Cahill and Taub  analysed the homotheties of the spherically symmetric distribution of self-gravitating perfect fluid satisfying the homothety
The first solution has 7 Noether symmetries and 6 isommetries, the second solution has 8 Noether symmetries in which 6 are the isometries, one homothety
and one pure Noether symmetry.
On the other hand, optical scaling occurs when the shape undergoes unbalanced homothety
(dilation) or some transformations which are not affine mappings.
A transformation matrix is then calculated to evaluate similarity between all images such as rotation or homothety
. Extreme points can also be statistically eliminated to reduce noise.
where [a.sub.D] and [a.sub.L] are scale factors or homothety
ratios, D is the diameter, L is the length, and the subscripts 1 and 2 mean parent and daughter tubes.
The simplest and most important example of a self-similar flow is when the evolution is a homothety
. Such a self-similar submanifold F with mean curvature vector [??] satisfies the following non-linear, elliptic system:
This transformation is called a homothety
with a centre O and a factor k.
Some powerful DGS such as Geogebra offer just the images of an arbitrary figure for the classical transformation (axis symmetry, homothety
, central symmetry, translation, rotation, inversion, etc.).
Approached as statistical and mathematical function, the index generated a whole axiomatic theory which defines it as an economic measure, a function F: D[right arrow]R, which projects a set or a set D of economic interest goals (information and data) into a set or a set of real numbers R, which satisfies a system of relevant economic conditions--for example, the properties of monotony, homogeneity or homothety
or relative identity (Wolfgang Eichhorn).
A homothetic tube MPC synthesis method is proposed by , which utilizes a more general parameterization of the state and control tubes based on homothety
i.e., U is an affine vector field and defines an infinitesimal homothety
The first type is based on relations invariant by translation, whereas the second type is based on relations invariant by homothety
, that is, by proportional transformation.