of affine

111 examples (0.02 sec)
  • If the family of affine distance functions can be shown to be a certain kind of family then the local structure is known.
  • Therefore one may think of a scheme as being covered by "coordinate charts" of affine schemes.
  • They are also useful for the study of affine curves.
  • Classification of affine crystallographic groups is a difficult problem, far from being solved.
  • For that reason a concept of affine algebraic group is redundant over a field -- we may as well use a very concrete definition.
  • In the case of affine Coxeter groups like, or, one mirror, usually the last, is translated off the origin.
  • He proved that, in analogy with the spherical case, every building of affine type and rank at least four arises from a group.
  • In the modern approach, this is closely related to the definition of affine connections on the frame bundle.
  • Quantitative analysis of affine region detectors take into account both the accuracy of point locations and the overlap of regions across two images.
  • The various types of affine geometry correspond to what interpretation is taken for rotation.
  • Properly then, positions have dimension of affine length, while displacements have dimension of vector length.
  • Sometimes other algebraic sites replace the category of affine schemes.
  • Such results are frequently proved using the methods of limits of affine schemes developed in EGA IV 8.
  • The following proof uses only notions of affine geometry, notably homothecies.
  • Typical examples of affine planes are All the affine planes defined over a field are isomorphic.
  • The distortion of affine mapping becomes much less noticeable on smaller polygons.
  • The dual function g is concave, even when the initial problem is not convex, because it is a point-wise infimum of affine functions.
  • Since the sphere is not an affine space, familiar properties of affine constructions may fail, though the constructed curves may otherwise be entirely satisfactory.
  • Thus a general affine manifold is viewed as curved deformation of the flat model geometry of affine space.
  • Examples with more than two variables include characters of some irreducible highest-weight representations of affine Kac-Moody algebras.
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