Related papers: Urania Propitia
The Bernoulli numbers are fascinating and ubiquitous numbers, they occur in several domains of Mathematics like Number theory (FLT), Group theory, Calculus and even in Physics. Since Bernoulli's work, they are yet studied to understand…
Dozens of research centers, foundations, international organizations and scientific societies, including the Institute of Mathematical Statistics, have joined forces to celebrate 2013 as a special year for the Mathematics of Planet Earth.…
These are notes for a mini-course of 3 lectures given at the St. Petersburg School in Probability and Statistical Physics (June 2012). My aim was to explain, on the example of a particular model, how ideas from the representation theory of…
Article to appear in the Encyclopedia of Complexity and Systems Science, Dr. R. A. Meyers (Ed.) (Springer Heidelberg, 2009).
The results of Iv. Prodanov on abstract spectra and separative algebras were announced in the journal "Trudy Mat. Inst. Steklova", 154, 1983, 200--208, but their proofs were never written by him in the form of a manuscript, preprint or…
The Unified Astronomy Thesaurus (UAT) is an open, interoperable and community-supported thesaurus which unifies the existing divergent and isolated Astronomy & Astrophysics vocabularies into a single high-quality, freely-available open…
This text is the English translation, due to Naoufal Bouchareb, of an unpublished manuscript of 1969 (the French version is available on HAL as hal-00384928) inspired by Zariski's theory of saturation. Its publication is justified by the…
Rejoinder to "Brownian distance covariance" by G\'abor J. Sz\'ekely and Maria L. Rizzo [arXiv:1010.0297]
This paper has been withdrawn by the author.
I present some reminiscences, both personal and scientific, over a lifetime of admiration of, and friendship with, one of the Grandmasters of our subject.
This is an exposition of recent developments in the theory of bounded differences between primes. Readers are expected to be beginners of analytic number theory. The present text is a substantially improved and augmented version of the one…
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 online book contains the proceedings of a meeting held at Michigan State University to celebrate the career and contributions of Horace A Smith. The meeting focused on the areas of astronomy which Horace worked on over the years and…
This is a personal and historical essay based on the Shaw Prize Lecture given in Hong Kong in September 2017 in association with the 2017 Shaw Prize in Astronomy.
These notes contain part of the lectures of an introductory course on orthogonal polynomials and special functions that I gave in the joint PhD Program in Mathematics UC|UP in the academic years 2015-2016 (at University of Porto) and…
This paper has been withdrawn because the content has been substantially improved in a later paper, arXiv:0806.1165.
This book is a valuable introduction to astrophyscial plasmas and fluids for graduate students of astronomy preparing either for a research career in the field or just aspiring to achieve a decent degree of familiarity with 99% of the…
This short note describes the history of cosmic ray research. A part of this document was presented orally at the international conference of CRIS 2010 held in Catania, Italy. The document is written being based on the English translation…
The present preprint completes the arXiv preprint #2202.11652, entitled "Pseudodifferential arithmetic and the Riemann hypothesis", devoted to a proof of the conjecture. The first 4 pages of that preprint were devoted to a set of necessary…
I review progress that has been made in nuclear astrophysics over the past few years and summarize some of the questions that remain. Topics selected include solar neutrinos, supernovae (the explosion and associated nucleosynthesis),…