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The standard torus is homogeneous under its diffeomorphism and homeomorphism groups, and the flat torus is homogeneous under its diffeomorphism, homeomorphism, and isometry groups. In mathematics, a homogeneous space is, very informally, a space that looks the same everywhere, as you move through it, with movement given by the action of a group.
If homogeneous coordinates of a point are multiplied by a non-zero scalar then the resulting coordinates represent the same point. Since homogeneous coordinates are also given to points at infinity, the number of coordinates required to allow this extension is one more than the dimension of the projective space being considered. For example ...
An inhomogeneous cosmology is a physical cosmological theory (an astronomical model of the physical universe's origin and evolution) which, unlike the dominant cosmological concordance model, assumes that inhomogeneities in the distribution of matter across the universe affect local gravitational forces (i.e., at the galactic level) enough to skew our view of the Universe. [3]
A solution describes a homogeneous mixture where the dispersed particles will not settle if the solution is left undisturbed for a prolonged period of time. A colloid is a heterogeneous mixture where the dispersed particles have at least in one direction a dimension roughly between 1 nm and 1 μm or that in a system discontinuities are found at ...
A solid solution, a term popularly used for metals, is a homogeneous mixture of two compounds in solid state and having a single crystal structure. [1] Many examples can be found in metallurgy , geology , and solid-state chemistry .
In mathematics, a homogeneous distribution is a distribution S on Euclidean space R n or R n \ {0} that is homogeneous in the sense that, roughly speaking, = ()for all t > 0.. More precisely, let : / be the scalar division operator on R n.
Of course, all matter is inhomogeneous at some scale, but frequently it is convenient to treat it as homogeneous. A good example is the continuum concept which is used in continuum mechanics . Under this assumption, materials such as fluids , solids , etc. can be treated as homogeneous materials and associated with these materials are material ...
In mathematics, a homogeneous polynomial, sometimes called quantic in older texts, is a polynomial whose nonzero terms all have the same degree. [1] For example, x 5 + 2 x 3 y 2 + 9 x y 4 {\displaystyle x^{5}+2x^{3}y^{2}+9xy^{4}} is a homogeneous polynomial of degree 5, in two variables; the sum of the exponents in each term is always 5.