## 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.