studies examine how students choose their thesis topics, there is little research on how different topic characteristics are linked to doctoral experience ...
Added: May 16, 2026
Kolachev N., Kovaleva G., Educational Research and Evaluation 2026 P. 1–24
This study investigates the psychometric structure and school-level associations between cognitive abilities of teachers and students. Using a cross-sectional quantitative design, we administered a PISA-based cognitive assessment tool measuring reading, mathematics, science literacy, and global competence to 5,391 eighth-grade students and 2,385 teachers from 84 schools in a Russian region. Bifactor modeling, measurement invariance testing, ...
Added: May 15, 2026
Gonchenko S., Lerman L., Turaev D., Regular and Chaotic Dynamics 2026 Vol. 31 No. 3 P. 349–369
We show that bifurcations of four-dimensional symplectic diffeomorphisms with a quadratic homoclinic tangency to a saddle periodic orbit with real multipliers produce 2-elliptic periodic orbits if the tangency is not partially hyperbolic. We show that a normal form for the rescaled first-return maps near such tangency is given by a four-dimensional symplectic H´enonlike map and study bifurcations of the ...
Added: May 15, 2026
Aleskerov F. T., Khutorskaya O., Stepochkina A. et al., Springer, 2026.
The book contains new models of bibliometric analysis based on centrality measures in network analysis, pattern analysis and stability analysis. A distinctive feature of these centrality measures is that they account for the parameters of vertices and group influence of vertices to a vertex. This reveals specific groups of publications, authors, terms, journals and affiliations ...
Added: May 15, 2026
Kuptsov P., Panyushev A., Stankevich N., Chaos 2026 Vol. 36 No. 5 Article 053138
We develop a machine-learning approach to reproduce the behavior of two versions of the van der Pol oscillator exhibiting a subcritical Andronov–Hopf bifurcation, with or without a codimension-2 Bautin point. We construct a neural-network model that functions as a recur rent map and train it on short segments of oscillator trajectories. The results show that, ...
Added: May 15, 2026