相关论文: Georg Cantor and his heritage
The present article is devoted to some examples of functions whose arguments represented in terms of certain series of the Cantor type.
A class of Cantor-type spaces and related geometric structures are discussed.
In this brief note, there is a short recollection of my scientific interactions with the great Russian mathematician Sergey Konstantinovich Godunov.
Reflections on the Concept of Data and its Implications for Science and Society
Schmidt games and the Cantor winning property give alternative notions of largeness, similar to the more standard notions of measure and category. Being intuitive, flexible, and applicable to recent research made them an active object of…
These are some brief notes on the translation from Razborov's recently-developed notion of flag algebra into the lexicon of functions and measures on certain abstract Cantor spaces (totally disconnected compact metric spaces).
This is a short overview of the influence of mathematicians and their ideas on the creative contribution of Mikhailo Lomonosov on the occasion of the tercentenary of his birth.
Let $\mathcal{C}\subseteq[0,1]$ be a Cantor set. In the classical $\mathcal{C}\pm\mathcal{C}$ problems, modifying the ``size'' of $\mathcal{C}$ has a magnified effect on $\mathcal{C}\pm\mathcal{C}$. However, any gain in $\mathcal{C}$…
This article, dedicated, with admiration to Reuben Hersh, for his forthcoming 90th birthday, argues that mathematics today is not yet a science, but that it is high time that it should become one.
Following in the footsteps of P. Erd\H{o}s and A. R\'enyi we compute the Hausdorff dimension of sets of numbers whose digits with respect to their $Q$-Cantor series expansions satisfy various statistical properties. In particular, we…
Since the theory developed by Georg Cantor, mathematicians have taken a sharp interest in the sizes of infinite sets. We know that the set of integers is infinitely countable and that its cardinality is Aleph0. Cantor proved in 1891 with…
A recursion relation of hyperelliptic psi functions of genus two, which was derived by D.G. Cantor (J. reine angew. Math. 447 (1994) 91-145), is studied. As Cantor's approach is algebraic, another derivation is presented as a natural…
In this article, we explore the notion of infinity by studying Cantor's contribution to this field. A brief history of set theory is given. As an example of infinity, we consider Hilbert's famous hotel. A graphical construction is used to…
Talk given at ICM '98, Berlin, reviewing some of the recent developments in understanding of string theory for a mathematical audience (to appear in Documenta Mathematica).
Remarks at the Irving Kaplansky Memorial about a collaboration during the early period of the renewal of contacts between mathematicians and theoretical physicists.
These notes, associated with a topics course, are largely concerned with Hausdorff measures and a class of metric spaces which behave like Cantor sets.
The present report, has been inspired by the need of the author and its colleagues to understand the underlying theory of Wirtinger's Calculus and to further extend it to include the kernel case. The aim of the present manuscript is…
Notes from lectures given at the Autumn School on Algebraic and Arithmetic Geometry at the Johannes Gutenberg-Universit\"at Mainz in October 2017.
A Thesis about Euler discussing the possibilities and limits of his method of work in Mathematics.
Life and the mathematical legacy of the great mathematician A.V. Pogorelov.