Homogeneity is a sameness of constituent structure.
Homogeneity, homogeneous, or homogenization may also refer to:
In mathematics
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Transcendental law of homogeneity of Leibniz
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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 ' ...
for a Lie group G, or more general transformation group
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Homogeneous function
In mathematics, a homogeneous function is a function of several variables such that, if all its arguments are multiplied by a scalar, then its value is multiplied by some power of this scalar, called the degree of homogeneity, or simply the ''deg ...
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Homogeneous polynomial
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Homogeneous equation (linear algebra): systems of linear equations with zero constant term
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Homogeneous differential equation
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Homogeneous distribution
In mathematics, a homogeneous distribution is a distribution ''S'' on Euclidean space R''n'' or that is homogeneous in the sense that, roughly speaking,
:S(tx) = t^m S(x)\,
for all ''t'' > 0.
More precisely, let \mu_t : x\mapsto x/t be the scala ...
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Homogeneous linear transformation
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Homogeneous relation: binary relation on a set
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Asymptotic homogenization, a method to study partial differential equations with highly oscillatory coefficients
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Homogenization of a 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, x^5 + 2 x^3 y^2 + 9 x y^4 is a homogeneous polynomial of degree 5, in two variables; t ...
, a mathematical operation
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Homogeneous (large cardinal property) In set theory and in the context of a large cardinal property, a subset, ''S'', of ''D'' is homogeneous for a function ''f'' if ''f'' is constant in finite subsets of ''S''. More precisely, given a set ''D'', let \mathcal_(D) be the set of all finit ...
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Homogeneous coordinates, used in projective spaces
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Homogeneous element and homogeneous ideal in a graded ring
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Homogeneous model in model theory
In statistics
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Homogeneity (statistics)
In statistics, homogeneity and its opposite, heterogeneity, arise in describing the properties of a dataset, or several datasets. They relate to the validity of the often convenient assumption that the statistical properties of any one part of a ...
, logically consistent data matrices
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Homogeneity of variance
In chemistry
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Homogeneous catalysis, a sequence of chemical reactions that involve a catalyst in the same phase as the reactants
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Homogeneous (chemistry), a property of a mixture showing no variation in properties
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Homogenization (chemistry)
Homogenization or homogenisation is any of several processes used to make a mixture of two mutually non-soluble liquids the same throughout. This is achieved by turning one of the liquids into a state consisting of extremely small particles distr ...
, intensive mixing of mutually insoluble substance or groups of substance to obtain a soluble suspension or constant
Other uses
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Homogeneity (physics)
In physics, a homogeneous material or system has the same properties at every point; it is uniform without irregularities.
(accessed November 16, 2009).
Tanton, James.
"homogeneous."
Encyclopedia of Mathematics.
New York: Facts On File, Inc., 2 ...
, translational invariance or compatibility of units in equations
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Homogenization (climate)
Homogenization in climate research means the removal of non-climatic changes. Next to changes in the climate itself, raw climate records also contain non-climatic jumps and changes, for example due to relocations or changes in instrumentation. Th ...
, the process of removing non-climatic changes from climate data
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Homogenization (biology), a process that involves breaking apart cells — releasing organelles and cytoplasm
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Homogeneity (ecology), all of the same or similar kind or nature
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Milk#Creaming and homogenization, to prevent separation of the cream
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Heterogeneity (disambiguation)
Heterogeneity is a diverseness of constituent structure.
Heterogeneity or heterogeneous may also refer to:
Data analysis
* Heterogeneity in statistics
* Heterogeneity in economics
* Study heterogeneity, a concept in statistics
* Heterogeneous ...
, links relating to objects or systems consisting of multiple items having a large number of structural variations
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Monoculturalism
Monoculturalism is the policy or process of supporting, advocating, or allowing the expression of the culture of a single social or ethnic group. It generally stems from beliefs within the dominant group that their cultural practices are superior t ...
, ethnic homogeneity or the advocacy of it
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Zygosity
See also
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{{disambiguation