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Set of points at distance less than one from a given point
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
Unit_disk
Intersection graph of unit disks in the plane
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_disk_graph
Circle with radius of one
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.
Unit_circle
Model of hyperbolic geometry
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
Poincaré_disk_model
Plane figure, bounded by circle
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
Disk_(mathematics)
Topological space formed from distances
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
Vietoris–Rips_complex
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
History of IBM magnetic disk drives
History_of_IBM_magnetic_disk_drives
Concept within complex analysis
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)
Hardy_space
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
Disk_covering_problem
Problem of solving a partial differential equation subject to prescribed boundary values
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}
Dirichlet_problem
General category of storage mechanisms
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
Disk_storage
Statement in complex analysis
analysis typically viewed to be about holomorphic functions from the open unit disk D := { z ∈ C : | z | < 1 } {\displaystyle \mathbb {D} :=\{z\in \mathbb
Schwarz_lemma
Mathematical concept
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
Poisson_kernel
Electro-mechanical data storage device
A hard disk drive (HDD), hard disk, hard drive, or fixed disk is an electro-mechanical computer data storage device that stores and retrieves digital data
Hard_disk_drive
Metric tensor describing constant negative (hyperbolic) curvature
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
Poincaré_metric
on compact sets as t tends to infinity. Let D {\displaystyle D} be the unit disk in the complex plane with the Poincaré metric d s 2 = 4 | d z | 2 ( 1
Busemann_function
Mathematical theorem
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
Bloch's theorem (complex analysis)
Bloch's_theorem_(complex_analysis)
Polynomial sequence
polynomials are a sequence of polynomials that are orthogonal on the unit disk. Named after optical physicist Frits Zernike, laureate of the 1953 Nobel
Zernike_polynomials
Logical or physical division of storage media
the Advanced Format (AF). The sector is the minimum storage unit of a disk drive. Most disk partitioning schemes are designed to have files occupy an integral
Disk_sector
Theorem in complex analysis
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
Fatou's_theorem
Model of hyperbolic geometry
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
Beltrami–Klein_model
Mathematical formula in complex analysis
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
Jensen's_formula
Concept in geometry
as the area of a circle in informal contexts, strictly speaking, the term disk refers to the interior region of the circle, while circle is reserved for
Area_of_a_circle
Analytic function with prescribed zeros
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 | ) < ∞
Blaschke_product
Extends the Jordan curve theorem to characterize the inner and outer regions
the open unit disk extends continuously to a homeomorphism between their closures, mapping the Jordan curve homeomorphically onto the unit circle. To
Schoenflies_problem
Class of mathematical functions
{\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
Weierstrass_elliptic_function
Analytic function in mathematics
open unit disk. Nevertheless, f has dense singularities on the unit circle, and cannot be analytically continued outside of the open unit disk, as the
Lacunary_function
Mathematical theorem
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\}
Riemann_mapping_theorem
Floppy disk drive for the Apple II computer
The Disk II Floppy Disk Subsystem, often rendered as Disk ][, is a 5 +1⁄4-inch floppy disk drive designed by Steve Wozniak at the recommendation of Mike
Disk_II
Mathematical inequality
of a complex polynomial function on the unit disk with the maximum modulus of its derivative on the unit disk. It was proven by Sergei Bernstein while
Bernstein's theorem (polynomials)
Bernstein's_theorem_(polynomials)
Study of space and shapes locally given by a convergent power series
{\displaystyle D_{1}} onto the unit disk and existence of w = g ( z ) {\displaystyle w=g(z)} mapping D 2 {\displaystyle D_{2}} onto the unit disk. Thus g − 1 f {\displaystyle
Geometric_function_theory
were available. Unit production peaked in 2010 at about 650 million units, and has been in a slow decline since then. The IBM 350 Disk File was developed
History_of_hard_disk_drives
Operator on a Hilbert space that shifts basis vectors
the space of bounded smooth functions on the unit interval, but has a continuous spectrum (on the unit disk), when acting on the Hilbert space of square-integrable
Unilateral_shift_operator
One-dimensional complex manifold
connected Hausdorff space that is endowed with an atlas of charts to the open unit disk of the complex plane: for every point x ∈ X {\displaystyle x\in X} there
Riemann_surface
polyhedral graphs have greedy embeddings in the Euclidean plane, and that unit disk graphs have greedy embeddings in Euclidean spaces of moderate dimensions
Greedy_embedding
Picard's theorem. It states that for a holomorphic function f in the open unit disk that does not take the values 0 or 1, the value of |f(z)| can be bounded
Schottky's_theorem
Simply connected Riemann surface is equivalent to an open disk, complex plane, or sphere
is conformally equivalent to one of three Riemann surfaces: the open unit disk, the complex plane, or the Riemann sphere. The theorem is a generalization
Uniformization_theorem
Statement in complex analysis; formerly the Bieberbach conjecture
necessary condition on a holomorphic function in order for it to map the open unit disk of the complex plane injectively to the complex plane. It was posed by
De_Branges's_theorem
Fractal named after mathematician Benoit Mandelbrot
the complement of the Mandelbrot set and the complement of the closed unit disk. Mandelbrot had originally conjectured that the Mandelbrot set is disconnected
Mandelbrot_set
self-mappings of the unit disk, called a Loewner semigroup. This semigroup corresponds to a time dependent holomorphic vector field on the disk given by a one
Loewner_differential_equation
Construction in functional analysis, useful to solve differential equations
means the unit circle must lie in the continuous spectrum of T. So for the left shift T, σp(T) is the open unit disk and σc(T) is the unit circle, whereas
Decomposition of spectrum (functional analysis)
Decomposition_of_spectrum_(functional_analysis)
Space which has no holes through it
{\displaystyle S^{1}} and D 2 {\displaystyle D^{2}} denotes the unit circle and closed unit disk in the Euclidean plane respectively. An equivalent formulation
Simply_connected_space
Theorem in complex analysis
sending the unit disk to some region in the complex plane bounded by a Jordan curve extends continuously to a homeomorphism from the unit circle onto
Carathéodory's theorem (conformal mapping)
Carathéodory's_theorem_(conformal_mapping)
Series representing modular forms
The real part of G6 as a function of q on the unit disk. Negative numbers are black.
Eisenstein_series
powers of the moduli of the derivative of conformal maps into the open unit disk, on certain subsets of C {\displaystyle \mathbb {C} } Fuglede's conjecture
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Mathematical operation
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
Cayley_transform
Extension of the Schwarz lemma for hyperbolic geometry
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
Schwarz–Ahlfors–Pick_theorem
Modular function in mathematics
the elements of Q(τ) which fix Λ under multiplication form a ring with units, called an order. The other lattices with generators {1, τ′}, associated
J-invariant
Job control language for IBM mainframes
could specify the device type in generic terms, e.g., UNIT=DISK, UNIT=TAPE, or UNIT=SYSSQ (tape or disk). Of course, if it mattered one could specify a model
Job_Control_Language
Type of software utility
disk utility is a utility focused on the functionality of computer disks. A disk utility may support one or more of the following capabilities: disk partitioning
Disk_utility
holomorphic functions f ( z ) {\displaystyle f(z)} defined on the open unit disk D = { z ∈ C : | z | < 1 } {\displaystyle \mathbb {D} =\{z\in \mathbb {C}
Schur_class
Manifold with inversion symmetry
common complexification SL(2,C). In this case the non-compact space is the unit disk, a homogeneous space for SU(1,1). It is a bounded domain in the complex
Hermitian_symmetric_space
Theorem in complex analysis
to the unit disk D {\displaystyle \mathbb {D} } such that f ( φ − 1 ( z ) ) {\displaystyle f(\varphi ^{-1}(z))} is holomorphic on the unit disk and has
Liouville's theorem (complex analysis)
Liouville's_theorem_(complex_analysis)
Point at infinity in hyperbolic geometry
hyperbolic geometry. For instance, the unit circle forms the Cayley absolute of the Poincaré disk model and the Klein disk model. The real line forms the Cayley
Ideal_point
mapping, or a semigroup of mappings, of the unit disk in the complex numbers into itself. Let D be the unit disk in the complex numbers. Let f be a holomorphic
Koenigs_function
powers of the moduli of the derivatives of conformal maps into the open unit disk. The conjecture was formulated by James E. Brennan in 1978. Let W be a
Brennan_conjecture
Model of the extended complex plane plus a point at infinity
{\displaystyle \xi } -chart, and the equator of the unit sphere are all identified. The unit disk | ζ | < 1 {\displaystyle |\zeta |<1} is identified with
Riemann_sphere
Polygon associated with a compact Riemann surface
exactly one of the following: the Riemann sphere, the complex plane, the unit disk D or equivalently the upper half-plane H. In the first case of genus zero
Fundamental_polygon
Removable disk storage medium
A floppy disk, diskette, or floppy diskette is a type of disk storage made from a thin, flexible disk coated with a magnetic storage medium. It is enclosed
Floppy_disk
Nonlinear differential operator used to study conformal mappings
to determine the unique conformal map between the upper half-plane or unit disk and any bounded polygon in the complex plane, the edges of which are circular
Schwarzian_derivative
Characteristic polynomial whose associated linear system is stable
roots lie in the open left half-plane, or all its roots lie in the open unit disk. The first condition provides stability for continuous-time linear systems
Stable_polynomial
Graph formed by touching unit circles
different components may have different lengths. Every penny graph is a unit disk graph and a matchstick graph. Like planar graphs more generally, they
Penny_graph
Area of discrete mathematics
dimension is an interval graph. The intersection graph of unit disks in the plane is a unit disk graph. The intersection of a circle packing is a coin graph
Graph_theory
Video game console peripheral
The Family Computer Disk System, commonly shortened to the Famicom Disk System, is a peripheral for Nintendo's Family Computer (Famicom) home video game
Famicom_Disk_System
Computer bus used for data storage systems
mainframe hard disk drives beginning with the 3333 in 1972. The 3333 was the first unit in a string of up to eight 3330 type hard disk drives; it contained
Hard_disk_drive_interface
Storage of digital data readable by computers
memory close to the CPU and storage further away. In modern computers, hard disk drives (HDDs) or solid-state drives (SSDs) are usually used as storage. A
Computer_data_storage
sets of a sequence of holomorphic univalent functions, defined on the unit disk in the complex plane and fixing 0, can be formulated purely geometrically
Carathéodory_kernel_theorem
Diffraction pattern in optics
In optics, the Airy disk (or Airy disc) and Airy pattern are descriptions of the best-focused spot of light that a perfect lens with a circular aperture
Airy_disk
Real-valued function
the unit disk and plays a major role in the theory of Hardy spaces: by using definition 2, it is possible to define the BMO(T) space on the unit circle
Bounded_mean_oscillation
Conjecture about the roots of polynomials
(z-r_{n}),\qquad (n\geq 2)} with all roots r1, ..., rn inside the closed unit disk |z| ≤ 1, each of the n roots is at a distance no more than 1 from at least
Sendov's_conjecture
Concept in probability theory
in the boundary of D {\displaystyle D} . If D {\displaystyle D} is the unit disk and the curve γ {\displaystyle \gamma } is parameterized by "capacity"
Schramm–Loewner_evolution
Natural number
degree-7 monic polynomials with integer coefficients and all roots in the unit disk. On an infinite chessboard, there are 277 squares that a knight can reach
277_(number)
Graph representing intersections between given sets
graphs known as cocomparability graphs. A unit disk graph is defined as the intersection graph of unit disks in the plane. A circle graph is the intersection
Intersection_graph
Theorem that curves of bounded curvature contain a unit disk
states that every simple closed curve of curvature at most one encloses a unit disk. Although a version of this was published for convex curves by Wilhelm
Pestov–Ionin_theorem
Mapping which preserves all topological properties of a given space
and translated versions of the tan or arg tanh functions). The closed unit disk D 2 {\textstyle D^{2}} centered at the origin and the square [ − 1 , 1
Homeomorphism
Statement in complex analysis
\to \mathbb {C} } from the unit disk D {\displaystyle \mathbf {D} } onto a subset of the complex plane contains the disk whose center is f ( 0 ) {\displaystyle
Koebe_quarter_theorem
Partition of a graph's nodes into cliques
other special classes of graphs, including the cubic planar graphs and unit disk graphs. The same hardness of approximation results that are known for
Clique_cover
Set of holomorphic functions
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
Disk_algebra
Poisson integrals of homeomorphisms are diffeomorphisms
Poisson integral of a homeomorphism of the unit circle is a harmonic diffeomorphism of the open unit disk. The result was stated as a problem by Radó
Radó–Kneser–Choquet_theorem
Partial differential equation
Lp(C) for all 1 < p < ∞. The same method applies equally well on the unit disk and upper half plane and plays a fundamental role in Teichmüller theory
Beltrami_equation
First computer to use magnetic disk storage
moving-head hard disk drive (magnetic disk storage) for secondary storage. The system was publicly announced on September 14, 1956, with test units already installed
IBM_305_RAMAC
Mathematical tree in the hyperbolic plane
Poincaré disk model of hyperbolic geometry, though the Klein-Beltrami model can also be used. Both display the entire hyperbolic plane within a unit disk, making
Hyperbolic_tree
Concept in combinatorics (part of mathematics)
}(1-aq^{k}).} This is an analytic function of q in the interior of the unit disk, and can also be considered as a formal power series in q. The special
Q-Pochhammer_symbol
Conformal mapping in complex analysis
Schwarz–Christoffel mapping is a conformal map of the upper half-plane or the complex unit disk onto the interior of a simple polygon. Such a map is guaranteed to exist
Schwarz–Christoffel_mapping
Shape containing unit line segments in all directions
of points in Euclidean space which contains a unit line segment in every direction. For instance, a disk of radius 1/2 in the Euclidean plane, or a ball
Kakeya_set
Branch of geometry that studies combinatorial properties and constructive methods
include Euclidean graphs, the 1-skeleton of a polyhedron or polytope, unit disk graphs, and visibility graphs. Topics in this area include: Graph drawing
Discrete_geometry
A floppy disk is a disk storage medium composed of a thin and flexible magnetic storage medium encased in a rectangular plastic carrier. It is read and
History_of_the_floppy_disk
Isometric automorphisms of a hyperbolic space
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
Hyperbolic_motion
First sector of partitioned PC computer disk
identify uniquely the disk medium (as opposed to the disk unit—the two not necessarily being the same for removable hard disks). The disk signature was introduced
Master_boot_record
Data security technology
people or processes. Disk encryption uses disk encryption software or hardware to encrypt every bit of data that goes on a disk or disk volume. It is used
Disk_encryption
Mathematical theory in the field of algebraic geometry
specific versions of the theorem. For example, if S {\displaystyle S} is the unit disk in C {\displaystyle \mathbb {C} } , then "semistable" means that the special
Semistable_reduction_theorem
Abstract approach to algebraic geometry
covering spaces of the unit disk in the complex plane with the origin removed: the finite covering realised by the zn map of the disk, thought of by means
Grothendieck's_Galois_theory
the conformal isomorphism from the complement (exterior) of the closed unit disk D ¯ {\displaystyle {\overline {\mathbb {D} }}} to the complement of the
External_ray
Disk utility for macOS
Disk Utility is a system utility for performing disk and disk volume-related tasks on macOS. Features include: Create, convert, backup, compress, and
Disk_Utility
Buffer between a computer and a storage disk
computer storage, a disk buffer (often ambiguously called a disk cache or a cache buffer) is the embedded memory in a hard disk drive (HDD) or solid-state
Disk_buffer
Sphere with radius one, usually centered on the origin of the space
the unit sphere in the dual number plane. Ball n {\displaystyle n} -sphere Sphere Superellipse Unit circle Unit disk Unit tangent bundle Unit square
Unit_sphere
Construction for minimal surfaces
{\displaystyle g} be functions on either the entire complex plane or the unit disk, where g {\displaystyle g} is meromorphic and f {\displaystyle f} is analytic
Weierstrass–Enneper parameterization
Weierstrass–Enneper_parameterization
Study of graphs defined by geometric means
dimension is an interval graph; the intersection graph of unit disks in the plane is a unit disk graph. The Circle packing theorem states that the intersection
Geometric_graph_theory
On when a space equals the closed convex hull of its extreme points
{\displaystyle \mathbb {R} ^{2},} the unit circle is not convex but the closed unit disk is convex and furthermore, this disk is equal to the convex hull of
Krein–Milman_theorem
Type of continuous linear operator
complex-analytic example is given by the Cauchy integral operator. For the unit disk D {\displaystyle \mathbb {D} } , define ( T f ) ( z ) = 1 2 π i ∫ ∂ D
Compact_operator
UNIT DISK
UNIT DISK
Male
English
Variant spelling of English Unni, UNI means "afflicted, depressed."
Boy/Male
Muslim/Islamic
Unit of army
Girl/Female
Irish English
Together.
Female
Egyptian
, Anahita ("pure, spotless").
Boy/Male
Hindu
Knower of virtues, Talented, Excellent, Virtuous
Boy/Male
Bengali, English, Hindu, Indian
Dark Blue
Girl/Female
American, British, English, Irish
Fair
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Punjabi, Telugu
Holy; Untouched; Good; Pure
Boy/Male
Indian
Unit of army
Boy/Male
Muslim
Unit of army
Female
English
English name derived from the vocabulary word, UNITY means "oneness, unity."
Female
Hebrew
(×וּרִית) Hebrew name URIT means "fire, light."
Female
Welsh
Variant spelling of Welsh Enid, ENIT means "soul."
Girl/Female
Hebrew
Light.
Boy/Male
Hindu
Pure or holy
Boy/Male
Indian
Who Won Every Time
Boy/Male
Hindu
Joyful unending, Calmness
Boy/Male
Celebrity, Gujarati, Hindu, Indian, Jain, Kannada, Malayalam, Marathi, Punjabi, Sanskrit, Sikh, Tamil, Telugu
Grown; Awakened; Shining
Boy/Male
Indian
Progress
Girl/Female
Hebrew
Graceful.
UNIT DISK
UNIT DISK
Surname or Lastname
English
English : patronymic from Sim.German and Jewish (Ashkenazic) : variant of Samson.
Girl/Female
Norse Celtic Scandinavian
From Britain.
Boy/Male
Hindu
Girl/Female
Muslim
Well-established, Well-found
Boy/Male
Hindu, Indian, Marathi
A Sage
Surname or Lastname
German
German : variant of Buss.North German (Büsse) : metonymic occupational name for a maker of boxes and containers or for a gunsmith, from Middle Low German büsse, busse ‘box’, ‘gun’, ‘rifle’.English : variant spelling of Buss.
Boy/Male
Hindu, Indian
Type of Liquid
Female
Scottish
Older form of Scottish Diorbhail, DIORBHORGUIL means "true testimony."
Surname or Lastname
English and Irish (of Norman origin)
English and Irish (of Norman origin) : variant of Nangle.
Girl/Female
Spanish American
From Briseis, the woman Achilles loved in Homer's Iliad.
UNIT DISK
UNIT DISK
UNIT DISK
UNIT DISK
UNIT DISK
v. t.
To unite closely; to knit together.
v. t.
United; joint; as, unite consent.
v. t.
To knit or bind together; to unite closely.
imp. & p. p.
of Knit
n.
The number greater by a unit than seven; eight units or objects.
n.
The number greater than eight by a unit; nine units or objects.
n.
Any definite quantity, or aggregate of quantities or magnitudes taken as one, or for which 1 is made to stand in calculation; thus, in a table of natural sines, the radius of the circle is regarded as unity.
n.
The number greater by a unit than seventeen; eighteen units or objects.
v. t.
To knit together; to unite closely; to intertwine.
v. t.
To form, as a textile fabric, by the interlacing of yarn or thread in a series of connected loops, by means of needles, either by hand or by machinery; as, to knit stockings.
n.
Any one of numerous species of fresh-water mussels belonging to Unio and many allied genera.
v. t.
To put together so as to make one; to join, as two or more constituents, to form a whole; to combine; to connect; to join; to cause to adhere; as, to unite bricks by mortar; to unite iron bars by welding; to unite two armies.
n.
Concord; harmony; conjunction; agreement; uniformity; as, a unity of proofs; unity of doctrine.
v. t.
To remove the turns of (a rope or cable) from the bits; as, to unbit a cable.
n.
The number greater by a unit than two; three units or objects.
v. i.
To be united closely; to grow together; as, broken bones will in time knit and become sound.
n.
A single thing, as a magnitude or number, regarded as an undivided whole.
v. t.
To unite closely; to connect; to engage; as, hearts knit together in love.
a.
Of or pertaining to a unit or units; relating to unity; as, the unitary method in arithmetic.
v. t.
To unite.