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Homogenization
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] |
Asymptotic Homogenization
In mathematics and physics, homogenization is a method of studying partial differential equations with rapidly oscillating coefficients, such as : \nabla\cdot\left(A\left(\frac\right)\nabla u_\right) = f where \epsilon is a very small parameter and A\left(\vec y\right) is a 1-periodic coefficient: A\left(\vec y+\vec e_i\right)=A\left(\vec y\right), i=1,\dots, n. It turns out that the study of these equations is also of great importance in physics and engineering, since equations of this type govern the physics of inhomogeneous or heterogeneous materials. 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 properties such as shear modulus, elastic moduli, etc. Frequently, inhomogeneous mat ... [...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] |
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] |
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] |
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] |
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 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; the sum of the exponents in each term is always 5. The polynomial x^3 + 3 x^2 y + z^7 is not homogeneous, because the sum of exponents does not match from term to term. The function defined by a homogeneous polynomial is always a homogeneous function. An algebraic form, or simply form, is a function defined by a homogeneous polynomial. A binary form is a form in two variables. A ''form'' is also a function defined on a vector space, which may be expressed as a homogeneous function of the coordinates over any basis. A polynomial of degree 0 is always homogeneous; it is simply an element of the field or ring of the coefficients, usually called a constant or a scalar. A form of degree 1 is a linear form. A form of degree 2 is a quad ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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; the sum of the exponents in each term is always 5. The polynomial x^3 + 3 x^2 y + z^7 is not homogeneous, because the sum of exponents does not match from term to term. The function defined by a homogeneous polynomial is always a homogeneous function. An algebraic form, or simply form, is a function defined by a homogeneous polynomial. A binary form is a form in two variables. A ''form'' is also a function defined on a vector space, which may be expressed as a homogeneous function of the coordinates over any basis. A polynomial of degree 0 is always homogeneous; it is simply an element of the field or ring of the coefficients, usually called a constant or a scalar. A form of degree 1 is a linear form. A form of degree 2 is a quadratic fo ... [...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] |
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 an overall dataset are the same as any other part. In meta-analysis, which combines the data from several studies, homogeneity measures the differences or similarities between the several studies (see also Study heterogeneity). Homogeneity can be studied to several degrees of complexity. For example, considerations of homoscedasticity examine how much the variability of data-values changes throughout a dataset. However, questions of homogeneity apply to all aspects of the statistical distributions, including the location parameter. Thus, a more detailed study would examine changes to the whole of the marginal distribution. An intermediate-level study might move from looking at the variability to studying changes in the skewness. In additi ... [...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] |
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] |
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