Zobrazeno 1 - 10
of 49
pro vyhledávání: '"Kochetkov, Yury"'
Autor:
Kochetkov, Yury
We consider the space $P$ of generic complex 5-degree polynomials. Critical values of such polynomial, i.e. four points in the complex plane, either are vertices of a convex quadrangle $Q$, or vertices of a triangle $T$ with one point inside $T$. The
Externí odkaz:
http://arxiv.org/abs/2405.10594
Autor:
Kochetkov, Yury
A cubic Galois polynomial is a cubic polynomial with rational coefficients that defines a cubic Galois field. Its discriminant is a full square and its roots $x_1,x_2,x_3$ (enumerated in some order) are real. There exists (and only one) quadratic pol
Externí odkaz:
http://arxiv.org/abs/2401.11208
Autor:
Kochetkov, Yury
In this purely experimental work we try to represent the set of plane maps with 3 vertices and 3 faces as a bipartite ribbon graph. In particular, this construction allows one to estimate the genus of the initial set.
Comment: 5 pages, 9 figures
Comment: 5 pages, 9 figures
Externí odkaz:
http://arxiv.org/abs/2308.15080
Autor:
Kochetkov, Yury, Osipov, Alexandr
For a two dimensional vector $\bar v=(\alpha,\beta)$, where $\alpha>0, \beta>0$ are irrational numbers independent over $\mathbb{Q}$, we consider the set $D_n=\{(i\alpha\,{\rm mod}\,1,i\beta\,{\rm mod}\,1),i=1,\ldots,n\}$ in a two dimensional torus a
Externí odkaz:
http://arxiv.org/abs/2308.01848
Autor:
Kochetkov, Yury
A Latin square of order $n$ with symbols $a_1,\ldots,a_n$ can be considered as a multiplication table for binary operation in the set $A=\{a_1,\ldots,a_n\}$. We prove that, if this operation is associative, then $A$ is a group.
Comment: 2 pages
Comment: 2 pages
Externí odkaz:
http://arxiv.org/abs/2208.14806
Autor:
Kochetkov, Yury
A polynomial $p\in \mathbb{C}[z]$ with three finite values is called the Zolotarev polynomial. For a class of such polynomials with the given degree, given passport and simple critical points we define a \emph{combinatorial moduli space}. A combinato
Externí odkaz:
http://arxiv.org/abs/2208.02069
Autor:
Kochetkov, Yury
Let us consider a family $F(\alpha,\beta,\gamma,\delta)$ of convex quadrangles in the plane with given angles $\{\alpha,\beta,\gamma,\delta\}$ and with the perimeter $2\pi$. Such quadrangle $Q\in F(\alpha,\beta,\gamma,\delta)$ can be considered as a
Externí odkaz:
http://arxiv.org/abs/2106.15557
Autor:
Kochetkov, Yury
Let $M$ be the space of triangles, defined up to shifts, rotations and dilations. We define two maps $f:M\to M$ and $g:M\to M$. The map $f$ corresponds to a triangle of perimeter $\pi$ the triangle with angles numerically equal to edges of the initia
Externí odkaz:
http://arxiv.org/abs/2101.03734
Autor:
Kochetkov, Yury
A convex quadrangular pyramid $ABCDE$, where $ABCD$ is the base and $E$ -- the apex, is called \emph{strongly flexible}, if it belongs to a continuous family of pairwise non-congruent quadrangular pyramids that have the same lengths of corresponding
Externí odkaz:
http://arxiv.org/abs/2008.07285
Autor:
Kochetkov, Yury
Let $P=A_1\ldots A_n$ be a generic polygon in three-dimensional space and let $v_1,v_2,\ldots,v_n$ be vectors $\overline{A_1A_2},\overline{A_2A_3},\ldots,\overline{A_nA_1}$, respectively. $P$ will be called \emph{regular}, if there exist vectors $u_1
Externí odkaz:
http://arxiv.org/abs/2004.12106