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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.
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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.
Title English title Original airdate Production code 1 "Bolnica" The Hospital: December 22, 1974 (): 101: 2 "Garaža" The Garage: December 29, 1974 (): 102: 3 "Izdajnik" The Traitor
Cayley transform of upper complex half-plane to unit disk. On the upper half of the complex plane, the Cayley transform is: [1] [2] = +.Since {,,} is mapped to {,,}, and Möbius transformations permute the generalised circles in the complex plane, maps the real line to the unit circle.
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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).