Дробные кинетические уравнения

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

Symmetric Cubic Polynomials

Blokh A., Oversteegen L., Selinger N. et al., Arnold Mathematical Journal 2025 Vol. 12 No. 1 P. 1–40

We describe a model for the boundary of the connectedness locus of the parameter space of cubic symmetric polynomials. We show that there exists a monotone continuous function from the connectedness locus to the model which is a homeomorphism if the former is locally connected. ...

Added: May 13, 2026

Игры на сетях с линейным наилучшим ответом: модели и методы управления

Petrov I., Автоматика и телемеханика 2026 № 6 С. 82–118

Системам связанных агентов и сетевому управлению посвящено большое число отечественных и зарубежных исследований. Исторически, наибольший интерес в теории управления возникал к усредняющим системам и, в частности, к задаче консенсуса. Однако сетевое взаимодействие может характеризоваться более специфическими функциями, отражающими зависимость от действий соседей по сети, что особенно явно проявляется в моделях стратегического взаимодействия на сети, которое ...

Added: May 12, 2026

Архимед: научно-методический сборник

М.: ООО «Макс Пресс», 2026.

В настоящем сборнике представлены тезисы докладов участников семинара "Интеграция основного и дополнительного физико-математического образования", проходившего 11 февраля 2026 года в ГБОУ Школа №2007 ФМШ г. москвы, а также другие публикации, посвящённые вопросам дополнительного физико-математического образования. ...

Added: May 11, 2026

A two-point phase recovering from holographic data on a single plane

Novikov R., Sivkin V., Inverse Problems 2026 Vol. 42 No. 4 Article 045009

We consider a plane wave, a radiation solution, and the sum of these solutions (total solution) for the Helmholtz equation in an exterior region in Rd, d ⩾ 2. In this region, we consider a hyperplane X with sufficiently large distance s from the origin in Rd. We give two-point local formulas for approximate recovering the radiation ...

Added: May 11, 2026

Multivariate Newton interpolation in downward closed spaces reaches the optimal Bernstein–Walsh approximation rate

Hecht M., Hofmann P., Wicaksono D. et al., IMA Journal of Numerical Analysis 2026 Vol. 00 P. 1–30

Recent advances in Bernstein—Walsh theory have extended Bernstein’s Theorem to multiple dimensions, stating that a multivariate function can be approximated with a geometric rate in a downward-closed polynomial space if and only if it is analytic in a generalized Bernstein polyellipse. To compute approximations of this class of functions—which we term Bos–Levenberg–Trefethen–(BLT) functions—we extend the ...

Added: May 11, 2026

Weighted Chernoff Information and Optimal Loss Exponent in Context-Sensitive Hypothesis Testing

Kelbert M., Kalimulina E. Y., Entropy 2026 Vol. 28 Article 536

We study binary hypothesis testing for i.i.d. observations under a multiplicative context weight. For the optimal weighted total loss, defined as the sum of weighted type-I and typeII losses, we prove the logarithmic asymptotic L∗n = exp{−nDwC (P,Q) + o(n)}, n →∞, where Dw C is the weighted Chernoff information. The single-letter form of the exponent relies on ...

Added: May 7, 2026

Calogero–Sutherland hyperbolic system and Heckman–Opdam $$\mathfrak {gl}_n$$ gl n hypergeometric function

Белоусов Н. М., Черепанов Л. К., Деркачов С. Э. et al., Selecta Mathematica, New Series 2026 Vol. 32 Article 44

We prove equivalence of two integral representations for the wave functions of hyperbolic Calogero–Sutherland system. For this we study two families of Baxter operators related to hyperbolic Calogero–Sutherland and rational Ruijsenaars models; the first one as a limit from hyperbolic Ruijsenaars system, while the second one independently. Besides, computing asymptotics of integral representations and also ...

Added: May 6, 2026

Hodge Laplacian Eigenvalues on Surfaces with Boundary

Муравьев М. Ю., Annales Mathematiques du Quebec 2025

Recently Rohleder proposed a new variational approach to an inequality between the Neumann and Dirichlet eigenvalues in the simply connected planar case using the language of classical vector analysis. Interpreting his approach in terms of differential forms permits to generalize these results to a much broader context. The spectrum of the absolute boundary problem for ...

Added: May 6, 2026

Об изоморфизме задачи Козлова о движении ферромагнетика в магнитном поле и задачи Шоттки о движении четырехмерного твердого тела

Цыганов А. В., Порубов Е. О., Теоретическая и математическая физика 2026 Т. 227 № 2 С. 336–355

Теория тензорных инвариантов обыкновенных дифференциальных уравнений и классификация Картана простых алгебр Ли используется для установления изоморфизма задачи Козлова о движении ферромагнетика в магнитном поле и задачи Шоттки о движении четырехмерного твердого тела. Найдены новые полиномиальные и рациональные бивекторы Пуассона, инвариантные либо относительно пары коммутирующих фазовых потоков, либо относительно одного из пары потоков. ...

Added: May 5, 2026

Моделирование и оценка ресурсных затрат алгоритмов маршрутизации в сетях на кристалле с двумерной циркулянтной топологией

Монахова Э. А., Монахов О. Г., Rzaev E. et al., Прикладная дискретная математика 2026 Т. 71 С. 112–127

В настоящей работе исследовано совместное конструирование топологий семейств оптимальных по диаметру циркулянтных сетей $C(N; \pm 1, \pm s_2)$ и реализуемых для них оптимальных алгоритмов маршрутизации сложности $O(1)$. Предлагаемый алгоритм маршрутизации основан на использовании масштабируемых параметров $L$-образных шаблонов плотной укладки графов на плоскости для семейств оптимальных сетей. Определены аналитические формулы зависимости этих параметров от диаметра графов семейств ...

Added: May 4, 2026

On Undecidability Degree of Theory of Figures in Countable and Uncountable Linear Spaces

Dudakov S., Lobachevskii Journal of Mathematics 2025 Vol. 46 No. 12 P. 6092–6102

We study the additive theory of arbitrary ﬁgures in linear spaces, that is, the theory of addition extended to sets of vectors. Our main result is the following: if a linear space is inﬁnite, then the additive theory of ﬁgures admits interpreting second-order arithmetic and, therefore, it has such or higher degree of undecidability. For countably inﬁnite spaces, ...

Added: May 1, 2026

On the minimum number of maximal distance-k independent sets in trees

Taletskii D., / Series arXiv "math". 2026.

A vertex subset of a graph is called a \textit{distance-$k$ independent set} if the distance between any two of its distinct vertices is at least $k + 1$. For all $n,k \geq 1$, we determine the minimum possible number of inclusion-wise maximal distance-$k$ independent sets among all $n$-vertex trees. It equals~$n$ if $n \leq k ...

Added: May 1, 2026

On Arithmetic Mirror Symmetry for smooth Fano fourfolds

Ovcharenko M., / Series arXiv "math". 2026.

We introduce an explicit class of tempered Laurent polynomials in the sense of Villegas and Doran--Kerr in n⩽4 variables including all Landau--Ginzburg models for smooth Fano threefolds with very ample anticanonical class. We check that it contains Landau--Ginzburg models for various Fano fourfolds which are complete intersections in smooth toric varieties and Grassmannians of planes, ...

Added: April 30, 2026

CTRW modeling of quantum measurement and fractional equations of quantum stochastic filtering and control

Vassili Kolokoltsov, Fractional Calculus and Applied Analysis 2022 Vol. 25 No. 1 P. 128–165

Initially developed in the framework of quantum stochastic calculus, the main equations of quantum stochastic filtering were later on derived as the limits of Markov models of discrete measurements under appropriate scaling. In many branches of modern physics it became popular to extend random walk modeling to the continuous time random walk (CTRW) modeling, where ...

Added: October 30, 2022

The probabilistic point of view on the generalized fractional partial differential equations

Kolokoltsov V., Fractional Calculus and Applied Analysis 2019 Vol. 22 No. 3 P. 543–600

This paper aims at unifying and clarifying the recent advances in the analysis of the fractional and generalized fractional Partial Diﬀerential Equations of Caputo and Riemann-Liouville type arising essentially from the probabilistic point of view. This point of view leads to the path integral representation for the solutions of these equations, which is seen to ...

Added: November 14, 2019

Differential Equations on Measures and Functional Spaces

Kolokoltsov V., Switzerland: Birkhauser/Springer, 2019.

This is an advanced text on ordinary differential equations (ODES) in Banach and more general locally convex spaces, most notably the ODEs on measures and various function spaces. It yields the concise exposition of the fundamentals with the fast, but rigorous and systematic transition to the up-fronts of modern research in linear and nonlinear partial ...

Added: November 14, 2019

Small Scale Models for the Spreading of Matter in Disordered Porous Media

Kozyrev O., Logvinova K. V., European Journal of Scientific Research 2010 Vol. 45 No. 1 P. 64–78

In this study we investigate impurity dynamics in media with random characteristics for different physical assumptions. We first discuss possible models for diffusion in porous media on the small scale. Then we describe some random processes, which are able to represent the disorder in such a medium. After that, we recall the definition of a ...

Added: January 14, 2013

Models for the Average of the Solutions to a P.D.E. with Stochastic Coefficients

Logvinova K. V., Kozyrev O., European Journal of Scientific Research 2010 Vol. 45 No. 3 P. 383–390

In this study we investigate the successive approximation procedure allowed us to derive new equation, valid for the transport of dissolved matter in porous media, or in random force fields, on the macroscopic scale. To do this the diagram technique was exploited. ...

Added: January 9, 2013