On Romanoff’s theorem

A classic problem in data analysis is studying the systems of subsets defined by either a similarity or a dissimilarity function on X which is either observed directly or derived from a data set. For an electrical network there are two functions on the set of the nodes defined by the resistance matrix and the response ...

Added: May 28, 2026

Non-linear in-band interference cancellation on base of conjugate gradients method

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

New Numerical Invariants of an Unfolding of a Polycycle “Tears of the Heart”

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

ADDITIVE AUTOMORPHISMS OF REGULAR MATRIX GRAPH

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

Coping with AI errors with provable guarantees

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

Overcoming the Curse of Dimensionality with Synolitic AI

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

Stable On-the-Fly Learning for Dynamic Neural Networks With Delayed Inputs

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

Analysis of the alternating minimization method for low-rank canonical polyadic decomposition in the Chebyshev norm

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

B-facets in Dimension 4

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

The VCG Mechanism, the Core, and Assignment Stages in Auctions

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

Upper bounds for Steklov eigenvalues of a hypersurface of revolution

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

On smooth Fano threefolds with coregularity zero

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

Классификация градиентно-подобных потоков без гетероклинических пересечений на четырехмерных многообразиях

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

2-Elliptic Periodic Orbits near a Nonsimple Homoclinic Tangency in Four-Dimensional Symplectic Maps

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

Bibliometric Analysis by Network Models

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

Neural-network maps for two-parameter modeling of bistability and codimension-two bifurcations in two-dimensional flow dynamical systems

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

Bifurcations and Structural Stability of Generic PC-HC Families

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

The Sobolev space W_2^{1/2}: Simultaneous improvement of functions by a homeomorphism of the circle

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

Многообразие точек перегиба плоских кубик

Popov V., Труды Математического института им. В.А. Стеклова РАН 2025 Т. 329 С. 209–226

Let X be the variety of flexes of plane cubics. The following statements are proved in this paper: (1) X is an irreducible rational algebraic variety equipped with an effective algebraic action of the group PSL(3); (2) X is PSL(3)-equivariantly birationally isomorphic to a homogeneous fiber bundle over PSL(3)/K with fiber being a projective line, ...

Added: December 16, 2025

Алгеброгеометрические коды и декодирование на основе пар, исправляющих ошибки

Kuninets A., Malygina E., Раточка В. Л. et al., Прикладная дискретная математика 2023 № 62 С. 83–105

Рассматриваются теоретические основы алгебраических кривых и их функциональных полей, необходимые для построения алгеброгеометрических (АГ) кодов, а также пар, исправляющих ошибки, с целью их дальнейшего применения для декодирования кодов. Приведены теория, необходимая для обоснования корректности работы алгоритма декодирования АГ-кодов на основе пар, исправляющих ошибки, и сам алгоритм декодирования. Рассмотрены примеры построения АГ-кодов, ассоциированных с эллиптической кривой, ...

Added: December 12, 2025

Numbers of the form $k+f(k)$

Gabdullin M., Vitalii V. Iudelevich, Luca F., Journal of Number Theory 2024 Vol. 262 P. 58–85

For a function $f\colon \N\to\N$, let $$ N^+_f(x)=\{n\leq x: n=k+f(k) \mbox{ for some } k\}. $$ Let $\tau(n)=\sum_{d|n}1$ be the divisor function, $\omega(n)=\sum_{p|n}1$ be the prime divisor function, and $\varphi(n)=\#\{1\leq k\leq n: \gcd(k,n)=1 \}$ be Euler's totient function. We show that \begin{align*} &(1) \quad x \ll N^+_{\o}(x), \\ &(2) \quad x\ll N^+_{\tau}(x) \leq 0.94x, \\ &(3) \quad x \ll N^+_{\varphi}(x) \leq 0.93x. \end{align*} ...

Added: February 25, 2025

О многообразии точек перегиба плоских кубик

Popov V., Успехи математических наук 2024 Т. 79 № 6 С. 169–170

Let X be the variety of flexes of plane cubics. The following properties of the algebraic variety X are proven: (1) X is irreducible and endowed with a faithful algebraic action of the group G=PSL(3). (2) X is rational. (3) There is a subgroup K of G isomorphic to the binary tetrahedral group such that ...

Added: December 2, 2024

Compatible Poisson Brackets Associated with Elliptic Curves in G(2, 5)

Nikita Markarian, Polishchuk A., Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) 2024 Vol. 20 Article 037

We prove that a pair of Feigin–Odesskii Poisson brackets on P4 associated with elliptic curves given as linear sections of the Grassmannian G(2,5) are compatible if and only if this pair of elliptic curves is contained in a del Pezzo surface obtained as a linear section of G(2, 5). ...

Added: December 2, 2024

Moore matrices and Ulrich bundles on an elliptic curve

Buchweitz R., Pavlov A., L'Enseignement Mathématique 2024 Vol. 70 No. 1/2 P. 1–24

We give normal forms of determinantal representations of a smooth projective plane cubic in terms of Moore matrices. Building on this, we exhibit matrix factorizations for all indecomposable vector bundles of rank 2 and degree 0 without nonzero sections, also called Ulrich bundles, on such curves. ...

Added: May 24, 2024