相关论文: Georg Cantor and his heritage
A sketch of some of the fundamental notions related to the nature of knowledge is offered, with special focus on the role of mathematics and my own opinions. No single idea exposed here is entirely original; indeed, this topic has been…
We discuss counting problems linked to finite versions of Cantor's diagonal of infinite tableaux. We extend previous results of [2] by refining an equivalence relation that reduces significantly the exhaustive generation. New enumerative…
The article is devoted to one infinite parametric class of continuous functions with complicated local structure. In the article differential, integral, self-affine and other properties of functions, that their argument is represented by…
One of the variants for systematizing the activities of the historian of mathematics is proposed, as well as a scheme for organizing research and search work in the preparation of scientific articles and reports on the history of science.
In his Foundations of a General Theory of Manifolds, Georg Cantor praised Bernard Bolzano as a clear defender of actual infinity who had the courage to work with infinite numbers. At the same time, he sharply criticized the way Bolzano…
In 1996 Y. Kifer obtained a variational formula for the Hausdorff dimension of the set of points for which the frequencies of the digits in the Cantor series expansion is given. In this note we present a slightly different approach to this…
This text is a slightly expanded version of a survey article on certain aspects of low dimensional dynamics and number theory written after a kind invitation by the editors of the Notices of the American Mathematical Society.
This article is an expanded version of my talk at the Gathering for Gardner, 2012.
Some reflections on the role in the development of Mathematics of our unconscious perception of the world and just as unconscious organizing pulsions for those perceptions.
The article is devoted to modeling of the nega-$\tilde Q$-representation of real numbers. The representation is a generalization of representation by alternating Cantor series and positive $\tilde Q$-representation is a generalization of…
A generalization of the H\"older inequality is considered. Its relations with a previously obtained improvement of the Cauchy--Schwarz inequality are discussed.
``In this paper we give the history of Leonhard Euler's work on the pentagonal number theorem, and his applications of the pentagonal number theorem to the divisor function, partition function and divergent series. We have attempted to give…
This article present a method of mutual transformation between count model and composition model. Offer the mathematical view of classical radio and log-radio in compositional data analysis and expand the idea of mixture model of counts…
Universal representation of geometric patterns of disordered matters is investigated with the aid of general topology. By utilizing the result obtained in the previous study (S. Ohmori, et.al., Phys. Scr. 94, 105213 (2019)) that any…
In this paper I shall try to sketch some typical aspects of Erich Lehmann's contributions to statistics through his research, his teaching, his service to the profession and his personality.
This is a short historical note concerning the evolution of Wetzel's problem and Erdos' solution.
The primary aim of this chapter is, commemorating the 150th anniversary of Riemann's death, to explain how the idea of {\it Riemann sum} is linked to other branches of mathematics. The materials I treat are more or less classical and…
The sharing and citation of research data is becoming increasingly recognized as an essential building block in scientific research across various fields and disciplines. Sharing research data allows other researchers to reproduce results,…
Many people are familiar with the physico-chemical properties of gene sequences. In this paper I present a mathematical perspective: how do mathematical principles such as information theory, coding theory, and combinatorics influence the…
In 1891 Cantor presented two proofs with the purpose to establish a general theorem that any set can be replaced by a set of greater power. Cantor's power set theorem can be considered to be an extension of Cantor's 1891 second proof and…