Zobrazeno 1 - 10
of 421
pro vyhledávání: '"KURASOV, P."'
In this paper, we construct Fourier quasicrystals with unit masses in arbitrary dimensions. This generalizes a one-dimensional construction of Kurasov and Sarnak. To do this, we employ a class of complex algebraic varieties avoiding certain regions i
Externí odkaz:
http://arxiv.org/abs/2407.11184
Autor:
Pistol, Mats-Erik, Kurasov, Pavel
Quantum graphs have attracted attention from mathematicians for some time. A quantum graph is defined by having a Laplacian on each edge of a metric graph and imposing boundary conditions at the vertices to get an eigenvalue problem. A problem studyi
Externí odkaz:
http://arxiv.org/abs/2207.11998
We derive several upper bounds on the spectral gap of the Laplacian with standard or Dirichlet vertex conditions on compact metric graphs. In particular, we obtain estimates based on the length of a shortest cycle (girth), diameter, total length of t
Externí odkaz:
http://arxiv.org/abs/2206.10046
Autor:
Kurasov, Pavel
It is proven following [18[ that Laplacians with standard vertex continuous on metric trees and with standard and Dirichlet conditions on arbitrary metric graphs possess an infinite sequence of simple eigenvalues with the eigenfunctions not equal to
Externí odkaz:
http://arxiv.org/abs/2112.04233
Autor:
Kurasov, Pavel, Muller, Jacob
A new class of isospectral graphs is presented. These graphs are isospectral with respect to both the normalised Laplacian on the discrete graph and the standard differential Laplacian on the corresponding metric graph. The new class of graphs is obt
Externí odkaz:
http://arxiv.org/abs/2112.04230
Autor:
Ławniczak, Michał, Kurasov, Pavel, Bauch, Szymon, Białous, Małgorzata, Yunko, Vitalii, Sirko, Leszek
Publikováno v:
Physical Review E 101, 052320 (2020)
The Euler characteristic $\chi =|V|-|E|$ and the total length $\mathcal{L}$ are the most important topological and geometrical characteristics of a metric graph. Here, $|V|$ and $|E|$ denote the number of vertices and edges of a graph. The Euler char
Externí odkaz:
http://arxiv.org/abs/2007.10654
We introduce an abstract framework for the study of clustering in metric graphs: after suitably metrising the space of graph partitions, we restrict Laplacians to the clusters thus arising and use their spectral gaps to define several notions of part
Externí odkaz:
http://arxiv.org/abs/2005.01126
Autor:
Kurasov, Pavel, Sarnak, Peter
Explicit examples of {\bf positive} crystalline measures and Fourier quasicrystals are constructed using pairs of stable of polynomials, answering several open questions in the area.
Comment: 15 pages, 1 figure
Comment: 15 pages, 1 figure
Externí odkaz:
http://arxiv.org/abs/2004.05678
Autor:
Nikolay I. Lomakin, Lyudmila Ya. Solomakhina, Victoria V. Pokidova, Irina A. Ulanova, Alexander N. Kurasov, Yury A. Kachanov
Publikováno v:
Наука Красноярья, Vol 12, Iss 1, Pp 150-171 (2023)
Theoretical foundations for the development of environmental protection measures in Russia and the world, the issues of investing in environmental protection are studied. The scientific novelty lies in the fact that based on the use of a variational
Externí odkaz:
https://doaj.org/article/9bc6ffaf164f4212956c0642ea56f6cd
Publikováno v:
E3S Web of Conferences, Vol 486, p 03023 (2024)
The subject of the study is investigation the accuracy and identify the features of spatial information perception in virtual reality. During the experiment, the subjects were asked to estimate the distances to objects and between objects in virtual
Externí odkaz:
https://doaj.org/article/ce35175b9e614fb78d6382d6b8914236