from The American Heritage® Dictionary of the English Language, 5th Edition.
- adjective Of or relating to a transformation of coordinates that is equivalent to a linear transformation followed by a translation.
- adjective Of or relating to the geometry of affine transformations.
from The Century Dictionary.
- To refine. Holland.
- Related; akin; affined.
- noun A relative by marriage; one akin.
from the GNU version of the Collaborative International Dictionary of English.
- transitive verb obsolete To refine.
from Wiktionary, Creative Commons Attribution/Share-Alike License.
- adjective mathematics Assigning
finite valuesto finite quantities.
- adjective mathematics Describing a function expressible as (which is not
linear, but is similar).
- adjective mathematics Of or pertaining to a
transformationthat mapsparallel lines to parallel lines and finite pointsto finite points.
- adjective comparable, chemistry Having mutual affinity, of two materials.
- noun genealogy A relative by
- verb To
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
- noun (anthropology) kin by marriage
- adjective (anthropology) related by marriage
- adjective (mathematics) of or pertaining to the geometry of affine transformations
from The American Heritage® Dictionary of the English Language, 4th Edition
We modeled the eating, lying, and standing dynamics of a cow using a piecewise affine dynamical system.
We formulate a mathematical model for daily activities of a cow (eating, lying down, and stand - ing) in terms of a piecewise affine dynamical system.
To say that a spacetime is singular then is to say that there is at least one maximally extended path that has a bounded (generalized affine) length.
Unlike proper length, this generalized affine length depends on some arbitrary choices (roughly speaking, the length will vary depending on the coordinates one chooses).
Thus the question of whether a path has a finite or infinite generalized affine length is a perfectly well-defined question, and that is all we'll need.
The axioms that Ketonen considers are those of projective and affine geometry, the former taken from Skolem's 1920 paper discussed in the first section above.
A maximal spacetime is singular if and only if it contains an inextendible path of finite generalized affine length.
Thus, for example, the notions of Euclidean geometry are invariant under similarity transformations, those of affine geometry under affine transformations, and those of topology under bicontinuous transformations.
The chief problem facing this definition of singularities is that the physical significance of generalized affine length is opaque, and thus it is unclear what the relevance of singularities, defined in this way, might be.
This may involve 11-dimensions for the space directions for gauge potentials we measure as affine connections on the base spacetime.