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Homogeneity (other)
Homogeneity is a sameness of constituent structure. Homogeneity, homogeneous, or homogenization may also refer to: In mathematics * Transcendental law of homogeneity of Leibniz * Homogeneous space for a Lie group G, or more general transformation group * Homogeneous function * Homogeneous polynomial * Homogeneous equation (linear algebra): systems of linear equations with zero constant term * Homogeneous differential equation * Homogeneous distribution * Homogeneous linear transformation * Homogeneous relation: binary relation on a set * Asymptotic homogenization, a method to study partial differential equations with highly oscillatory coefficients * Homogenization of a polynomial, a mathematical operation * Homogeneous (large cardinal property) * Homogeneous coordinates, used in projective spaces * Homogeneous element and homogeneous ideal in a graded ring * Homogeneous model in model theory In statistics * Homogeneity (statistics), logically consistent data matrices * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Homogeneity
Homogeneity and heterogeneity are concepts often used in the sciences and statistics relating to the uniformity of a substance or organism. A material or image that is homogeneous is uniform in composition or character (i.e. color, shape, size, weight, height, distribution, texture, language, income, disease, temperature, radioactivity, architectural design, etc.); one that is heterogeneous is distinctly nonuniform in at least one of these qualities. Heterogeneous Mixtures, in chemistry, is where certain elements are unwillingly combined and, when given the option, will separate. Etymology and spelling The words ''homogeneous'' and ''heterogeneous'' come from Medieval Latin ''homogeneus'' and ''heterogeneus'', from Ancient Greek ὁμογενής (''homogenēs'') and ἑτερογενής (''heterogenēs''), from ὁμός (''homos'', “same”) and ἕτερος (''heteros'', “other, another, different”) respectively, followed by γένος (''genos'', “kind”); -ou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Homogeneous Model
In mathematical logic, model theory is the study of the relationship between formal theories (a collection of sentences in a formal language expressing statements about a mathematical structure), and their models (those structures in which the statements of the theory hold). The aspects investigated include the number and size of models of a theory, the relationship of different models to each other, and their interaction with the formal language itself. In particular, model theorists also investigate the sets that can be defined in a model of a theory, and the relationship of such definable sets to each other. As a separate discipline, model theory goes back to Alfred Tarski, who first used the term "Theory of Models" in publication in 1954. Since the 1970s, the subject has been shaped decisively by Saharon Shelah's stability theory. Compared to other areas of mathematical logic such as proof theory, model theory is often less concerned with formal rigour and closer in spirit t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heterogeneity (other)
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 relation Biology and medicine * Heterogeneous conditions in medicine are those conditions which have several causes/etiologies * A ''heterogeneous taxon'', a taxon that contains a great variety of individuals or sub-taxa; usually this implies that the taxon is an artificial grouping * Genetic heterogeneity, multiple origins causing the same disorder in different individuals. * Allelic heterogeneity, different mutations at the same locus causing the same disorder. Chemistry *A heterogeneous reaction, a reaction in chemical kinetics that takes place at the interface of two or more phases, i.e. between a solid and a gas, a liquid and a gas, or a solid and a liquid *A heterogeneous catalysis, one in which the catalyst is in a different p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Milk
Milk is a white liquid food produced by the mammary glands of mammals. It is the primary source of nutrition for young mammals (including breastfed human infants) before they are able to digest solid food. Immune factors and immune-modulating components in milk contribute to milk immunity. Early- lactation milk, which is called colostrum, contains antibodies that strengthen the immune system, and thus reduces the risk of many diseases. Milk contains many nutrients, including protein and lactose. As an agricultural product, dairy milk is collected from farm animals. In 2011, dairy farms produced around of milk from 260 million dairy cows. India is the world's largest producer of milk and the leading exporter of skimmed milk powder, but it exports few other milk products. Because there is an ever-increasing demand for dairy products within India, it could eventually become a net importer of dairy products. New Zealand, Germany and the Netherlands are the largest export ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Homogeneity (ecology)
In ecology, species homogeneity is a lack of biodiversity. Species richness is the fundamental unit in which to assess the homogeneity of an environment. Therefore, any reduction in species richness, especially endemic species, could be argued as advocating the production of a homogeneous environment. Monocultures Homogeneity in agriculture and forestry; in particular, industrial agriculture and forestry use a limited number of species. About 7,000 plants (2.6% of all plant species) have been collected or cultivated for human consumption. Of these, a mere 200 have been domesticated and only a dozen contribute about 75% of the global intake of plant-derived calories. 95% of world consumption of protein derives from a few domesticated species, i.e. poultry, cattle and pigs. There are about 1,000 commercial fish species, but in aquaculture fewer than 10 species dominate global production. Human food production therefore rests on the tips of pyramids of biodiversity, leaving the major ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Homogenization (biology)
Homogenization, in cell biology or molecular biology, is a process whereby different fractions of a biological sample become equal in composition. It can be a disease sign in histopathology, or an intentional process in research: A homogenized sample is equal in composition throughout, so that removing a fraction does not alter the overall molecular make-up of the sample remaining, and is identical to the fraction removed. Induced homogenization in biology is often followed by molecular extraction and various analytical techniques, including ELISA and western blot. Methods Homogenization of tissue in solution is often performed simultaneously with cell lysis. To prevent lysis however, the tissue (or collection of cells, e.g. from cell culture) can be kept at temperatures slightly above zero to prevent autolysis, and in an isotonic solution to prevent osmotic damage. If freezing the tissue is possible, cryohomogenization can be performed under "dry" conditions, and is often the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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. The most used principle to remove these inhomogeneities is the relative homogenization approach in which a candidate station is compared to a reference time series based on one or more neighboring stations. The candidate and reference station(s) experience about the same climate, non-climatic changes that happen only in one station can thus be identified and removed. Climate observations To study climate change and variability, long instrumental climate records are essential, but are best not used directly. These datasets are essential since they are the basis for assessing century-scale trends or for studying the natural (long-term) variability of climate, amongst others. The value of these datasets, however, strongly depends on the homoge ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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., 2005. Science Online. Facts On File, Inc. "A polynomial in several variables p(x,y,z,…) is called homogeneous ..more generally, a function of several variables f(x,y,z,…) is homogeneous ..Identifying homogeneous functions can be helpful in solving differential equations ndany formula that represents the mean of a set of numbers is required to be homogeneous. In physics, the term homogeneous describes a substance or an object whose properties do not vary with position. For example, an object of uniform density is sometimes described as homogeneous." James. homogeneous (math). (accessed: 2009-11-16) A uniform electric field (which has the same strength and the same direction at each point) would be compatible with homogeneity (all po ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 distributed uniformly throughout the other liquid. A typical example is the homogenization of milk, wherein the milk fat globules are reduced in size and dispersed uniformly through the rest of the milk. Definition Homogenization (from "homogeneous;" Greek, ''homogenes'': ''homos,'' same + ''genos,'' kind) is the process of converting two immiscible liquids (i.e. liquids that are not soluble, in all proportions, one in another) into an emulsion (Mixture of two or more liquids that are generally immiscible). Sometimes two types of homogenization are distinguished: primary homogenization, when the emulsion is created directly from separate liquids; and secondary homogenization, when the emulsion is created by the reduction in size of droplets ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Homogeneous (chemistry)
In chemistry, a mixture is a material made up of two or more different chemical substances which are not chemically bonded. A mixture is the physical combination of two or more substances in which the identities are retained and are mixed in the form of solutions, suspensions and colloids. Mixtures are one product of mechanically blending or mixing chemical substances such as elements and compounds, without chemical bonding or other chemical change, so that each ingredient substance retains its own chemical properties and makeup. Despite the fact that there are no chemical changes to its constituents, the physical properties of a mixture, such as its melting point, may differ from those of the components. Some mixtures can be separated into their components by using physical (mechanical or thermal) means. Azeotropes are one kind of mixture that usually poses considerable difficulties regarding the separation processes required to obtain their constituents (physical or chemical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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. In contrast, heterogeneous catalysis describes processes where the catalysts and substrate are in distinct phases, typically solid-gas, respectively. The term is used almost exclusively to describe solutions and implies catalysis by organometallic compounds. Homogeneous catalysis is an established technology that continues to evolve. An illustrative major application is the production of acetic acid. Enzymes are examples of homogeneous catalysts. Examples Acid catalysis The proton is a pervasive homogeneous catalyst because water is the most common solvent. Water forms protons by the process of self-ionization of water. In an illustrative case, acids accelerate (catalyze) the hydrolysis of esters: :CH3CO2CH3 + H2O CH3CO2H + CH3OH At neutral pH, aqueous solutions of m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Homogeneity Of Variance
In statistics, a sequence (or a vector) of random variables is homoscedastic () if all its random variables have the same finite variance. This is also known as homogeneity of variance. The complementary notion is called heteroscedasticity. The spellings ''homoskedasticity'' and ''heteroskedasticity'' are also frequently used. Assuming a variable is homoscedastic when in reality it is heteroscedastic () results in unbiased but inefficient point estimates and in biased estimates of standard errors, and may result in overestimating the goodness of fit as measured by the Pearson coefficient. The existence of heteroscedasticity is a major concern in regression analysis and the analysis of variance, as it invalidates statistical tests of significance that assume that the modelling errors all have the same variance. While the ordinary least squares estimator is still unbiased in the presence of heteroscedasticity, it is inefficient and generalized least squares should be used ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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