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Parametrization (other)
Parametrization, also spelled parameterization, parametrisation or parameterisation, is the process of defining or choosing parameters. Parametrization may refer more specifically to: * Parametrization (geometry), the process of finding parametric equations of a curve, surface, etc. ** Parametrization by arc length, a natural parametrization of a curve * Parameterization theorem or ''s''''mn'' theorem, a result in computability theory * Parametrization (atmospheric modeling) Parametrization (or parameterization) in an atmospheric model (either weather model or climate model) is a method of replacing processes that are too small-scale or complex to be physically represented in the model by a simplified process. This can ..., a method of approximating complex processes See also * Parameter (other) * All pages with titles containing ''Parametrization'' (or a spelling variant) {{dab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parameter
A parameter (), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical, when identifying the system, or when evaluating its performance, status, condition, etc. ''Parameter'' has more specific meanings within various disciplines, including mathematics, computer programming, engineering, statistics, logic, linguistics, and electronic musical composition. In addition to its technical uses, there are also extended uses, especially in non-scientific contexts, where it is used to mean defining characteristics or boundaries, as in the phrases 'test parameters' or 'game play parameters'. Modelization When a system theory, system is modeled by equations, the values that describe the system are called ''parameters''. For example, in mechanics, the masses, the dimensions and shapes (for solid bodies), the densities and t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parametrization (geometry)
In mathematics, and more specifically in geometry, parametrization (or parameterization; also parameterisation, parametrisation) is the process of finding parametric equations of a curve, a surface, or, more generally, a manifold or a variety, defined by an implicit equation. The inverse process is called implicitization. "To parameterize" by itself means "to express in terms of parameters". Parametrization is a mathematical process consisting of expressing the state of a system, process or model as a function of some independent quantities called parameters. The state of the system is generally determined by a finite set of coordinates, and the parametrization thus consists of one function of several real variables for each coordinate. The number of parameters is the number of degrees of freedom of the system. For example, the position of a point that moves on a curve in three-dimensional space is determined by the time needed to reach the point when starting from a fixed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parametrization By Arc Length
Differential geometry of curves is the branch of geometry that deals with smooth curves in the plane and the Euclidean space by methods of differential and integral calculus. Many specific curves have been thoroughly investigated using the synthetic approach. Differential geometry takes another path: curves are represented in a parametrized form, and their geometric properties and various quantities associated with them, such as the curvature and the arc length, are expressed via derivatives and integrals using vector calculus. One of the most important tools used to analyze a curve is the Frenet frame, a moving frame that provides a coordinate system at each point of the curve that is "best adapted" to the curve near that point. The theory of curves is much simpler and narrower in scope than the theory of surfaces and its higher-dimensional generalizations because a regular curve in a Euclidean space has no intrinsic geometry. Any regular curve may be parametrized by the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parameterization Theorem
In computability theory the ' theorem, written also as "smn-theorem" or "s-m-n theorem" (also called the translation lemma, parameter theorem, and the parameterization theorem) is a basic result about programming languages (and, more generally, Gödel numberings of the computable functions) (Soare 1987, Rogers 1967). It was first proved by Stephen Cole Kleene (1943). The name ' comes from the occurrence of an ''S'' with subscript ''n'' and superscript ''m'' in the original formulation of the theorem (see below). In practical terms, the theorem says that for a given programming language and positive integers ''m'' and ''n'', there exists a particular algorithm that accepts as input the source code of a program with free variables, together with ''m'' values. This algorithm generates source code that effectively substitutes the values for the first ''m'' free variables, leaving the rest of the variables free. The smn-theorem states that given a function of two arguments g(x,y) whi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parametrization (atmospheric Modeling)
Parametrization (or parameterization) in an atmospheric model (either weather model or climate model) is a method of replacing processes that are too small-scale or complex to be physically represented in the model by a simplified process. This can be contrasted with other processes—e.g., large-scale flow of the atmosphere—that are explicitly resolved within the models. Associated with these parametrizations are various ''parameters'' used in the simplified processes. Examples include the descent rate of raindrops, convective clouds, simplifications of the atmospheric radiative transfer on the basis of atmospheric radiative transfer codes, and cloud microphysics. Radiative parametrizations are important to both atmospheric and oceanic modeling alike. Atmospheric emissions from different sources within individual grid boxes also need to be parametrized to determine their impact on air quality. Clouds Weather and climate model gridboxes have sides of between and . A typ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
