Related papers: Sobolev of the Euler School
The article describes the biography and manifold contributions to research in mathematics of Mikhail Aleksandrovich Shubin.
Yurii Fedorovich Smirnov (1935-2008) was a famous theoretical physicist. He achieved his career mainly at the Institute of Nuclear Physics of Moscow. These notes describe some particular facets of the contributions of the late Professor…
The nineteenth century Russian author Leo Tolstoy based his egalitarian views on sociology and history on mathematical and probabilistic views, and he also proposed a mathematical theory of waging war.
These personal reminiscences of the great Russian mathematician Sergey K. Godunov (1929-2023) arose from a request by his daughter, Ekaterina, to contribute a piece to a book she is writing about her father's life. I was honoured to accept…
This short review is dedicated to academician Yakov Borisovich Zeldovich, the science of his epoch and the creation of modern accretion theory.
The essay is devoted to the personality of the prominent theorist D.V. Volkov and his pioneer works in quantum field theory and elementary particle physics.
The year 2017 marked the 130th anniversary of the prominent Russian mathematician Vladimir Ivanovich Smirnov. We review some aspects of his life and his mathematical accomplishments.
This paper presents three new families of fractional Sobolev spaces and their accompanying theory in one-dimension. The new construction and theory are based on a newly developed notion of weak fractional derivatives, which are natural…
In this note, we investigate the history of algebra briefly. We particularly focus on the history of rings, semirings, and the distributive law.
We expose some simple facts at the interplay between mathematics and the real world, putting in evidence mathematical objects " nonlinear generalized functions" that are needed to model the real world, which appear to have been generally…
Detlef D\"urr (1951-2021) was a theoretical and mathematical physicist who worked particularly on the foundations of quantum mechanics, electromagnetism, and statistical mechanics. This piece is a rather personal look back at him and his…
Distribution theory is a cornerstone of the theory of partial differential equations. We report on the progress of formalizing the theory of tempered distributions in the interactive proof assistant Lean, which is the first formalization in…
The two of us have shared a fascination with James Victor Uspensky's 1937 textbook $Introduction \, to \, Mathematical \, Probability$ ever since our graduate student days: it contains many interesting results not found in other books on…
The spectral theorem of the linear 2D Euler operator in Sobolev spaces is presented as a corollary of the spectral theorem in $\ell_2$ space in [Li,00]. Study on the (dashed) line model introduced in [Li,01] is continued. Specifically,…
This presentation goes beyond celebratory narration of the life and scientific achievements of Russia's first modern scientist Mikhail Vasilievich Lomonosov (1711-1765). Coming from the notion of complexity of sciences, we introduce "a…
The idea of convexity feeds generation, separation, calculus, and approximation. Generation appears as duality; separation, as optimality; calculus, as representation; and approximation, as stability. This is an overview of the origin,…
Andrei Kolmogorov's Grundbegriffe der Wahrscheinlichkeits-rechnung put probability's modern mathematical formalism in place. It also provided a philosophy of probability--an explanation of how the formalism can be connected to the world of…
In this note we present a new proof of Sobolev's inequality under a uniform lower bound of the Ricci curvature. This result was initially obtained in 1983 by Ilias. Our goal is to present a very short proof, to give a review of the famous…
Mikhail Lomonosov (1711-1765) was a Russian polymath and one of the giants of the European Enlightenment. This English translation of his seminal work Oration on Benefits of Chemistry continues the series of translations of nine most…
This is the editor's preface to the special issue of Journal of Spectral Theory, in memory of Yuri Safarov.