Zobrazeno 1 - 10
of 11 148
pro vyhledávání: '"Radchenko, A."'
We define a Hopf algebra of polylogarithms of an infinite field, which is a candidate for a conjectural Hopf algebra of framed mixed Tate motives. Our definition is elementary and mimics Goncharov's construction of higher Bloch groups. We also discus
Externí odkaz:
http://arxiv.org/abs/2411.15071
Autor:
Radchenko, Gleb, Fill, Victoria Andrea
Recent advancements in edge computing have significantly enhanced the AI capabilities of Internet of Things (IoT) devices. However, these advancements introduce new challenges in knowledge exchange and resource management, particularly addressing the
Externí odkaz:
http://arxiv.org/abs/2410.08651
Autor:
Radchenko, Danylo, Ramos, João P. G.
This work focuses on two questions raised by H. Hedenmalm and A. Montes-Rodr\'iguez on Heisenberg Uniqueness Pairs for perturbed lattice crosses. The first of them deals with a complete characterization of $\beta>0$ for which, for a fixed $\theta \in
Externí odkaz:
http://arxiv.org/abs/2410.04557
Autor:
Radchenko, Vadym
Random functions $\mu(x)$, generated by values of stochastic measures are considered. The Besov regularity of the continuous paths of $\mu(x)$, $x\in[0,1]^d$ is proved. Fourier series expansion of $\mu(x)$, $x\in[0,2\pi]$ is obtained. These results a
Externí odkaz:
http://arxiv.org/abs/2409.06497
We use cutting-edge mixed integer optimization (MIO) methods to develop a framework for detection and estimation of structural breaks in time series regression models. The framework is constructed based on the least squares problem subject to a penal
Externí odkaz:
http://arxiv.org/abs/2408.05665
We show that any finite family of pairwise intersecting balls in $\mathbb{E}^n$ can be pierced by $(\sqrt{3/2}+o(1))^n$ points improving the previously known estimate of $(2+o(1))^n$. As a corollary, this implies that any $2$-illuminable spiky ball i
Externí odkaz:
http://arxiv.org/abs/2408.01341
Autor:
Radchenko, Vadym
Publikováno v:
Modern Stoch. Theory Appl. 10 (2023), 229-246
We study the class of one-dimensional equations driven by a stochastic measure $\mu$. For $\mu$ we assume only $\sigma$-additivity in probability. This class of equations include the Burgers equation and the heat equation. The existence and uniquenes
Externí odkaz:
http://arxiv.org/abs/2407.15434
Autor:
Radchenko, Vadym
Publikováno v:
Modern Stoch. Theory Appl. 10 (2023), 197-209
We consider the stochastic transport equation where the randomness is given by the symmetric integral with respect to stochastic measure. For stochastic measure, we assume only $\sigma$-additivity in probability and continuity of paths. The existence
Externí odkaz:
http://arxiv.org/abs/2407.15232
We study the function $\varphi_1$ of minimal $L^1$ norm among all functions $f$ of exponential type at most $\pi$ for which $f(0)=1$. This function, first studied by H\"{o}rmander and Bernhardsson in 1993, has only real zeros $\pm \tau_n$, $n=1,2, \l
Externí odkaz:
http://arxiv.org/abs/2407.00970
For every $n\ge 2$, we construct a body $U_n$ of constant width $2$ in $\mathbb{E}^n$ with small volume and symmetries of a regular $n$-simplex. $U_2$ is the Reuleaux triangle. To the best of our knowledge, $U_3$ was not previously constructed, and i
Externí odkaz:
http://arxiv.org/abs/2406.18428