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In mathematics, a dilation is a function from a metric space into itself that satisfies the identity. for all points , where is the distance from to and is some positive real number. [1] In Euclidean space, such a dilation is a similarity of the space. [2] Dilations change the size but not the shape of an object or figure.
For one gets a point reflection at point. Homothety of a pyramid. In mathematics, a homothety (or homothecy, or homogeneous dilation) is a transformation of an affine space determined by a point S called its center and a nonzero number called its ratio, which sends point to a point by the rule [1] for a fixed number . Using position vectors: .
Dilation is commutative, also given by = =. If B has a center on the origin, then the dilation of A by B can be understood as the locus of the points covered by B when the center of B moves inside A. The dilation of a square of size 10, centered at the origin, by a disk of radius 2, also centered at the origin, is a square of side 14, with ...
The smallest constant is sometimes called the (best) Lipschitz constant [4] of f or the dilation or dilatation [5]: p. 9, Definition 1.4.1 [6] [7] of f. If K = 1 the function is called a short map , and if 0 ≤ K < 1 and f maps a metric space to itself, the function is called a contraction .
Dilution factor. The "dilution factor" is an expression which describes the ratio of the aliquot volume to the final volume. Dilution factor is a notation often used in commercial assays. For example, in solution with a 1/5 dilution factor (which may be abbreviated as x5 dilution), entails combining 1 unit volume of solute (the material to be ...
Definition of the Lorentz factor γ. The Lorentz factor or Lorentz term (also known as the gamma factor[1]) is a quantity expressing how much the measurements of time, length, and other physical properties change for an object while it moves. The expression appears in several equations in special relativity, and it arises in derivations of the ...
A packing density or packing fraction of a packing in some space is the fraction of the space filled by the figures making up the packing. In simplest terms, this is the ratio of the volume of bodies in a space to the volume of the space itself. In packing problems, the objective is usually to obtain a packing of the greatest possible density.
The invariance properties of molecular descriptors can be defined as the ability of the algorithm for their calculation to give a descriptor value that is independent of the particular characteristics of the molecular representation, such as atom numbering or labeling, spatial reference frame, molecular conformations, etc. Invariance to molecular numbering or labeling is assumed as a minimal ...