Banach–Mazur Distance from the Parallelogram to the Affine-Regular Hexagon and Other Affine-Regular Even-Gons
نویسندگان
چکیده
Abstract We show that the Banach–Mazur distance between parallelogram and affine-regular hexagon is $$\frac{3}{2}$$ 3 2 we conclude diameter of family centrally-symmetric planar convex bodies just . A proof this fact does not seem to be published earlier. Asplund announced without a in his paper proving any at most Analogously, deal with distances remaining even-gons.
منابع مشابه
Parallelogram-Free Distance-Regular Graphs
Let 1=(X, R) denote a distance-regular graph with distance function and diameter d 4. By a parallelogram of length i (2 i d ), we mean a 4-tuple xyzu of vertices in X such that (x, y)= (z, u)=1, (x, u)=i, and (x, z)= ( y, z)= ( y, u)=i&1. We prove the following theorem. Theorem. Let 1 denote a distanceregular graph with diameter d 4, and intersection numbers a1=0, a2 {0. Suppose 1 is Q-polynomi...
متن کاملAffine Processes Are Regular
We show that stochastically continuous, time-homogeneous affine processes on the canonical state space R>0 × R n are always regular. In the paper of Duffie, Filipovic, and Schachermayer (2003) regularity was used as a crucial basic assumption. It was left open whether this regularity condition is automatically satisfied, for stochastically continuous affine processes. We now show that the regul...
متن کاملRegular cyclic coverings of regular affine maps
The regular coverings of regular affine algebraic maps are considered, and a large family of totally ramified coverings—the so-called Steinberg and Accola coverings—are fully classified.
متن کاملsome remarks on regular subgroups of the affine group
let $v$ be a vector space over a field $f$ of characteristic $pgeq 0$ and let $t$ be a regular subgroup of the affine group $agl(v)$. in the finite dimensional case we show that, if $t$ is abelian or $p>0$, then $t$ is unipotent. for $t$ abelian, pushing forward some ideas used in [a. caranti, f. dalla volta and m. sala, abelian regular subgroups of the affine group and r...
متن کاملParallelogram-free distance-regular graphs having completely regular strongly regular subgraphs
Let = (X,R) be a distance-regular graph of diameter d . A parallelogram of length i is a 4-tuple xyzw consisting of vertices of such that ∂(x, y)= ∂(z,w)= 1, ∂(x, z)= i, and ∂(x,w)= ∂(y,w)= ∂(y, z)= i− 1. A subset Y of X is said to be a completely regular code if the numbers πi,j = | j (x)∩ Y | (i, j ∈ {0,1, . . . , d}) depend only on i = ∂(x,Y ) and j . A subset Y of X is said to be strongly c...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Results in Mathematics
سال: 2021
ISSN: ['1420-9012', '1422-6383']
DOI: https://doi.org/10.1007/s00025-021-01368-8