Chamfering operation on k-orbit maps

Map operations and k-orbit maps

A k-orbit map is a map with k flag-orbits under the action of its automorphism group. We give a basic theory of k-orbit maps and classify them up to k 6 4. “Hurwitz-like” upper bounds for the cardinality of the automorphism groups of 2orbit and 3-orbit maps on surfaces are given. Furthermore, we consider effects of operations like medial and truncation on k-orbit maps and use them in classifyin...

Additive maps on C$^*$-algebras commuting with $|.|^k$ on normal elements

Let $mathcal {A} $ and $mathcal {B} $ be C$^*$-algebras. Assume that $mathcal {A}$ is of real rank zero and unital with unit $I$ and $k>0$ is a real number. It is shown that if $Phi:mathcal{A} tomathcal{B}$ is an additive map preserving $|cdot|^k$ for all normal elements; that is, $Phi(|A|^k)=|Phi(A)|^k $ for all normal elements $Ainmathcal A$, $Phi(I)$ is a projection, and there exists a posit...

k-Arbiter Join Operation

k-Arbiter is a useful concept for solving the distributed h-out of-k resources allocation problem. The distributed h-out of-k resources allocation algorithms based on k-arbiter have the benefits of high fault-tolerance and low communication cost. However, according to the definition of k-arbiter, it is required to have a non-empty intersection among any (k+1) quorums in a k-arbiter. Consequentl...

Commuting maps on rank-k matrices

$k$-power centralizing and $k$-power skew-centralizing maps on‎ ‎triangular rings

‎Let $mathcal A$ and $mathcal B$ be unital rings‎, ‎and $mathcal M$‎ ‎be an $(mathcal A‎, ‎mathcal B)$-bimodule‎, ‎which is faithful as a‎ ‎left $mathcal A$-module and also as a right $mathcal B$-module‎. ‎Let ${mathcal U}=mbox{rm Tri}(mathcal A‎, ‎mathcal M‎, ‎mathcal‎ ‎B)$ be the triangular ring and ${mathcal Z}({mathcal U})$ its‎ ‎center‎. ‎Assume that $f:{mathcal U}rightarrow{mathcal U}$ is...