Zobrazeno 1 - 10
of 103
pro vyhledávání: '"Laczkovich, Miklós"'
Autor:
Kiss, Gergely, Laczkovich, Miklós
Let $K$ be a nonempty finite subset of the Euclidean space $\mathbb{R}^k$ $(k\ge 2)$. We prove that if a function $f\colon \mathbb{R}^k\to \mathbb{C}$ is such that the sum of $f$ on every congruent copy of $K$ is zero, then $f$ vanishes everywhere. I
Externí odkaz:
http://arxiv.org/abs/2403.01279
Autor:
Laczkovich, Miklos
A polygon $P$ is called a reptile, if it can be decomposed into $k\ge 2$ nonoverlapping and congruent polygons similar to $P$. We prove that if a cyclic quadrilateral is a reptile, then it is a trapezoid. Comparing with results of U. Betke and I. Osb
Externí odkaz:
http://arxiv.org/abs/2205.11068
Autor:
Laczkovich, Miklos, Vasenov, Ivan
We prove that for every $N\ne 4$ there is only one right triangle that tiles the regular $N$-gon.
Externí odkaz:
http://arxiv.org/abs/2109.07817
Autor:
Kiss, Gergely, Laczkovich, Miklós
A set of polynomials $M$ is called a {\it submodule} of $\mathbb{C} [x_1, \dots, x_n ]$ if $M$ is a translation invariant linear subspace of $\mathbb{C} [x_1, \dots, x_n ]$. We present a description of the submodules of $\mathbb{C} [x,y]$ in terms of
Externí odkaz:
http://arxiv.org/abs/2108.08817
Autor:
Kiss, Gergely, Laczkovich, Miklós
It is known that if $f\colon {\mathbb R}^2 \to {\mathbb R}$ is a polynomial in each variable, then $f$ is a polynomial. We present generalizations of this fact, when ${\mathbb R}^2$ is replaced by $G\times H$, where $G$ and $H$ are topological Abelia
Externí odkaz:
http://arxiv.org/abs/2101.03094
Autor:
Laczkovich, Miklos
Let $G$ be a topological Abelian semigroup with unit, let $E$ be a Banach space, and let $C(G,E)$ denote the set of continuous functions $f\colon G\to E$. A function $f\in C(G,E)$ is a generalized polynomial, if there is an $n\ge 0$ such that $\Delta
Externí odkaz:
http://arxiv.org/abs/2004.08936
Autor:
Laczkovich, Miklos
Let $G$ be a topological commutative semigroup with unit. We prove that a continuous function $f\colon G\to \cc$ is a generalized exponential polynomial if and only if there is an $n\ge 2$ such that $f(x_1 +\ldots +x_n )$ is decomposable; that is, if
Externí odkaz:
http://arxiv.org/abs/1812.06434
Autor:
Kiss, Gergely, Laczkovich, Miklós
Let $R$ be an integral domain of characteristic zero. We prove that a function $D\colon R\to R$ is a derivation of order $n$ if and only if $D$ belongs to the closure of the set of differential operators of degree $n$ in the product topology of $R^R$
Externí odkaz:
http://arxiv.org/abs/1803.01025
Autor:
Héra, Kornélia, Laczkovich, Miklós
Publikováno v:
Acta Math. Hungar. 150, (2016), 479-511
We prove that if a circular arc has angle short enough, then it can be continuously moved to any prescribed position within a set of arbitrarily small area.
Externí odkaz:
http://arxiv.org/abs/1802.00290