Zobrazeno 1 - 10
of 62
pro vyhledávání: '"Makai Jr., E."'
Autor:
Jerónimo-Castro, J., Makai Jr, E.
High proved the following theorem. If the intersections of any two congruent copies of a plane convex body are centrally symmetric, then this body is a circle. In our paper we extend the theorem of High to the sphere and the hyperbolic plane, and par
Externí odkaz:
http://arxiv.org/abs/2407.13396
Let $\{p_1, \ldots , p_n \} \subset {\Bbb{R}}^2$ be a separated point set, i.e., any two points have a distance at least $1$. Let $k \ge 1$ be an integer, and $1 \le t_1 < \ldots < t_k$ be real numbers. Let $\delta > 0$. Suppose for all $1 \le \ell (
Externí odkaz:
http://arxiv.org/abs/2112.08852
We improve our earlier upper bound on the numbers of antipodal pairs of points among $n$ points in ${\mathbb{R}}^3$, to $2n^2/5+O(n^c)$, for some $c<2$. We prove that the minimal number of antipodal pairs among $n$ points in convex position in ${\mat
Externí odkaz:
http://arxiv.org/abs/2103.13182
Autor:
Makai, Jr, E.
We consider triangle faced convex polyhedra inscribed in the unit sphere $S^2$ in ${\Bbb{R}}^3$. One way of measuring their deviation from regular polyhedra with triangular faces is to consider the quotient of the lengths of the longest and the short
Externí odkaz:
http://arxiv.org/abs/1909.02874
Autor:
Böröczky, K. J., Makai Jr, E.
H. Guggenheimer generalized the planar volume product problem for locally convex curves $C$ enclosing the origin $k \ge 2$ times. He conjectured that the minimal volume product $V(C)V(C^*)$ for these curves is attained if the curve consists of the lo
Externí odkaz:
http://arxiv.org/abs/1905.11766
A set $\cal P$ of $n$ points in $R^d$ is separated if all distances of distinct points are at least~$1$. Then we may ask how many of these distances, with multiplicity, lie in an interval $[t, t + 1]$. The authors and J. Spencer proved that the maxim
Externí odkaz:
http://arxiv.org/abs/1901.01055
Autor:
Makai, Jr., E., Zemánek, J.
We generalize earlier results about connected components of idempotents in Banach algebras, due to B. Sz\H{o}kefalvi Nagy, Y. Kato, S. Maeda, Z. V. Kovarik, J. Zem\'anek, J. Esterle. Let $A$ be a unital complex Banach algebra, and $p(\lambda) = \prod
Externí odkaz:
http://arxiv.org/abs/1807.01552
Autor:
Jerónimo-Castro, J., Makai, Jr, E.
High proved the following theorem. If the intersections of any two congruent copies of a plane convex body are centrally symmetric, then this body is a circle. In our paper we extend the theorem of High to spherical, Euclidean and hyperbolic spaces,
Externí odkaz:
http://arxiv.org/abs/1708.01510
Let $L \subset {\Bbb R}^3$ be the union of unit balls, whose centres lie on the $z$-axis, and are equidistant with distance $2d \in [2, 2\sqrt{2}]$. Then a packing of unit balls in ${\Bbb R}^3$ consisting of translates of $L$ has a density at most $\
Externí odkaz:
http://arxiv.org/abs/1706.05282
Autor:
Makai, Jr., E., Martini, H.
G. Fejes T\'oth posed the following problem: Determine the infimum of the densities of the lattices of closed balls in $\bR^n$ such that each affine $k$-subspace $(0 \le k \le n-1)$ of $\bR^n$ intersects some ball of the lattice. We give a lower esti
Externí odkaz:
http://arxiv.org/abs/1612.01307