• 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...
    15 KB (2,491 words) - 22:59, 6 July 2025
  • 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...
    8 KB (1,150 words) - 19:31, 30 June 2025
  • 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...
    13 KB (2,131 words) - 15:16, 27 March 2025
  • 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...
    5 KB (805 words) - 04:07, 13 December 2024
  • 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...
    22 KB (3,616 words) - 20:40, 27 April 2025
  • 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...
    76 KB (11,410 words) - 20:15, 22 May 2025
  • Thumbnail for Base pair
    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...
    35 KB (4,152 words) - 08:10, 30 June 2025
  • 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...
    13 KB (2,270 words) - 10:22, 20 April 2025
  • Thumbnail for Radial distribution function
    In statistical mechanics, the radial distribution function, (or pair correlation function) g ( r ) {\displaystyle g(r)} in a system of particles (atoms...
    30 KB (4,541 words) - 17:03, 25 May 2025
  • In mathematical logic and set theory, an ordinal notation is a partial function mapping the set of all finite sequences of symbols, themselves members...
    16 KB (1,889 words) - 18:27, 20 November 2024
  • The pair distribution function describes the distribution of distances between pairs of particles contained within a given volume. Mathematically, if a...
    6 KB (916 words) - 20:38, 6 September 2024
  • 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...
    9 KB (1,318 words) - 20:47, 12 May 2025
  • A × B under the Cantor pairing function is computable. In general, the image of a computable set under a computable function is computably enumerable...
    4 KB (500 words) - 23:17, 22 May 2025
  • 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...
    93 KB (12,955 words) - 20:50, 1 July 2025
  • 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...
    28 KB (4,381 words) - 01:01, 29 March 2025
  • Fueter and George Pólya, states that the only quadratic polynomial pairing functions are the Cantor polynomials. In 1873, Georg Cantor showed that the...
    3 KB (614 words) - 13:42, 28 November 2024
  • Thumbnail for Graph of a 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...
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  • Thumbnail for UE Boom
    PC Magazine, remarking favorably on its design, volume and stereo pairing function. He noted that there was emphasis on the low-midrange tones. Greenwald...
    6 KB (717 words) - 03:50, 2 March 2025
  • Thumbnail for Ordered pair
    projections of the ordered pair. Cartesian products and binary relations (and hence functions) are defined in terms of ordered pairs, cf. picture. Let ( a...
    24 KB (3,697 words) - 09:06, 19 March 2025
  • 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...
    10 KB (1,180 words) - 18:27, 2 May 2025
  • 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...
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  • Thumbnail for Bijection
    Bijection (redirect from Bijective function)
    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...
    19 KB (2,508 words) - 09:01, 28 May 2025
  • Thumbnail for Error function
    In mathematics, the error function (also called the Gauss error function), often denoted by erf, is a function e r f : C → C {\displaystyle \mathrm {erf}...
    48 KB (7,340 words) - 13:25, 22 June 2025
  • Thumbnail for Wobble base pair
    wobble base pair is illustrated through experimentation where the Guanine-Uracil pairing is changed to its natural Guanine-Cytosine pairing. Oligoribonucleotides...
    12 KB (1,445 words) - 08:21, 23 June 2025
  • elementary pairing function, and π 1 , π 2 {\displaystyle \pi _{1},\pi _{2}} be its projection functions for inversion. Theorem: Any function constructible...
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  • Thumbnail for Au pair
    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...
    63 KB (9,255 words) - 05:00, 29 June 2025
  • the image of a function that has the set of the n first natural numbers as its domain. Tuples may be also defined from ordered pairs by a recurrence...
    16 KB (2,224 words) - 06:56, 3 May 2025
  • Thumbnail for Complex analysis
    traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is...
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  • Thumbnail for Trigonometric functions
    mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of...
    77 KB (10,653 words) - 18:24, 2 July 2025
  • 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...
    9 KB (1,193 words) - 17:38, 30 December 2024