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Stable vector bundles on the families of curves
European Journal of Mathematics. 2022. Vol. 8. No. 2. P. 540–550.
Fedor Bogomolov, Lukzen E.
We offer a new approach to proving the Chen–Donaldson–Sun theorem which we demonstrate with a series of examples. We discuss the existence of a construction of a special metric on stable vector bundles over the surfaces formed by a family of curves and its relation to the one-dimensional cycles in the moduli space of stable bundles on curves.
Degtyarev A., Bakhurin S., Yudin N., DSPA 2026 P. 1–6
This paper investigates one possible solution to the problem of self-interference cancellation (SIC) arising in the design of in-band full-duplex (IBFD) communication systems. Self-interference cancellation is performed in the digital domain using multilayer nonlinear models adapted via gradient-based optimization. The presence of local minima and saddle points during the adaptation of multilayer models limits the ...
Added: May 26, 2026
Ilyashenko Y., Shilin I., Stanislav Minkov, Russian Journal of Mathematical Physics 2026 Vol. 33 No. 1 P. 89–106
In this paper, new numerical invariants of structurally unstable vector fields in the plane
are found. One of the main tools is an improved asymptotics of sparkling saddle connections that
occur when a separatrix loop of a hyperbolic saddle breaks. Another main tool is a new topological
invariant of two arithmetic progressions, both perturbed and unperturbed, on the ...
Added: May 26, 2026
Gusev I., Maksaev A., Promyslov V., Journal of Mathematical Sciences 2025 Vol. 299 No. 6
The regular graph of the space of n × m matrices over a field F is defined as the undirected graph whose vertices are matrices of rank min(n, m), and distinct matrices A and B are connected by an edge if and only if rk(A + B) < min(n, m). In this paper, for |F| ...
Added: May 25, 2026
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
Chertopolokhov V., Mukhamedov A., Bugriy G. 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 Article 18
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 Article 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
Gurevich E., Saraev I., Известия РАН. Серия математическая 2026 Т. 90 № 3 С. 19–56
In this paper, we consider a class of gradient-like ows without heteroclinic
intersections, dened on closed manifolds of dimension four. We show that for
such ows, the problem of complete topological classication can be reduced to
the combinatorial problem of distinguishing special framed graphs describing
the mutual arrangement of invariant manifolds and the action of the ow on a
wandering ...
Added: May 18, 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
Dorovskiy A., / Series arXiv "math". 2026.
In this paper the structural stability of generic families of vector fields of the PC-HC class on the two-dimensional sphere is proved. A classification of these families up to moderate equivalence in neighborhoods of their large bifurcation supports is presented, based on such invariants as the configuration and the characteristic set. The realization lemma is proved. ...
Added: May 14, 2026
Lebedev V., Journal of Mathematical Analysis and Applications 2026 Vol. 563 No. 2 Article 130787
It is known that for every continuous real-valued
function $f$ on the circle $\mathbb T=\mathbb R/2\pi\mathbb Z$ there exists a
change of variable, i.e., a self-homeomorphism $h$ of $\mathbb T$, such that
the superposition $f\circ h$ is in the Sobolev space $W_2^{1/2}(\mathbb T)$.
We obtain new results on simultaneous improvement of functions by a single
change of variable in relation ...
Added: May 14, 2026
Interpretable Machine Learning in Guided Synthesis of Stable Sols Based on Nanosized Titanium Oxides
Glushko A., Neznanov A., Kuz'micheva G. et al., , in: 2026 International Conference on Artificial Intelligence, Computer, Data Sciences and Applications (ACDSA), 5-7 Feb. 2026.: IEEE, 2026. P. 1–6.
This report discusses the guided synthesis of sols containing nanosized titanium(IV) oxides for use in biological and medical applications. These sols vary in size (from ∼2 up to 2000nm) and different stability (from 0 up to 90 days). They are synthesized under changing fabrication conditions (temperature, hydrolysis duration, titanium-containing precursors composition and concentration) without surfactants. ...
Added: April 29, 2026
Sergei Koltcov, Surkov A., Filippov V. et al., PeerJ Computer Science 2024 Vol. 10 P. 41
Topic modeling is a widely used instrument for the analysis of large text collections.
In the last few years, neural topic models and models with word embeddings have
been proposed to increase the quality of topic solutions. However, these models
were not extensively tested in terms of stability and interpretability. Moreover, the
question of selecting the number of topics ...
Added: February 16, 2024
Fateeva A., Shutkov I., Mazur D. et al., Mendeleev Communications 2022 Vol. 32 No. 2 P. 186–188
Preparation of novel imidazole ligands containing 3-(benzyloxy)pyridinone moiety is described. The Ruiii and Ruii leader-compounds containing the above-mentioned ligands were synthesized by coordination of imidazole group. The stability of the obtained compounds was explored in buffer solution and in the presence of DMSO, respectively, and their antiproliferative activity was assessed. ...
Added: September 14, 2023
Shabarov V., Kaliasov P., Peplin F., Ship Technology Research 2020 Vol. 67 No. 2 P. 101–108
Accurate determination of longitudinal stability characteristics of wing-in-ground (WIG) effect vehicles is an essential step in their design. In order to estimate WIG vehicle’s stability, one needs to determine aerodynamic derivatives, including unsteady ones. The latter are very hard to obtain via wind tunnel tests, so traditionally they are expressed via steady derivatives. The method ...
Added: September 4, 2022
Ruderman M., Petrukhin N., Solar Physics 2021 Vol. 296 Article 106
We study kink oscillations of a straight magnetic tube in the presence of siphon flows. The
tube consists of a core and a transitional or boundary layer. The flow velocity is parallel to
the tube axis, has constant magnitude, and confined in the tube core. The plasma density
is constant in the tube core and it monotonically decreases ...
Added: July 1, 2021
Nesterov Y., Protasov V., SIAM Journal on Matrix Analysis and Applications 2020 Vol. 41 No. 1 P. 1–28
The problem of nding the closest stable matrix for a dynamical system has many
applications. It is studied for both continuous and discrete-time systems and the corresponding
optimization problems are formulated for various matrix norms. As a rule, nonconvexity of these
formulations does not allow nding their global solutions. In this paper, we analyze positive discretetime
systems. They also ...
Added: July 30, 2020
Moiseeva V., Nazarova M., Novikov P. et al., , in: 2018 Neuroscience Meeting Planner. San Diego, CA: Society for Neuroscience, 2018. Online.: San Diego: Society for Neuroscience, 2018. P. 1–2.
Cortical mapping with transcranial magnetic stimulation (TMS) is a promising approach for non-invasive investigation of the motor cortex in humans. However, apart from the parameters reflecting general corticospinal excitability, e.g., resting motor threshold (RMT) and mean amplitude of the motor evoked potentials, the reproducibility of other TMS motor maps metrics remains controversial or unknown. We ...
Added: October 31, 2018