相关论文: You Can Enter Cantor's Paradise
We collect here various conjectures on congruences made by the author in a series of papers, some of which involve binary quadratic forms and other advanced theories. Part A consists of 100 unsolved conjectures of the author while…
Talk presented at the conference ``Historical and Philosophical Reflections on the Foundations of Quantum Field Theory,'' at Boston University, March 1996. It will be published in the proceedings of this conference.
Talk given at the conference "Visions in Mathematics toward the year 2000", August 1999, Tel-Aviv.
Ce texte est une d\'emontration compl\`ete de la conjecture de Catalan \'elabor\' ee \`a la suite d'un s\'eminaire fait \`a Lausanne entre 2002 et 2004, juste apr\`es l'annonce de la merveilleuse preuve de Preda Mihailescu
We establish various new results on a problem proposed by K. Mahler in 1984 concerning rational approximation to fractal sets by rational numbers inside and outside the set in question, respectively. Some of them provide a natural…
We present a point of view on results of the paper of Geronimo and Johnson [Comm. Math, Phys. 193 (1998)] that allow infinitely dimensional generalization up to the case when spectrum is supported on a Cantor set of positive Lebesgue…
In this paper, we present the Cantor Intersection Theorem and a formulation of Baire Theorem in complete PM spaces. In addition, the Heine-Borel property for PM spaces is considered in detail.
This review is the updated and enlarged version of a talk delivered by J. S. on the occasion of the 1982 meeting of Nobel laureates at Lindau, and of talks given by B.-G. E. at several West German universities and Max Planck institutes in…
This is an extended version of my 2018 Heinemann prize lecture describing the work for which I got the prize. The citation is very broad so this describes virtually all my work prior to 1995 and some afterwards. It discusses work in…
This is an expanded version of my talk given at the International Conference ``Algebra and Number Theory'' dedicated to the 80th anniversary of V. E. Voskresenskii, which was held at the Samara State University in May 2007. The goal is to…
Some research institutions demand researchers to distribute the incomes they earn from publishing papers to their researchers and/or co-authors. In this study, we deal with the Impact Factor-based ranking journal as a criteria for the…
A 1910 theorem of Brouwer characterizes the Cantor set as the unique totally disconnected, compact metric space without isolated points. A 1920 theorem of Sierpinski characterizes the rationals as the unique countable metric space without…
The existence of two different Cantor sets, one of them contained in the set of Liouville numbers and the other one inside the set of Diophantine numbers, is proved. Finally, a necessary and sufficient condition for the existence of a…
This contribution contains the introductory historical remarks that I presented at IAU Symposium 270 on "Computational Star Formation" held in Barcelona, Spain, May 31 - June 4, 2010. I give a personal view of some of the early histoy of…
Sir Michael Atiyah was considered as one of the world's foremost mathematicians, He is best known for his work in algebraic topology and the co-development of a branch of mathematics called topological K-theory together with the…
This is a work in two parts devoted to solutions of the so-called {\em four Landau's problems} in Number Theory, listed by Edmund Landau at the 1912 International Congress of Mathematics. In Part I the {\em Goldbach's conjecture} is proved.…
The integration-by-parts formula discovered by Malliavin for the Ito map on Wiener space is proved using the two-parameter stochastic calculus. It is also shown that the solution of a one-parameter stochastic differential equation driven by…
We show that for any pair of self-similar Cantor sets with sum of Hausdorff dimensions greater than 1, one can create an interval in the sumset by applying arbitrary small perturbations (without leaving the class of self-similar Cantor…
This paper presents a detailed, self-contained proof of a BBP-type formula for $\pi^2$ expressed in the golden ratio base, $\phi$. The formula was discovered empirically by the author in 2004. The proof presented herein is built upon a…
This manuscript presents shortly the results obtained by participants of the scientific seminar which is held more than twenty years under leadership of the author at Donetsk University. In the list of references main publications are…