In mathematics, the open unit disk (or disc) around P (where P is a given point in the plane), is the set of points whose distance from P is less than...

a unit disk graph is the intersection graph of a family of unit disks in the Euclidean plane. That is, it is a graph with one vertex for each disk in...

unit circle is called the open unit disk, while the interior of the unit circle combined with the unit circle itself is called the closed unit disk....

every point of the open unit disk to another point on the open unit disk to the right of the given one. But for the closed unit disk it fixes every point...

Poincaré disk model, also called the conformal disk model, is a model of 2-dimensional hyperbolic geometry in which all points are inside the unit disk, and...

contains a simplex for every clique in the unit disk graph, so it is the clique complex or flag complex of the unit disk graph. More generally, the clique complex...

frequently historical, as in IBM's usage of the disk form beginning in 1956 with the "IBM 350 disk storage unit".) Audio information was originally recorded...

magnetic disk storage devices from 1956 to 2003, when it sold its hard disk drive business to Hitachi. Both the hard disk drive (HDD) and floppy disk drive...

on the upper half-plane. The Poincaré disk model defines a model for hyperbolic space on the unit disk. The disk and the upper half plane are related by...

H p {\displaystyle H^{p}} are spaces of holomorphic functions on the unit disk or upper half plane. They were introduced by Frigyes Riesz (Riesz 1923)...

explicitly. For example, the solution to the Dirichlet problem for the unit disk in R2 is given by the Poisson integral formula. If f {\displaystyle f}...

result in complex analysis about holomorphic functions from the open unit disk to itself. The lemma is less celebrated than deeper theorems, such as...

In mathematics, an infinite geometric series of the form ∑ n = 1 ∞ a r n − 1 = a + a r + a r 2 + a r 3 + ⋯ {\displaystyle \sum _{n=1}^{\infty }ar^{n-1...

disks of radius r ( n ) {\displaystyle r(n)} can be arranged in such a way as to cover the unit disk? More unsolved problems in mathematics The disk covering...

the Advanced Format (AF). The sector is the minimum storage unit of a hard drive. Most disk partitioning schemes are designed to have files occupy an integral...

from the unit disk U to itself, or from the upper half-plane H to itself, will not increase the Poincaré distance between points. The unit disk U with the...

two-dimensional Laplace equation, given Dirichlet boundary conditions on the unit disk. The kernel can be understood as the derivative of the Green's function...

A hard disk drive (HDD), hard disk, hard drive, or fixed disk is an electro-mechanical data storage device that stores and retrieves digital data using...

disk model, and the Cayley–Klein model, is a model of hyperbolic geometry in which points are represented by the points in the interior of the unit disk...

behaviour of holomorphic functions defined on the unit disk. It gives a lower bound on the size of a disk in which an inverse to a holomorphic function exists...

{\displaystyle K=\left\{(x,y)\in \mathbb {R} ^{2}:x^{2}+y^{2}=1\right\}} ; the unit circle, there exists a (non-rational) parameterization using the sine function...

analytic in the unit disk, with zeros a 1 , a 2 , … , a n {\displaystyle a_{1},a_{2},\ldots ,a_{n}} located in the interior of the unit disk, then for every...

spaces. A sequence of points ( a n ) {\displaystyle (a_{n})} inside the unit disk is said to satisfy the Blaschke condition when ∑ n ( 1 − | a n | ) < ∞...

polynomials are a sequence of polynomials that are orthogonal on the unit disk. Named after optical physicist Frits Zernike, laureate of the 1953 Nobel...

unit disk and their pointwise extension to the boundary of the disk. If we have a holomorphic function f {\displaystyle f} defined on the open unit disk...

to the unit disk. In terms of the models of hyperbolic geometry, this Cayley transform relates the Poincaré half-plane model to the Poincaré disk model...

the disk algebra A(D) (also spelled disc algebra) is the set of holomorphic functions ƒ : D → C {\displaystyle \mathbb {C} } (where D is the open unit disk...

whose inverse is also holomorphic) from U {\displaystyle U} onto the open unit disk D = { z ∈ C : | z | < 1 } . {\displaystyle D=\{z\in \mathbb {C} :|z|<1\}...

the open unit disk extends continuously to a homeomorphism between their closures, mapping the Jordan curve homeomorphically onto the unit circle. To...

the real line on the complex plane, and the Poincaré disk model where the absolute is the unit circle in the complex plane. Hyperbolic motions can also...