Zobrazeno 1 - 10
of 173
pro vyhledávání: '"Musin, Oleg"'
Autor:
Lupton, Gregory, Musin, Oleg, Scoville, Nicholas A., Staecker, P. Christopher, Treviño-Marroquín, Jonathan
We define a second (higher) homotopy group for digital images. Namely, we construct a functor from digital images to abelian groups, which closely resembles the ordinary second homotopy group from algebraic topology. We illustrate that our approach c
Externí odkaz:
http://arxiv.org/abs/2310.08706
Autor:
Musin, Oleg R.
We present an extension of known semidefinite and linear programming upper bounds for spherical codes. We apply the main result for the distance distribution of a spherical code and show that this method can work effectively In particular, we get a s
Externí odkaz:
http://arxiv.org/abs/2309.13854
Autor:
Jang, Donghoon, Musin, Oleg R.
In the present paper, we consider an action of the circle group on a compact oriented 4-manifold. We derive the Atiyah-Hirzebruch formula for the manifold, and associate a graph in terms of data on the fixed point set. We show in the case of isolated
Externí odkaz:
http://arxiv.org/abs/2307.04576
Autor:
Bludov, Mikhail V., Musin, Oleg R.
Balanced sets appeared in the 1960s in cooperative game theory as a part of nonempty core conditions. In this paper we present a classification of balanced families containing only 2-element subsets. We also discuss generalizations of the classical S
Externí odkaz:
http://arxiv.org/abs/2302.13453
Autor:
Grebennikov, Alexandr, Isaeva, Xenia, Malyutin, Andrei V., Mikhailov, Mikhail, Musin, Oleg R.
We study the algorithmic complexity of fair division problems with a focus on minimizing the number of queries needed to find an approximate solution with desired accuracy. We show for several classes of fair division problems that under certain natu
Externí odkaz:
http://arxiv.org/abs/2112.13622
Autor:
Musin, Oleg R.
We consider a generalization of Sperner's lemma for a triangulation $T$ of $(m+1)$-discs $D$ whose vertices are colored in $c=n+2$ colors. A proper coloring of $T$ on the boundary of $D$ determines a simplicial mapping $f:S^m \to S^n$ and the element
Externí odkaz:
http://arxiv.org/abs/2007.08715
Autor:
Musin, Oleg R.
Publikováno v:
SIAM Journal on Discrete Mathematics, 2021, Vol. 35, No. 3 : pp. 1578-1591
In the present paper, we consider the majorization theorem (also known as Karamata's inequality) and the respective minima of the majorization (the so-called M-sets) for f-energy potentials of $m$-point configurations on the unit sphere. In particula
Externí odkaz:
http://arxiv.org/abs/2001.04067
Autor:
Dragnev, Peter D., Musin, Oleg R.
We enumerate and classify all stationary logarithmic configurations of d+2 points on the unit (d-1)-sphere in d-dimensions. In particular, we show that the logarithmic energy attains its relative minima at configurations that consist of two orthogona
Externí odkaz:
http://arxiv.org/abs/1909.09909
Autor:
Musin, Oleg R.
Publikováno v:
Arnold Mathematical Journal; Vol 6:1 (2020); 119-130
In 1915, Ramanujan proved asymptotic inequalities for the sum of divisors function, assuming the Riemann hypothesis (RH). We consider a strong version of Ramanujan's theorem and define highest abundant numbers that are extreme with respect to the Ram
Externí odkaz:
http://arxiv.org/abs/1905.09327
Autor:
Musin, Oleg R.
In this paper we present an extension of known semidefinite and linear programming upper bounds for spherical codes and consider a version of this bound for distance graphs. We apply the main result for the distance distribution of a spherical code.<
Externí odkaz:
http://arxiv.org/abs/1903.05767