Related papers: Kolmogorov and Aleksandrov in Sevan Monastery, Arm…
This is a contemporary review of the involvement of Mileva Maric, Albert Einsteins first wife, in his theoretical work between the period of 1900 to 1905. Separate biographies are outlined for both Mileva and Einstein, prior to their…
These are the notes of a course for the summer school Model Theory in Bilbao hosted by the Basque Center for Applied Mathematics (BCAM) and the Universidad del Pa\'is Vasco/Euskal Herriko Unibertsitatea in September 2023. The goal of this…
A research project aimed at the development of an automated theorem proving system was started in Kiev (Ukraine) in early 1960s. The mastermind of the project, Academician V.Glushkov, baptized it "Evidence Algorithm", EA. The work on the…
Let $f : X\to X$ be a dominating meromorphic map on a compact K\"ahler manifold $X$ of dimension $k$. We extend the notion of topological entropy $h^l_{\mathrm{top}}(f)$ for the action of $f$ on (local) analytic sets of dimension $0\leq l…
This paper describes the structure of solutions to Kolmogorov's equations for nonhomogeneous jump Markov processes and applications of these results to control of jump stochastic systems. These equations were studied by Feller (1940), who…
This is the fourth in a series of articles devoted to showing that a typical covering map of large degree to a fixed, regular graph has its new adjacency eigenvalues within the bound conjectured by Alon for random regular graphs. In this…
I was lucky to meet (and even cooperate at some extent) with Israel M. Gelfand, and tried to write down (mainly in 2003-2013) my recollections about his work style and lessons I learned from him about teaching and writing mathematics…
Kolmogorov-Arnold Networks (KANs) have been recently proposed as a machine learning framework that is more interpretable and controllable than the multi-layer perceptron. Various network architectures have been proposed within the KAN…
Kolmogorov's Calculus of Problems is an interpretation of Heyting's intuitionistic propositional calculus published by A.N. Kolmogorov in 1932. Unlike Heyting's intended interpretation of this calculus, Kolmogorov's interpretation does not…
This is an English translation of six articles, originally written in Ukrainian, by the semigroup theorist Anton Kazimirovich Sushkevich (1889-1961). The articles date between 1935 and 1939, and were all written in Kharkiv. A preface is…
The article presents the results of a study of petroglyphs on a unique stone slab discovered near the kurgan 1 of the kurgan field Varvarinsky I (Rostov Oblast, Russia). During the study was done comparing it with plates of Srubna burials…
Kolmogorov complexity and algorithmic probability are defined only up to an additive resp. multiplicative constant, since their actual values depend on the choice of the universal reference computer. In this paper, we analyze a natural…
This preprint appeared firstly in Russian in 1997. Some truncated versions of this preprint were published in English and French, here a fully translated version is presented. The translation in English was done by O. V. Feodoritova and V.…
These notes are part of the research seminar with title "Theory of Bergman spaces and related function spaces" that took place in the University of Crete, Department of Mathematics (September 2006- December 2007), in the framework of the…
This manuscript is an extended version of the author's habilitation thesis defended on May 21, 2021 at M.V. Lomonosov Moscow State University. It is devoted to the study of (co)stability of radicals, existence of (co)invariant Levi and…
A number of recent works have sought to generalize the Kolmogorov-Sinai entropy of probability-preserving transformations to the setting of Markov operators acting on the integrable functions on a probability space $(X,\mu)$. These have…
The paper presents a course on Combinatorial Algorithms that is based on the drafts of the author that he used while teaching the course in the Department of Informatics and Applied Mathematics of Yerevan State University, Armenia from…
A report at Arbeitstagung, June 1999, Bonn, on the joint work with V.Gorbounov, F.Malikov and A.Vaintrob.
These are lectures notes for a 4h30 mini-course held in Ulaanbaatar, National University of Mongolia, August 5-7th 2015, at the summer school "Stochastic Processes and Applications". It aims at presenting an introduction to basic results of…
Kolmogorov-Sinai entropy is an invariant of measure-preserving actions of the group of integers that is central to classification theory. There are two recently developed invariants, sofic entropy and Rokhlin entropy, that generalize…