Affine

An affine algebraic group over a field k is a representable covariant functor from the category of commutative algebras over k to the category of groups such that the representing algebra is finitely generated.

Now, let P, Q, and R be three noncollinear points that are left fixed by an affine transformation T.

In our example of the affine cryptosystem family, deciphering is also accomplished by an affine map, namely P#92;equiva#123;-1#125;C-a#123;-1#125;b#92;bmodN, and so the deciphering transformation uses the same algorithm as the enciphering transformation, except with a different key, namely, the pair (a#123;-1#125;,-a#123;-1#125;b).

Clearly every linear functional is affine, and every affine function is both convex and concave.

1970 [Routledge and Kegan Paul], Raymond Firth, Jane Hubert, Anthony Forge, Families and Their Relatives: Kinship in a Middle-Class Sector of London, 2006, Taylor & Francis (Routledge), page 135, The element of personal idiosyncracy may be expected to be most marked in regard to affines (i.e. those related by marriage) and particularly with the consanguines of affines, who are linked by still more tenuous bonds. There are many possible degrees of affinal relationship here, but broadly affines separate into two main types: spouse of consanguine of Ego, and consanguine of spouse of Ego—exemplified by my brother's wife, and my wife's brother.

In contrast to bonds of kaḅisu membership, which require ritual maintenance and can produce intense factional rivalries, and those of affines, which demand ongoing exchanges, unmediated relations of blood are created by nothing more than physical procreation.[…]People's ability to swivel between these two rhetorical possibilities reflects the inherent tension that lies between affines, who are both others and extensions of oneself.

For the Cubeo the Vekürüwá and Okómiwa were, as they say, designated to be their affines, in a manner that was calculated to emphasize their similarities rather than the formal differences that set contemporary intermarriages apart. I suspect that Cubeo themselves sense that an excessive intimacy with the contingent of affines may have been suitable for a formative period of still ambiguous distinctions, but not for the real social world.

The next stage is remelting: the affined sugar is dissolved in hot water and the syrup formed is made alkaline by adding milk of lime.

affined the sequential regions to run only on CPU 0

the affined CPU will be randomly allocated