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1. Homogeneous space: In mathematics, particularly in the theories of Lie groups, algebraic groups and topological groups, a homogeneous space for a group G is a non-empty manifold or topological space X on which G acts transitively. The elements of G are ... (Topological space in group theory) [100%] 2023-03-30 [Topological groups] [Lie groups]...
2. Homogeneous space: h0476901.png 132 0 132 A set together with a given transitive group action. More precisely, $ M $ is a homogeneous space with group $ G $ if a mapping$$ ( g ,\ x ) \rightarrow g x $$ of the set $ G \times M $ into $ M ... (Mathematics) [100%] 2023-07-09
3. Symplectic homogeneous space: A symplectic manifold $ ( M, \omega ) $ together with a transitive Lie group $ G $ of automorphisms of $ M $. The elements of the Lie algebra $ \mathfrak g $ of $ G $ can be regarded as symplectic vector fields on $ M $, i.e. (Mathematics) [81%] 2023-10-25
4. Riemannian space, homogeneous: A Riemannian space $ ( M, \gamma ) $ together with a transitive effective group $ G $ of motions (cf. Motion) on it. (Mathematics) [81%] 2023-09-28
5. Quantum homogeneous space: A unital algebra $A$ that is a co-module for a quantum group $\operatorname{Fun}_{q}(G)$ (cf. Quantum groups) and for which the structure mapping $L : A \rightarrow \operatorname { Fun }_{q} (G) \otimes A$ is an algebra ... (Mathematics) [81%] 2023-12-03
6. Principal homogeneous space: A principal $ G $- object in the category of algebraic varieties or schemes. If $ S $ is a scheme and $ \Gamma $ is a group scheme over $ S $, then a principal $ G $- object in the category of schemes over $ \Gamma $ is said to ... (Mathematics) [81%] 2023-10-11
7. Principal homogeneous space: In mathematics, a principal homogeneous space, or torsor, for a group G is a homogeneous space X for G in which the stabilizer subgroup of every point is trivial. Equivalently, a principal homogeneous space for a group G is a ... [81%] 2024-02-18 [Group theory] [Topological groups]...
8. Homogeneous coordinates: Coordinates having the property that the object determined by them does not change if all the coordinates are multiplied by the same non-zero number. Such, for example, are projective coordinates; Plücker coordinates and pentaspherical coordinates. (Mathematics) [65%] 2023-10-17
9. Homogeneous graph: In mathematics, a k-ultrahomogeneous graph is a graph in which every isomorphism between two of its induced subgraphs of at most k vertices can be extended to an automorphism of the whole graph. A k-homogeneous graph obeys a ... [65%] 2022-07-20 [Graph families]
10. Homogeneous coordinates: In mathematics, homogeneous coordinates or projective coordinates, introduced by August Ferdinand Möbius in his 1827 work Der barycentrische Calcul, are a system of coordinates used in projective geometry, just as Cartesian coordinates are used in Euclidean geometry. They have the ... (Coordinate system used in projective geometry) [65%] 2022-06-25 [Linear algebra] [Projective geometry]...
11. Homogeneous polynomial: In mathematics, a homogeneous polynomial, sometimes called quantic in older texts, is a polynomial whose nonzero terms all have the same degree. For example, \displaystyle{ x^5 + 2 x^3 y^2 + 9 x y^4 }[/math] is a homogeneous ... (Polynomial whose all nonzero terms have the same degree) [65%] 2022-09-20 [Homogeneous polynomials] [Multilinear algebra]...
12. Homogeneous Serbia: Homogeneous Serbia is a written discourse by Stevan Moljević. The work emphasized that the state drew its strength from the degree to which its population identifies itself within the state, contrary to the presumptions of Ilija Garašanin, who believed that the ... (Discourse by Stevan Moljević advocating for Greater Serbia) [65%] 2023-12-10 [1941 documents] [1941 in Yugoslavia]...
13. Homogeneous relation: In mathematics, a homogeneous relation (also called endorelation) on a set X is a binary relation between X and itself, i.e. it is a subset of the Cartesian product X × X. (Binary relation over a set and itself) [65%] 2023-11-16 [Binary relations]
14. Homogeneous catalysis: In chemistry, homogeneous catalysis is catalysis by a soluble catalyst in a solution. Homogeneous catalysis refers to reactions where the catalyst is in the same phase as the reactants, principally in solution. (Chemistry) [65%] 2023-10-26 [Homogeneous catalysis] [Catalysis]...
15. Homogeneous function: of degree $ \lambda $ A function $ f $ such that for all points $ ( x _ {1} \dots x _ {n} ) $ in its domain of definition and all real $ t > 0 $, the equation $$ f ( t x _ {1} \dots t x _ {n ... (Mathematics) [65%] 2023-09-16
16. Homogeneous mixture: A homogeneous mixture is a mixture whose composition is consistent through out the entire volume of the mixture. An example of a homogeneous mixture is lightly salted water; no matter where in the sample the concentration is measured it will ... [65%] 2023-02-15 [Solution Chemistry] [Chemistry]...
17. Homogeneous variety: In algebraic geometry, a homogeneous variety is an algebraic variety of the form G/P, G a linear algebraic group, P a parabolic subgroup. It is a smooth projective variety. [65%] 2024-02-06 [Algebraic varieties]
18. Homogeneous alignment: In liquid crystals homogeneous alignment, sometimes called planar alignment, is the state of alignment where molecules align in parallel to a substrate. The opposite method is homeotropic alignment. (Chemistry) [65%] 2024-01-01 [Liquid crystals]
19. Homogeneous function: In mathematics, a function f, is homogeneous of degree p, if The degree of homogeneity p is a positive integral number. Let f be differentiable and homogeneous of order p, then By the chain rule From the homogeneity, Compare Eqs ... [65%] 2023-05-21
20. Homogeneous tree: In descriptive set theory, a tree over a product set \displaystyle{ Y\times Z }[/math] is said to be homogeneous if there is a system of measures \displaystyle{ \langle\mu_s\mid s\in{}^{\lt \omega}Y\rangle }[/math] such that ... [65%] 2022-02-09 [Descriptive set theory]