Related papers: The Delone Peak
I share fond memories of my former PhD advisor Alexei Starobinsky with whom I was closely associated for nearly 45 years. I reflect upon my early years in Moscow when I worked with him on my thesis, and touch upon the seminal work on…
The recollection of souvenirs on great theoretical physicist, addressed to wide physical audience on the occasion of Bogoliubov centenary. Contains four parts: 1. Personal impressions; 2. Joint work; 3. Bogoliubov cp. Landau and 4.…
For a long time it was known that deuteron, as a weakly coupled nucleon pair, has no excited states. However, A.M. Baldin et al, commenting results of the first physical experiment with accelerated nuclei at JINR synchrophasotron, assumed…
A permutation $\sigma=\sigma_1 \sigma_2 \cdots \sigma_n$ has a descent at $i$ if $\sigma_i>\sigma_{i+1}$. A descent $i$ is called a peak if $i>1$ and $i-1$ is not a descent. The size of the set of all permutations of $n$ with a given…
PhD Thesis under the supervision of Professor Nedyalko Nenov.
Several works in the last few years devoted to measure fundamental probes of contemporary cosmology have suggested the existence of a delocalized dominant component (the "dark energy"), in addition to the several-decade-old evidence for…
We consider diffraction of Delone sets in Euclidean space. We show that the set of Bragg peaks with high intensity is always Meyer (if it is relatively dense). We use this to provide a new characterization for Meyer sets in terms of…
This paper introduces nucleus clustering in Voronoi tessellations of plane surfaces with applications in the geometry of digital images. A \emph{nucleus cluster} is a collection of Voronoi regions that are adjacent to a Voronoi region…
The height of a rational number $p/q$ is denoted by $h(p/q)$ and equals $\text{max}(|p|,|q|)$ provided p/q is written in lowest terms. The height of a rational tuple $(x_1,...,x_n)$ is denoted by $h(x_1,...,x_n)$ and equals…
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…
This article is an attempt to review 50 years of high-energy cosmic particle physics at the Institute for Nuclear Research of the Russian Academy of Sciences. It is written by an outsider whose scientific career, to a large part, was formed…
Linearly repetitive Delone sets are shown to be rectifiable by a bi-Lipschitz homeomorphisms of the Euclidean space that sends the Delone set to the set of points with integer coordinates.
This text is written in remembrance of Vladimir (Volodia) Sidorenko, honoring his scientific work, his kindness, and the warm and humorous spirit he brought into the community.
Antarctica provides a unique environment for astronomy. The cold, dry and stable air found above the high plateau, as well as the pure ice below, offers new opportunities across the photon & particle spectrum. The summits of the plateau…
The 150th anniversary of the birth of the outstanding Russian mathematician Vladimir Andreevich Steklov falls on January 9, 2014. In this paper (it is a part of survey to be published in January 2014), we describe advances in one of several…
A Delaunay decomposition is a cell decomposition in R^d for which each cell is inscribed in a Euclidean ball which is empty of all other vertices. This article introduces a generalization of the Delaunay decomposition in which the Euclidean…
In the paper, we prove that in an arbitrary Delone set $X$ in $3D$ space, the subset $X_6$ of all points from $X$ at which local groups have axes of the order not greater than 6 is also a Delone set. Here, under the local group at point…
Higher-order Voronoi diagrams and Delaunay mosaics in polygonal metrics have only recently been studied, yet no tools exist for visualizing them. We introduce a tool that fills this gap, providing dynamic interactive software for…
With a view to establishing measure theoretic approximation properties of Delone sets, we study a setup which arises naturally in the problem of averaging almost periodic functions along exponential sequences. In this setting, we establish…
The article is devoted to the issue of the polar form of octonions. This is a~continuation of the works initiated by Hahn and Snopek in their articles from 2011. The results presented in the article show errors made in previous…