Speed of Convergence of Chernoff Approximations to Solutions of Evolution Equations

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

Simultaneous approximation of the score function and its derivatives by deep neural networks

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

Conservative Entropy and Energy Correct Difference Methods for One-Dimensional Quasi-Gasdynamic Systems of Equations

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

О числе Пикара и размерности алгебраических однородных пространств

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

An archaic reference-free method to jointly infer Neanderthal and Denisovan introgressed segments in modern human genomes,

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

Uniqueness theorem for completely non-degenerate B-groups

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

Серия инвариантных характеристик реальных сетей

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

Нетривиальное поведение пирамидальных уединенных волн в обобщенном уравнении Гарднера

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

Pre-Calabi-Yau algebras and oriented gravity properad

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

Combinatorics on finite words and the length of a finite-dimensional associative algebra

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

A Three-Party W-State Quantum Secret Sharing Protocol with X-Gate Encoding and Forbidden-Outcome Detection

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

Hamiltonian Sets of Polygonal Paths in Assembly Graphs

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_(2⁢𝑛+1) −1, ...

Added: September 27, 2026

О приложениях обобщённого потенциала Бесселя к решению сингулярного уравнения Шрёдингера дробного порядка и теории ёмкости

Shishkina E., Современная математика. Фундаментальные направления 2026 Т. 72 № 1 С. 52–67

In this paper, we construct a weighted Sobolev space of fractional order based on the generalized Bessel potential.We apply these results to the analysis of the singular fractional Schr¨odinger equation. To solve the Cauchy problem for this equation, we prove an estimate that relates the norm of the solution to the norm of the initial condition in the ...

Added: September 26, 2026

A Semigroup Approach for Constructing the Fractional Power of the Laplace–Bessel Operator

Shishkina E., Computational Mathematics and Mathematical Physics 2026 Vol. 66 No. 5 P. 804–815

This article demonstrates that the Laplace–Bessel operator generates a strongly continuous semigroup on a weighted Lebesgue space. Using this semigroup, we define the fractional Laplace– Bessel operator via Balakrishnan’s formula. Furthermore, we derive three distinct representations for fractional powers of the negative Laplace–Bessel operator. ...

Added: September 26, 2026

Matrix Approach To The Fractional Calculus

Kolokoltsov V., Shishkina E., Journal of Theoretical Probability 2026 P. 39–83

In this paper, we introduce a new construction of fractional derivatives and integrals with respect to a function, based on a matrix approach. We believe that this is a powerful tool in both analytical and numerical calculations.We begin with the differential operator with respect to a function that generates a semigroup. By discretizing this operator, we obtain a matrix ...

Added: September 26, 2026

AN ANALOGUE OF ROGERS’ THEOREM ON SIEVING IN COMMUTATIVE RINGS

Petr Kucheriaviy, Bulletin of the Australian Mathematical Society 2026

We prove that an analogue of Rogers’ theorem on sieving holds for an order if and only if the order is a Dedekind domain. We also prove that it holds for a finite commutative ring if and only if the ring is a direct product of local rings with linearly ordered ideals. ...

Added: September 25, 2026

Билинейные теоремы сложения и последовательности Сомоса

Пелевин Ф. Е., Математические заметки 2026 Т. 120 № 1 С. 159–163

Две не равные тождественно нулю функции (последовательности элементов некоторого поля) будем называть эквивалентными, если они удовлетворяют функциональному уравнению типа теорем сложения тэта-функций. Основной результат работы состоит в том, что рассматриваемое отношение действительно является отношением эквивалентности. ...

Added: September 25, 2026

Computable isomorphisms of relative regular Boolean algebras

Shimanogov I. N., Vyalyi M., Siberian Mathematical Journal 2026 Vol. 67 No. 5 P. 1203–1212

We consider a class of Boolean algebras formed by intersections of regular languages with a given language. In the case where such an algebra is isomorphic to the algebra of regular languages, we prove the existence of an isomorphism that is computable using oracles for the regular realizability problem and the infinite regular realizability problem. This result yields ...

Added: September 25, 2026

Dual role of Poisson impulses in Hindmarsh–Rose networks: Disorder, pattern formation, and synchronization

Ramazanov I., Bukh A., Shepelev Igor A., Chaos 2026 No. 36 P. 083150–083150

We investigate how stochastic Poisson impulsive forcing influences the spatiotemporal dynamics of a two-dimensional network of Hindmarsh–Rose neurons. Unlike continuous noise, impulsive forcing introduces discrete, state-dependent perturbations, making the system response highly sensitive to both the statistics and the spatial structure of the input. In most of the parameter space, stochastic impulses destabilize the initial ...

Added: September 24, 2026

Pairings on the algebra of Laurent series over a ring

Levashev V., / Series arXiv "math". 2026. No. 2609.06010.

We prove that continuous A-bilinear pairings on the ring of Laurent series that are invariant under continuous automorphisms coincide, up to a constant, with the pairing given by the residue of a differential form over any commutative associative ring with identity. ...

Added: September 24, 2026

О схеме Ньютона–Канторовича для эволюционных уравнений

Dymov A. V., Kuksin S., Труды Математического института им. В.А. Стеклова РАН 2024 Т. 327 С. 79–86

Предложена конструктивная форма метода Ньютона–Канторовича для построения решений эволюционных уравнений с малыми нелинейностями, применимая к уравнениям в линейных пространствах, не являющихся банаховыми. Описано лишь основное содержание метода без конкретизации используемых норм и необходимых ε–δ-деталей. ...

Added: May 8, 2026

Chernoff Approximations of the Solution of Linear ODE with Variable Coefficients

Remizov I., Владикавказский математический журнал 2025 Vol. 27 No. 4 P. 124–135

The Chernoff approximation method is a powerful and flexible tool of functional analysis, which allows in many cases to express exp(tL) in terms of variable coefficients of a linear differential operator L. In this paper, we prove a theorem that allows us to apply this method to find the resolvent of L. Our theorem states ...

Added: February 19, 2026

Upper and lower estimates for rate of convergence in the Chernoff product formula for semigroups of operators

Oleg E. Galkin, Ivan D. Remizov, Israel Journal of Mathematics 2025 Vol. 265 P. 929–943

This paper studies the rates of convergence of Chernoff approximations to operator semigroups. We show that the convergence, in general, can be arbitrarily fast or arbitrarily slow. Under natural assumptions, the main result provides an upper estimate for the convergence rates. As an illustration, the result is applied to the study of Chernoff approximations for ...

Added: November 23, 2024

Kipriyanov's Fractional Calculus Prehistory and Legacy

M. V. Kukushkin, Lobachevskii Journal of Mathematics 2023 Vol. 44 No. 8 P. 3411–3429

This paper is partly a historical survey of various approaches and methods in the fractional calculus, partly a description of the Kipriyanov extraordinary theory in comparisonwith the classical one. The significance and outstanding methods in constructing the independent Kipriyanov fractional calculus theory are convexly stressed, also we represent modern results involving the Kipriyanov operator and corresponding generalization under the ...

Added: November 27, 2023