Search results
Results From The WOW.Com Content Network
Unit disks are special cases of disks and unit balls; as such, they contain the interior of the unit circle and, in the case of the closed unit disk, the unit circle itself. Without further specifications, the term unit disk is used for the open unit disk about the origin , D 1 ( 0 ) {\displaystyle D_{1}(0)} , with respect to the standard ...
Every induced subgraph of a unit disk graph is also a unit disk graph. An example of a graph that is not a unit disk graph is the star K 1 , 6 {\displaystyle K_{1,6}} with one central node connected to six leaves: if each of six unit disks touches a common unit disk, some two of the six disks must touch each other.
This page was last edited on 17 May 2006, at 13:54 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may apply ...
A graph of the vertices of a pentagon, realized as an intersection graph of disks in the plane. This is an example of a graph with sphericity 2, also known as a unit disk graph . In graph theory , the sphericity of a graph is a graph invariant defined to be the smallest dimension of Euclidean space required to realize the graph as an ...
In mathematics, a Fuchsian group is a discrete subgroup of PSL(2,R).The group PSL(2,R) can be regarded equivalently as a group of orientation-preserving isometries of the hyperbolic plane, or conformal transformations of the unit disc, or conformal transformations of the upper half plane, so a Fuchsian group can be regarded as a group acting on any of these spaces.
In mathematics, the Littlewood subordination theorem, proved by J. E. Littlewood in 1925, is a theorem in operator theory and complex analysis.It states that any holomorphic univalent self-mapping of the unit disk in the complex numbers that fixes 0 induces a contractive composition operator on various function spaces of holomorphic functions on the disk.
In particular, the Poisson kernel is commonly used to demonstrate the equivalence of the Hardy spaces on the unit disk, and the unit circle. The space of functions that are the limits on T of functions in H p (z) may be called H p (T). It is a closed subspace of L p (T) (at least for p ≥ 1).
In 1932, S. Gołąb proved that the perimeter of the unit disc can take any value in between 6 and 8. What is the precise statement of this theorem? I can easily give a metric on R 2 whose unit disc is equal to R 2 and the perimeter (defined as the unit disc's boundary) is therefore empty. AxelBoldt 19:20, 16 April 2006 (UTC)