Zobrazeno 1 - 10
of 189
pro vyhledávání: '"Taranchuk, A."'
Autor:
Taranchuk, Vladislav
In this short note, we provide a new infinite family of $K_{2, t+1}$-free graphs for each prime power $t$. Using these graphs, we show that it is possible to partition the edges of $K_n$ into parts, such that each part is isomorphic to our $K_{2, t+1
Externí odkaz:
http://arxiv.org/abs/2411.14364
Autor:
Taranchuk, M. J., Braun, R. J.
One of the main roles of the lipid layer (LL) of the tear film (TF) is to help prevent evaporation of the aqueous layer (AL). The LL thickness, composition, and structure all contribute to its barrier function. It is believed that the lipid layer is
Externí odkaz:
http://arxiv.org/abs/2404.17003
Autor:
Taranchuk, M. J., Braun, R. J.
The human tear film (TF) is thin multilayer fluid film that is critical for clear vision and ocular surface health. Its dynamics are strongly affected by a floating lipid layer and, in health, that layer slows evaporation and helps create a more unif
Externí odkaz:
http://arxiv.org/abs/2404.13225
Autor:
Taranchuk, Vladislav, Timmons, Craig
A complete partition of a graph $G$ is a partition of the vertex set such that there is at least one edge between any two parts. The largest $r$ such that $G$ has a complete partition into $r$ parts, each of which is an independent set, is the achrom
Externí odkaz:
http://arxiv.org/abs/2311.10379
Motivated by problems arising in tear film dynamics, we present a model for the extensional flow of thin sheets of nematic liquid crystal. The rod-like molecules of these substances impart an elastic contribution to its response. We rescale a weakly
Externí odkaz:
http://arxiv.org/abs/2304.03356
Autor:
Taranchuk, Vladislav
The components of the graphs $D(n, q)$ provide the best-known general lower bound for the number of edges in a graph with $n$ vertices and no cycles of length less than $g$. In this paper, we give a new, short, and simpler proof of the fact that the
Externí odkaz:
http://arxiv.org/abs/2212.13096
Autor:
Gupta, Himanshu, Taranchuk, Vladislav
Let $q = p^e$, where $p$ is a prime and $e$ is a positive integer. The family of graphs $D(k, q)$, defined for any positive integer $k$ and prime power $q$, were introduced by Lazebnik and Ustimenko in 1995. To this day, the connected components of t
Externí odkaz:
http://arxiv.org/abs/2207.04629
Autor:
Taranchuk, Vladislav, Timmons, Craig
Publikováno v:
In Finite Fields and Their Applications October 2024 99
Autor:
Lazebnik, Felix, Taranchuk, Vladislav
Let $p$ be an odd prime, $q=p^e$, $e\ge 1$, and $\mathbb{F} = \mathbb{F_q}$ denote the finite field of $q$ elements. Let $f: \mathbb{F}^2\to \mathbb{F}$ and $g: \mathbb{F}^3\to \mathbb{F}$ be functions, and let $P$ and $L$ be two copies of the 3-dime
Externí odkaz:
http://arxiv.org/abs/2109.03130
Autor:
Taranchuk, Vladislav
Let $\Pi$ be a projective plane of order $n$ and $\Gamma_{\Pi}$ be its Levi graph (the point-line incidence graph). For fixed $k \geq 3$, let $c_{2k}(\Gamma_{\Pi})$ denote the number of $2k$-cycles in $\Gamma_{\Pi}$. In this paper we show that $$ c_{
Externí odkaz:
http://arxiv.org/abs/2103.12255