from The American Heritage® Dictionary of the English Language, 5th Edition.
- noun Equality of measure.
- noun Equality of elevation above sea level.
- noun Mathematics A function between metric spaces which preserves distances, such as a rotation or translation in a plane.
- noun Biology A proportional change in the size of a part or parts of an organism as the organism grows.
from Wiktionary, Creative Commons Attribution/Share-Alike License.
- noun mathematics A
functionbetween metric spaces(or on a single metric space) having the property that the distancebetween two images is equal to the distance between their pre-images.
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
- noun equality of elevation above sea level
- noun equality of measure (e.g., equality of height above sea level or equality of loudness etc.)
- noun the growth rates in different parts of a growing organism are the same
- noun a one-to-one mapping of one metric space into another metric space that preserves the distances between each pair of points
from Wiktionary, Creative Commons Attribution/Share-Alike License
The metric has time dependent metric elements, which means there is no Killing isometry which defines energy conservation as a symmetry of the spacetime.
Temperature-mediated transitions between isometry and allometry in a colonial, modular invertebarte.
Further momentum is an isometry of this spacetime, so momentum is conserved.
The metric coefficients are time dependent, and this precludes the existence of a Killing vector K_t that defines an isometry and energy conservation law.
In effect cosmologies in their lack of such isometry permits the creation of momentum and energy — aka the big bang.
With a few [extremely non-generic] exceptions, namely the ones with maximal isometry groups, one can say definitely whether they are expanding or not.
This process of being dragged along is due to a symmetry (isometry) of space which preserves momentum.
(M², g²ab), respectively, and if there exists an isometry
Does it follow, as we would want determinism to guarantee, that Î¨ is extendible to an isometry from
(M*, g*ab) violates the condition that determinism was supposed to guarantee as Î¨ is not extendible to an isometry from D+ (Î£) onto