Zobrazeno 1 - 10
of 538
pro vyhledávání: '"Potapov, Vladimir"'
Autor:
Khomutov, Evgeni V., Dmitriev, Leonid S., Potapov, Vladimir Vladimirovich, Zenin, Oleg K., Zaitsev, Sergei Yu.
Publikováno v:
Известия Саратовского университета. Новая серия Серия: Физика, Vol 22, Iss 3, Pp 244-253 (2022)
Background and Objectives: Despite the fact that the methods of dynamic interfacial tensiometry and rheology are used to study blood and other biological fluids, in medicine there is no unified approach in the methodology of analysis and interpretati
Externí odkaz:
https://doaj.org/article/17c91b1eee8b452fb203c4af2503421a
A multidimensional nonnegative matrix is called polystochastic if the sum of entries in each line is equal to $1$. The set of all polystochastic matrices of order $n$ and dimension $d$ is a convex polytope $\Omega_n^d$. In the present paper, we compa
Externí odkaz:
http://arxiv.org/abs/2406.14160
Denote by Q_d the d-dimensional hypercube. Addressing a recent question we estimate the number of ways the vertex set of Q_d can be partitioned into vertex disjoint smaller cubes. Among other results, we prove that the asymptotic order of this functi
Externí odkaz:
http://arxiv.org/abs/2401.00299
Autor:
Potapov, Vladimir N.
It is disproved the Tokareva's conjecture that any balanced boolean function of appropriate degree is a derivative of some bent function. This result is based on new upper bounds for the numbers of bent and plateaued functions.
Comment: 3 pages
Comment: 3 pages
Externí odkaz:
http://arxiv.org/abs/2309.04244
Autor:
Potapov, Vladimir N.
The logarithm of the number of binary n-variable bent functions is asymptotically less than $11(2^n)/32$ as n tends to infinity. Keywords: boolean function, Walsh--Hadamard transform, plateaued function, bent function, upper bound
Comment: 11 pa
Comment: 11 pa
Externí odkaz:
http://arxiv.org/abs/2303.16547
Autor:
Krotov, Denis S., Potapov, Vladimir N.
Publikováno v:
Discrete Math. 347(1) 2024, 113657(1-9)
A frequency $n$-cube $F^n(q;l_0,...,l_{m-1})$ is an $n$-dimensional $q$-by-...-by-$q$ array, where $q = l_0+...+l_{m-1}$, filled by numbers $0,...,m-1$ with the property that each line contains exactly $l_i$ cells with symbol $i$, $i = 0,...,m-1$ (a
Externí odkaz:
http://arxiv.org/abs/2212.03694
Publikováno v:
J. Combin. Th. A, V. 201, (2024) 105801
This paper introduces the notion of mesh patterns in multidimensional permutations and initiates a systematic study of singleton mesh patterns (SMPs), which are multidimensional mesh patterns of length 1. A pattern is avoidable if there exist arbitra
Externí odkaz:
http://arxiv.org/abs/2208.12845
Autor:
Potapov, Vladimir N.
A coloring of vertices of a graph is called perfect if, for every vertex, the collection of colors of its neighbors depends only on its own color. The correspondent color partition of vertices is called equitable. We note that a number of bounds (Hof
Externí odkaz:
http://arxiv.org/abs/2204.03308
Autor:
Potapov, Vladimir N.
Publikováno v:
Journal of Combinatorial Designs. 2022. V. 30 (9). P. 626--633
An embedding of a code is a mapping that preserves distances between codewords. We prove that any code with code distance $\rho$ and length $d$ can be embedded into an MDS code with the same code distance and length but under a larger alphabet. As a
Externí odkaz:
http://arxiv.org/abs/2109.14962
Autor:
Potapov, Vladimir N.
Publikováno v:
Proceedings of 2021 XVII International Symposium on Problems of Redundancy in Information and Control Systems
The number of $n$-ary bent functions is less than $2^{3\cdot2^{n-3}(1+o(1))}$ as $n$ is even and $n\rightarrow\infty$. Keywords: Boolean function, bent function, upper bound
Externí odkaz:
http://arxiv.org/abs/2107.14583