Related papers: The Delone Peak
This note is written for a book dedicated to outstanding St-Petersburg mathematicians and timed to the ICM-2022 in St-Petersburg. In accordance with the plan of ICM-organizers, we try to tell about one of the most prominent Rokhlin's…
The $\alpha$ person is the dominant person in a group. We define the $\alpha$-author of a paper as the author of the paper with the highest $h$-index among all the coauthors, and an $\alpha$-paper of a scientist as a paper authored or…
We describe a randomized algorithm that, given a set $P$ of points in the plane, computes the best location to insert a new point $p$, such that the Delaunay triangulation of $P\cup\{p\}$ has the largest possible minimum angle. The expected…
The longer-lived excited nuclear states, referred as nuclear isomers, exist due to the hindered decays owing to their peculiar nucleonic structural surroundings. Some of these conditions, being exceptionally rare and limited to achieve,…
Because the decathlon tests many facets of athleticism, including sprinting, throwing, jumping, and endurance, many consider it to be the ultimate test of athletic ability. On this view, estimating the maximal decathlon score and…
We introduce Deligne cohomology that classifies U(1) fibre bundles over 3-manifolds endowed with connections. We show how the structure of Deligne cohomology classes provides a way to perform exact (non-perturbative) computations in U(1)…
We consider the practical computation of rational points on y^2=x(x^2+ax+b). The algebra necessary for a 4-descent procedure is described. A simple further descent is then described which only uses integer arithmetic. Numerous examples are…
Ya.B. Zeldovich was a pre-eminent Soviet physicist whose seminal contributions spanned many fields ranging from physical chemistry to nuclear and particle physics, and finally astrophysics and cosmology. March 8, 2014 marks Zeldovich's…
Recently, a full-scale data processing workflow of the Square Kilometre Array (SKA) Phase 1 was successfully executed on the world's fastest supercomputer Summit, proving that scientists have the expertise, software tools and computing…
This is a letter to the editor concerning Semjon Adlaj's article "An eloquent formula for the perimeter of an ellipse", AMS Notices 59, 8 (2012), 1094-1099.
This paper aims to give a brief account of the mathematical work of the 7th-century Armenian polymath and natural philosopher Anania Shirakatsi. The three sections of Anania's ``Book of Arithmetic'' -- tables of arithmetic operations, a…
In this thesis we consider a discretization of the Euler top given by Hirota und Kimura. Using the geometric description of the conserved quantities as quadrics in real 3-space, we find that there exist maps on rulings of quadrics in the…
Mikhail Lomonosov (1711-1765) is the eminent Russian polymath and a towering figure of the European Enlightenment. This English translation of his seminal work Discourse on Greater Accuracy of Navigation concludes the series of English…
The most studied and accepted pseudometric for probabilistic processes is one based on the Kantorovich distance between distributions. It comes with many theoretical and motivating results, in particular it is the fixpoint of a given…
In spite of the Lebesgue density theorem, there is a positive $\delta$ such that, for every non-trivial measurable set $S$ of real numbers, there is a point at which both the lower densities of $S$ and of the complement of $S$ are at least…
One of the most important discoveries in modern cosmology is cosmic acceleration. However, we find that today's universe could decelerate in the statistically preferred Chevallier-Polarski-Linder (CPL) scenario over the $\Lambda$CDM model…
The {\em hypermetric cone} is defined as the cone of semimetrics satisfying the {\em hypermetric inequalities}. Every {\em Delaunay polytope} corresponds to a ray of this polyhedral cone. The Delaunay polytopes, which correspond to extreme…
All inequivalent realizations of the Galilei algebras of dimensions not greater than five are constructed using the algebraic approach proposed by I. Shirokov. The varieties of the deformed Galilei algebras are discussed and families of…
A counter example of inheritance of convexity of domain of positive solution of Dirichlet boundary value problem and the hot spot problem that proposed by J. Rauch is given. The difficulty of these two problems is that the critical points…
In a recent interesting Letter [Phys. Rev. Lett. 108, 140401 (2012)] I. Bialynicki-Birula and his coauthor have derived the uncertainty relation for the photons in three dimensions. However, some of their arguments are problematical, and…