Related papers: Urania Propitia
We consider the little-known anthropic argument of Fontenelle dealing with the nature of cometary orbits, given a year before the publication of Newton's Principia. This is particularly interesting in view of the rapid development of the…
Laudation delivered at the International Congress of Mathematicians in Berlin following the award of the Fields Medal to Richard Borcherds.
A revised version of Hydra, an adaptive particle-particle, particle-mesh plus smoothed particle hydrodynamics code developed by; Hugh Couchman, University of Western Ontario, Frazer Pearce, University of Durham, Peter Thomas, University of…
This is a collection of variants of Schanuel's conjecture and the known dependencies between them. It was originally written in 2007, and made available for a time on my webpage. I have been asked by a few people to make it available again…
This is the written version of a talk given in memory of Gunnar K\"{a}ll\'{e}n, at the Departments of Theoretical Physics, Physics, and Astronomy of Lund University on February 13, 2009. It will be published in a collection of the papers of…
We highlight recent theoretical and observational progress in several areas of neutron star astrophysics, and discuss the prospect for advances in the next decade.
We are on the way to obtaining multi-dimensional "pictures" of the proton. The field is bursting with activities, both from the theoretical and experimental side. A brief selection of important achievements of the last years and open…
A review of Peter Byrne's biography of Hugh Everett III, "The Many Worlds of Hugh Everett III: Multiple Universes, Mutual Assured Destruction, and the Meltdown of a Nuclear Family", (Oxford University Press, 2010).
Quasirational (pro-$p$)presentations are studied. The difference between aspherical and quasirational presentations sheds some light on the Whitehead's conjecture. We confirm expectations O.V. Melnikov on existence of a proper class of…
A short essay on the life and mathematical heritage of Coble. A substantially edited version will be part of the series of biographical memoirs of past members of the National Academy of Sciences. Version 2: minor changes. Version 3. Typo…
Evolutionary role of the separation into two sexes from a cyberneticist's point of view. [I translated this 1965 article from Russian "Nauka i Zhizn" (Science and Life) in 1988. In a popular form, the article puts forward several useful…
A Comment on the Letter by B. Kraus {\it Phys. Rev. Lett.}{\bf 104}, 020504 (2010).
This book is mainly an exposition of the author's works and his joint works with his former students on explicit representations of finite-dimensional simple Lie algebras, related partial differential equations, linear orthogonal algebraic…
Talk given at Orbis Scientiae Conference, Coral Gables, FLA, Dec. 16-19, 1999. Talk surveys some recent three-neutrino models of neutrino masses and mixings.
In this paper, we continue to study properties of rational approximations to Euler's constant and values of the Gamma function defined by linear recurrences, which were found recently by A. I. Aptekarev and T. Rivoal. Using multiple…
This is a translation of the diploma thesis of Thomas Br\"ustle, Darstellungsk\"ocher der erblichen Algebren vom Typ $\tilde{A}_n$, written in German, at the University of Zurich, August 1990. Supervisor: P. Gabriel. Translated by K. Baur,…
This is a revised version of the preprint which has been available electronically for a while. The paper will now appear in J. Ramanujan Math. Soc.
These are notes on discrete mathematics for computer scientists. The presentation is somewhat unconventional. Indeed I begin with a discussion of the basic rules of mathematical reasoning and of the notion of proof formalized in a natural…
This paper has been withdrawn by the author due to an error in the main proof (thanks to Carlos D'Andrea)
Two papers recently published in Celestial Mechanics (Krasinsky 2006, and Krasinsky and Vasilyev 2006) have presented a model for Earth-rotation variations, called ERA-2005, based on numerical integration of a new set of equations for the…