Related papers: Sobolev of the Euler School
The prominent Russian mathematician Igor Rostislavovich Shafarevich passed away on February 19, 2017. In this article we supply his biography, discuss his many important contributions to number theory, algebra and algebraic geometry, and…
In this small note I try to summarize some observations about Euclid's remarkable role in mathematics and about the ambient philosophy.
The theory of equidistribution is about hundred years old, and has been developed primarily by number theorists and theoretical computer scientists. A motivated uninitiated peer could encounter difficulties perusing the literature, due to…
Based on a new theory of causality [1] and its development to the theory of the Universe [2], we show, in this paper, new ideas for building a theory of everything.
Apart from an account of classical preliminaries, this volume contains a systematic introduction to Sobolev spaces and functions of bounded variation with selected applications. This is installment III of a four part discussion of certain…
In 1737 Leonard Euler gave what we often now think of as a new proof, based on infinite series, of Euclid's theorem that there are infinitely many prime numbers. Our short paper uses a simple modification of Euler's argument to obtain new…
A simple proof of Euler's formula which states that the sum of the reciprocals of all natural numbers squared equals $\pi^2/6$ is presented based on the distribution theory introduced by Laurent Schwartz. Additional identities are obtained…
In this brief note, there is a short recollection of my scientific interactions with the great Russian mathematician Sergey Konstantinovich Godunov.
The goal of this modern presentation, followed by an English translation from the German, is to make available some parts of Lie's very systematic mathematical thought which deserve to join the contemporary literature, and above all also,…
The review presents rigorous results of the theory of fundamental equations of evolution of many-particle systems with collisions and also considers their connection with nonlinear kinetic equations describing the collective behavior of…
This is a short tribute to Alexandr Alexandrov (1912--1999).
Joseph-Nicolas Delisle was one of the most important scientists at the Saint Petersburg Academy of Sciences during the first period when Euler was working there. Euler was helping him in his work on astronomy and in geography. In this…
This is an overview of the life and works of Pavel Florensky, an important and singular figure of the period rightly described as the \emph{Silver Age of Russian mathematics}, with a substantial overlap with the \emph{Silver Age of Russian…
The aim of this paper is to study the historical evolution of mathematical thinking and its spatial spreading. To do so, we have collected and integrated data from different online academic datasets. In its final stage, the database…
The classical Multiplicative Ergodic Theorem (MET) of Oseledets is generalized here to cocycles taking values in a semi-finite von Neumann algebra. This allows for a continuous Lyapunov distribution.
Selected examples of possible origins of power-law distributions are presented.
Professor Sir Karl Popper (1902-1994) was one of the most influential philosophers of science of the twentieth century. However, in his most famous work he displays misunderstandings of science and mathematics at a basic level.
This paper is devoted to Poincar\'e's work in probability. Though the subject does not represent a large part of the mathematician's achievements, it provides significant insight into the evolution of Poincar\'e's thought on several…
A theory of Sobolev inequalities in arbitrary open sets of Euclidean space is established. Boundary regularity of domains is replaced with information on boundary traces of trial functions and of their derivatives up to some explicit…
A Thesis about Euler discussing the possibilities and limits of his method of work in Mathematics.