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Among other statements, Poitou–Tate duality establishes a perfect pairing between certain Shafarevich groups.Given a global field , a set S of primes, and the maximal extension which is unramified outside S, the Shafarevich groups capture, broadly speaking, those elements in the cohomology of (/) which vanish in the Galois cohomology of the local fields pertaining to the primes in S.
A pairing is called perfect if the above map is an isomorphism of R-modules and the other evaluation map ′: (,) is an isomorphism also. In nice cases, it suffices that just one of these be an isomorphism, e.g. when R is a field, M,N are finite dimensional vector spaces and L=R .
In parliamentary practice, pairing is an informal arrangement between the government and opposition parties whereby a member of a legislative body agrees or is designated by a party whip to be absent from the chamber or to abstain from voting when a member of the other party needs to be absent from the chamber due to other commitments, illness, travel problems, etc.
In mathematics, economics, and computer science, the stable marriage problem (also stable matching problem) is the problem of finding a stable matching between two equally sized sets of elements given an ordering of preferences for each element.
In mathematics, a dual system, dual pair or a duality over a field is a triple (,,) consisting of two vector spaces, and , over and a non-degenerate bilinear map:. In mathematics , duality is the study of dual systems and is important in functional analysis .
In 2016, Stein campaign co-chair Gloria Mattera criticized vote pairing schemes, stating that the campaign's position on vote pairing is that it is a failed strategy because voting for the "lesser evil" had led highly distrusted major party candidates, and that Americans should instead vote for the candidate who best represents their interests ...
A BLS digital signature, also known as Boneh–Lynn–Shacham [1] (BLS), is a cryptographic signature scheme which allows a user to verify that a signer is authentic.. The scheme uses a bilinear pairing:, where ,, and are elliptic curve groups of prime order , and a hash function from the message space into .
The statement that this is the only quadratic pairing function is known as the Fueter–Pólya theorem. [9] Whether this is the only polynomial pairing function is still an open question. When we apply the pairing function to k 1 and k 2 we often denote the resulting number as k 1, k 2 . [citation needed]