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Function uniquely mapping two numbers into a single number
mathematics, a pairing function is a process to uniquely encode two natural numbers into a single natural number. Any pairing function can be used in
Pairing_function
Type of Gödel numbering in mathematics
as a surplus member, or as the other member of an ordered pair by using a pairing function. We expect that there is an effective way for this information
Gödel_numbering_for_sequences
Technique in cryptography
Pairing-based cryptography is the use of a pairing between elements of two cryptographic groups to a third group with a mapping e : G 1 × G 2 → G T {\displaystyle
Pairing-based_cryptography
Thought experiment of infinite sets
already numbered (or use the axiom of countable choice). In general any pairing function can be used to solve this problem. For each of these methods, consider
Hilbert's paradox of the Grand Hotel
Hilbert's_paradox_of_the_Grand_Hotel
Association of one output to each input
mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the
Function_(mathematics)
Theorem equivalent to the Axiom of Choice
The opposite direction was already known (provable via an explicit pairing function for any aleph number), thus the statement and axiom of choice are equivalent
Tarski's_theorem_about_choice
Variant of heap data structure
guarantees. A pairing heap is either an empty heap, or a pairing tree consisting of a root element and a possibly empty list of pairing trees. The heap
Pairing_heap
Binary function non degenerative defined between the point of twist of an abelian variety
In mathematics, the Weil pairing is a pairing (bilinear form, though with multiplicative notation) on the points of order dividing n of an elliptic curve
Weil_pairing
The only quadratic pairing functions are the Cantor polynomials
Fueter and George Pólya, states that the only quadratic polynomial pairing functions are the Cantor polynomials. In 1873, Georg Cantor showed that the
Fueter–Pólya_theorem
Description of particle density in statistical mechanics
In statistical mechanics, the radial distribution function, (or pair correlation function) g ( r ) {\displaystyle g(r)} in a system of particles (atoms
Radial_distribution_function
Type of mathematical function
In mathematical logic and set theory, an ordinal notation is a partial function mapping the set of all finite sequences of symbols, themselves members
Ordinal_notation
Two nucleobases bound by hydrogen bonds
In addition to the canonical Watson–Crick pairing (A•T/U G•C), some conditions can also favour base-pairing with alternative base orientation, and number
Base_pair
Distribution of distances between pairs of particles in a given volume
The pair distribution function describes the distribution of distances between pairs of particles contained within a given volume. Mathematically, if a
Pair_distribution_function
elementary pairing function, and π 1 , π 2 {\displaystyle \pi _{1},\pi _{2}} be its projection functions for inversion. Theorem: Any function constructible
Gödel's_β_function
Mathematical logic concept
B and A × B (with the ordered pair of natural numbers mapped to a single natural number with the Cantor pairing function) are computably enumerable sets
Computably_enumerable_set
Type of logical system
that include a pairing function. This is a function of arity 2 that takes pairs of elements of the domain and returns an ordered pair containing them
First-order_logic
Function computable with bounded loops
recursive functions with two or more arguments can be encoded as unary primitive recursive functions by using a primitive recursive pairing function with two
Primitive_recursive_function
Set with algorithmic membership test
A × B under the Cantor pairing function is computable. In general, the image of a computable set under a computable function is computably enumerable
Computable_set
Mathematical set that can be enumerated
numbers. Equivalently, a set is countable if there exists an injective function from it into the natural numbers; this means that each element in the set
Countable_set
Portable Bluetooth speaker
PC Magazine, remarking favorably on its design, volume and stereo pairing function. He noted that there was emphasis on the low-midrange tones. Greenwald
UE_Boom
Mathematician (1845–1918)
(mathematics) Epsilon numbers (mathematics) Factorial number system Pairing function List of things named after Georg Cantor Grattan-Guinness 2000, p. 351
Georg_Cantor
Pair of functions in combinatorics
a Wilf–Zeilberger pair, or WZ pair, is a pair of functions that can be used to certify certain combinatorial identities. WZ pairs are named after Herbert
Wilf–Zeilberger_pair
In mathematics a Steinberg symbol is a pairing function which generalises the Hilbert symbol and plays a role in the algebraic K-theory of fields. It is
Steinberg_symbol
Sigmoid shape special function
mathematics, the error function (also called the Gauss error function), often denoted by e r f {\displaystyle \mathbf {erf} } , is the function erf ( z ) = 2
Error_function
Zeta-like functions approximate arbitrary holomorphic functions
universality of zeta functions is the remarkable ability of the Riemann zeta function and other similar functions (such as the Dirichlet L-functions) to approximate
Zeta_function_universality
Functions of an angle
mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of
Trigonometric_functions
One-to-one correspondence
a pairing is a function with domain X. It is more common to see properties (1) and (2) written as a single statement: Every element of X is paired with
Bijection
Pair of mathematical objects
projections of the ordered pair. Cartesian products and binary relations (and hence functions) are defined in terms of ordered pairs, cf. picture. Let ( a
Ordered_pair
Helper from a foreign country working for, and living as part of, a host family
complicated application process. The tradition of au pairing is well established in Austria, and prospective au pairs are served by several agencies that are accustomed
Au_pair
Pair of electrons bound together at low temperature, allowing for superconductivity
the 1972 Nobel Prize in Physics. Although Cooper pairing is a quantum effect, the reason for the pairing can be seen from a simplified classical explanation
Cooper_pair
Smirnov (1971), named them after Georg Cantor because of Cantor's pairing function and Cantor's theorem that an infinite set X has the same number of
Jónsson–Tarski_algebra
Mathematical description of quantum state
In quantum mechanics, a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system. The most common
Wave_function
Cantor algebra Cantor cube Cantor distribution Cantor function Cantor normal form Cantor pairing function Cantor set Cantor space Cantor tree surface Cantor's
List of things named after Georg Cantor
List_of_things_named_after_Georg_Cantor
Real function with secant line between points above the graph itself
function is called convex if the line segment between any two distinct points on the graph of the function lies above or on the graph of the function
Convex_function
Finite ordered list of elements
image of a function that has the set of the first n natural numbers as its domain (1, 2, ..., n). Tuples may be also defined from ordered pairs by a recurrence
Tuple
Representation of a mathematical function
In mathematics, the graph of a function f {\displaystyle f} is the set of ordered pairs ( x , y ) {\displaystyle (x,y)} , where f ( x ) = y . {\displaystyle
Graph_of_a_function
Order-preserving mathematical function
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept
Monotonic_function
Concept in set theory
powerset of ω × ω {\displaystyle \omega \times \omega } . Using a pairing function on ω {\displaystyle \omega } such as ( n , k ) ↦ ( n 2 + 2 n k + k
Code_(set_theory)
Concept in computability theory
equivalent (here ( − , − ) {\displaystyle (-,-)} denotes an effective pairing function). A reduction showing A ≤ T B {\displaystyle A\leq _{T}B} can be constructed
Turing_reduction
Mathematical methods
required: first, an ordered pair (n,m) is treated as a single number using a fixed primitive recursive pairing function; second, for each natural number
Realizability
Process of pairing food dishes with wine to enhance the dining experience
Wine and food pairing is the process of pairing food dishes with wine to enhance the dining experience. In many cultures, wine has had a long history
Wine_and_food_pairing
American physicist (born 1949)
phase-sensitive experiments in the elucidation of the orbital symmetry of the pairing function in high-Tc superconductors". Kirtley, Tsuei, and co-workers used scanning
John_R._Kirtley
Multiplicative function in number theory
The Möbius function μ ( n ) {\displaystyle \mu (n)} is a multiplicative function in number theory introduced by the German mathematician August Ferdinand
Möbius_function
RNA base pair that does not follow Watson–Crick base pair rules
wobble base pair is illustrated through experimentation where the Guanine-Uracil pairing is changed to its natural Guanine-Cytosine pairing. Oligoribonucleotides
Wobble_base_pair
American solid state physicist
phase-sensitive experiments in the elucidation of the orbital symmetry of the pairing function in high-Tc superconductors." He was elected in 1995 a fellow of the
Dale_J._van_Harlingen
infinite pseudo-intersection. P 1. The powerset function 2. A poset pairing function A pairing function is a bijection from X×X to X for some set X pairwise
Glossary_of_set_theory
Quickly growing function
Ackermann function, named after Wilhelm Ackermann, is one of the simplest and earliest-discovered examples of a total computable function that is not
Ackermann_function
Mathematical conjecture
which, as Freeman Dyson pointed out to him, is the same as the pair correlation function of random Hermitian matrices. Under the assumption that the Riemann
Montgomery's pair correlation conjecture
Montgomery's_pair_correlation_conjecture
Generalized function whose value is zero everywhere except at zero
under the duality pairing ⟨ ⋅ , ⋅ ⟩ {\displaystyle \langle \cdot ,\cdot \rangle } of tempered distributions with Schwartz functions. Thus δ ^ {\displaystyle
Dirac_delta_function
Analytic function in mathematics
The Riemann zeta function or Euler–Riemann zeta function, denoted by the lowercase Greek letter ζ (zeta), is a mathematical function of a complex variable
Riemann_zeta_function
Branch of mathematics studying functions of a complex variable
traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of a complex variable of
Complex_analysis
Hyperbolic analogues of trigonometric functions
In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just
Hyperbolic_functions
Mapping arbitrary data to fixed-size values
A hash function is any function that can be used to map data of arbitrary size to fixed-size values, though there are some hash functions that support
Hash_function
Hierarchy of complexity classes for formulas defining sets
k-tuples of natural numbers. These are in fact related by the use of a pairing function. The following meanings can be attached to the notation for the arithmetical
Arithmetical_hierarchy
Mathematical function having a characteristic S-shaped curve or sigmoid curve
sigmoid function is any mathematical function whose graph has a characteristic S-shaped or sigmoid curve. A common example of a sigmoid function is the
Sigmoid_function
R {\displaystyle R} are left and right projection functions respectively for the pairing function ( − , − ) {\displaystyle (-,-)} . Statman, Rick (1997)
Cartesian_monoid
Method of solution to differential equations
In mathematics, a Green's function (or Green function) is the impulse response of an inhomogeneous linear differential operator defined on a domain with
Green's_function
Formal power series
generating function is a representation of an infinite sequence of numbers as the coefficients of a formal power series. Generating functions are often
Generating_function
Pairs of sequences
, bN − 1) be a pair of bipolar sequences, meaning that a(k) and b(k) have values +1 or −1. Let the aperiodic autocorrelation function of the sequence
Complementary_sequences
Nucleic acid pairing variations
A Hoogsteen base pair is a variation of base-pairing in nucleic acids such as the A•T pair. In this manner, two nucleobases, one on each strand, can be
Hoogsteen_base_pair
Generalization of Turing computability
effective way. The following inductive definition is typical; it uses a pairing function ⟨ ⋅ , ⋅ ⟩ {\displaystyle \langle \cdot ,\cdot \rangle } . The number
Hyperarithmetical_theory
Function used in signal processing
processing and statistics, a window function (also known as an apodization function or tapering function) is a mathematical function that is zero-valued outside
Window_function
Concept in probability and statistics
stochastic process, the autocovariance is a function that gives the covariance of the process with itself at pairs of time points. Autocovariance is closely
Autocovariance
Sequence of integers
In combinatorial mathematics, a Langford pairing, also called a Langford sequence, is a permutation of the sequence of 2n numbers 1, 1, 2, 2, ..., n,
Langford_pairing
Continuous function that is not absolutely continuous
In mathematics, the Cantor function is an example of a function that is continuous, but not absolutely continuous. It is a notorious counterexample in
Cantor_function
Base pairs in molecular genetics
formation of base pairs giving rise to 12 such possible base pairing edge identities, each of which can in principle form base pairing with any edge of
Non-canonical_base_pairing
Mathematical transform that expresses a function of time as a function of frequency
takes a function as input and outputs another function that describes the extent to which various frequencies are present in the original function. The output
Fourier_transform
Short-range wireless technology standard
introduction of Secure Simple Pairing in Bluetooth v2.1. The following summarizes the pairing mechanisms: Legacy pairing: This is the only method available
Bluetooth
Class of mathematical functions
elliptic functions are elliptic functions that take a particularly simple form. They are named for Karl Weierstrass. This class of functions is also referred
Weierstrass_elliptic_function
Input to a mathematical function
pair ( x , y ) {\displaystyle (x,y)} . The hypergeometric function is an example of a four-argument function. The number of arguments that a function
Argument_of_a_function
Point where function's value is zero
sometimes called a root) of a real-, complex-, or generally vector-valued function f {\displaystyle f} , is a member x {\displaystyle x} of the domain of
Zero_of_a_function
Mathematical function, used to describe magnetization
Langevin functions are a pair of special functions that appear when studying an idealized paramagnetic material in statistical mechanics. These functions are
Brillouin and Langevin functions
Brillouin_and_Langevin_functions
Mathematical concept
In mathematics, the inverse function of a function f (also called the inverse of f) is a function that undoes the operation of f. The inverse of f exists
Inverse_function
Theorem in computability theory
{\displaystyle \langle \bullet ,\bullet \rangle } denote some computable pairing function. We build X as a set of elements ⟨ x , y ⟩ {\displaystyle \langle x
Selman's_theorem
Theorem in differential topology
n-spheres. For the ordinary sphere, or 2‑sphere, if f is a continuous function that assigns a vector in ℝ3 to every point p on a sphere such that f(p)
Hairy_ball_theorem
Conjecture on zeros of the zeta function
Unsolved problem in mathematics Do all non-trivial zeros of the Riemann zeta function have a real part equal to one half? More unsolved problems in mathematics
Riemann_hypothesis
Generalized mathematical function
In mathematics, a multivalued function, multiple-valued function, many-valued function, or multifunction, is a function that has two or more values in
Multivalued_function
Probability that random variable X is less than or equal to x
cumulative distribution function (CDF) of a real-valued random variable X {\displaystyle X} , or just distribution function of X {\displaystyle X} ,
Cumulative distribution function
Cumulative_distribution_function
Figurate number
are connected to theta functions, in particular the Ramanujan theta function. The number of line segments between closest pairs of dots in the triangle
Triangular_number
Potential energy of two interacting objects as a function of their distance
In physics, a pair potential is a function that describes the potential energy of two interacting objects solely as a function of the distance between
Pair_potential
Chromosomes that pair in fertilization
cells have very tightly regulated homologous pairing (separated into chromosomal territories, and pairing at specific loci under control of developmental
Homologous_chromosome
Concept in computability theory, a field of mathematics
where ⟨ n , k ⟩ {\displaystyle \langle n,k\rangle } is the Cantor pairing function. Note that the cylindrification operation increases the input arity
Cylindrification
⟩ {\displaystyle \langle \bullet ,\bullet \rangle } be a standard pairing function. A set A ⊆ N {\displaystyle A\subseteq \mathbb {N} } is enumeration
Enumeration_reducibility
Mathematical-logic system
as λ-calculus) is a formal system for expressing computation based on function abstraction and application using variable binding and substitution. Untyped
Lambda_calculus
Brazilian-American cryptographer (born 1965)
research works on elliptic curve cryptography and pairing-based cryptography, including the eta pairing technique, identity-based cryptographic protocols
Paulo_S._L._M._Barreto
Function defined by a hypergeometric series
hypergeometric function 2F1(a, b; c; z) is a special function represented by the hypergeometric series, that includes many other special functions as specific
Hypergeometric_function
Lossless, but memory-consuming, data compression algorithm
Re-Pair (short for recursive pairing) is a grammar-based compression algorithm that, given an input text, builds a straight-line program, i.e. a context-free
Re-Pair
Mathematical function
In mathematics, the Jacobi elliptic functions are a set of basic elliptic functions. They are found in the description of the motion of a pendulum, as
Jacobi_elliptic_functions
Chemical reaction between oppositely-charged ions in solution
pairing will become more significant in superheated water. Solvents with a dielectric constant in the range, roughly, 20–40, show extensive ion-pair formation
Ion_association
Creation of particle-antiparticle pair from a neutral boson
section of pair production must be calculated through quantum electrodynamics in the form of Feynman diagrams and results in a complicated function. To simplify
Pair_production
Simpler variant of the Riemann zeta function
Riemann xi function is a variant of the Riemann zeta function, and is defined so as to have a particularly simple functional equation. The function is named
Riemann_xi_function
Meromorphic function on the complex plane
An L-function is a meromorphic function on the complex plane, and one out of several categories of mathematical objects studied in analytic number theory
L-function
Strong form of uniform continuity
continuous function is limited in how fast it can change: there exists a real number such that, for every pair of points on the graph of this function, the
Lipschitz_continuity
Nitrogen-containing biological compounds that form nucleosides
ensures a constant width for the DNA. The A–T pairing is based on two hydrogen bonds, while the C–G pairing is based on three. In both cases, the hydrogen
Nucleotide_base
Biological phenomenon in meiosis
Synapsis or syzygy is the pairing of two chromosomes that occurs during meiosis. It allows matching-up of homologous pairs prior to their segregation,
Synapsis
Pair of zeros of the Riemann zeta function
In the study of the Riemann hypothesis, a Lehmer pair is a pair of zeros of the Riemann zeta function that are unusually close to each other. They are
Lehmer_pair
Mathematical functions related to Weierstrass's elliptic function
mathematics, the Weierstrass functions are special functions of a complex variable that are auxiliary to the Weierstrass elliptic function. They are named for
Weierstrass_functions
number is positive, zero, or negative (its sign). Specifically, the signum function, often represented as sgn, is defined as: sgn x = { − 1 , x < 0 0 , x
Concordant_pair
Arithmetic function related to the divisors of an integer
theory, a divisor function is an arithmetic function related to the divisors of an integer. When referred to as the divisor function, it counts the number
Divisor_function
Mathematical function
In mathematics, the trigamma function, denoted ψ1(z) or ψ(1)(z), is the second of the polygamma functions, and is defined by ψ 1 ( z ) = d 2 d z 2 ln
Trigamma_function
PAIRING FUNCTION
PAIRING FUNCTION
Boy/Male
Indian
Gleam of a jewel
Surname or Lastname
English
English : perhaps be a nickname from Middle English daring ‘trembling’, ‘crouching or transfixed with fear’.
Male
Welsh
Breton and Welsh form of Irish Gaelic Pádraig, PADRIG means "patrician; of noble descent."
Boy/Male
Arabic, Hindu, Indian, Islamic, Muslim, Pakistani, Russian, Urdu
Bird
Surname or Lastname
English
English : from a pet form of Paul.Altered form, in the New Netherland Dutch community, of Paling. Compare Paulding.
Girl/Female
Australian, German, Hebrew, Irish
Star of the Easy
Girl/Female
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Fairy
Surname or Lastname
English
English : from the Norman personal name Warin, derived from Germanic war(in) ‘guard’, and used as a short form of various compound names with this first element. Compare, for example, Warner 2. The name was popular in France and among the Normans, partly as a result of the popularity of the Carolingian lay Guérin de Montglave.
Boy/Male
Welsh
noble'.
Boy/Male
Muslim
Loving, Caring, Daring
Boy/Male
Latin Teutonic
True.
Girl/Female
Hindu, Indian, Marathi
Fairy's Daughter
Surname or Lastname
English
English : variant of Waring.
Boy/Male
Muslim
Gleam of a jewel
Boy/Male
Muslim/Islamic
Loving Caring, Daring
Surname or Lastname
English and German
English and German : patronymic from the personal name Paul.
Boy/Male
British, English, German, Latin, Teutonic
Watchman; True
Biblical
ploughing plough or till
Boy/Male
Indian
Loving, Caring, Daring
Surname or Lastname
English and Irish
English and Irish : reduced form of Mannering.
PAIRING FUNCTION
PAIRING FUNCTION
Boy/Male
American, British, Chinese, Christian, Danish, English, French, German, Gujarati, Indian, Swedish, Swiss
Noble Friend; Magical; Elfin; Elf Friend or Old Friend
Girl/Female
English
Modernand Laurie referring to the laurel tree or sweet bay tree symbolic of honor and victory.
Boy/Male
Arthurian Legend
A kingdom.
Boy/Male
Hindu
Boy/Male
Sikh
Winner of world
Boy/Male
Arabic
A Sound from Heaven
Female
Slavic
(Богдана) Feminine form of Slavic Bogdan, BOGDANA means "gift from God."Â
Surname or Lastname
English (chiefly Wiltshire and Somerset)
English (chiefly Wiltshire and Somerset) : variant spelling of Nash 1.
Female
English
Variant spelling of English Zillah, ZILLA means "shade, shadow."
Female
English
Variant spelling of English Keren-happuch, KEREN-HAPUCH means "horn of antimony," a black paint used for eye-shadow.
PAIRING FUNCTION
PAIRING FUNCTION
PAIRING FUNCTION
PAIRING FUNCTION
PAIRING FUNCTION
adv.
Exceedingly; excessively; surpassingly; as, passing fair; passing strange.
n.
A walk or a ride in the open air; a short excursion for health's sake.
v. t.
That which is pared off.
a.
Pouring out; pouring forth freely.
a.
Pairing with more than one female.
a.
Relating to the act of passing or going; going by, beyond, through, or away; departing.
n.
In painting, the first coat of color, as the priming in house painting and the like.
v. i.
See To pair off, under Pair, v. i.
n.
The act of parting or dividing; the state of being parted; division; separation.
p. pr. & vb. n.
of Pain
n.
A failing short; a becoming deficient; failure; deficiency; imperfection; weakness; lapse; fault; infirmity; as, a mental failing.
n.
An exposure to air, or to a fire, for warming, drying, etc.; as, the airing of linen, or of a room.
p. pr. & vb. n.
of Pare
n.
A shaking; a tremulous motion; as, the jarring of a steamship, caused by its engines.
v.
Given when departing; as, a parting shot; a parting salute.
p. pr. & vb. n.
of Air
v. i.
The act or process of uniting or arranging in pairs or couples.
n.
A present; originally, one given or purchased at a fair.
p. pr. & vb. n.
of Pair
v. t.
The act of cutting off the surface or extremites of anything.