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Canonic Variations
The adjective canonical is applied in many contexts to mean "according to the canon" the standard, rule or primary source that is accepted as authoritative for the body of knowledge or literature in that context. In mathematics, "canonical example" is often used to mean "archetype". Science and technology * Canonical form, a natural unique representation of an object, or a preferred notation for some object Mathematics * * Canonical coordinates, sets of coordinates that can be used to describe a physical system at any given point in time * Canonical map, a morphism that is uniquely defined by its main property * Canonical polyhedron, a polyhedron whose edges are all tangent to a common sphere, whose center is the average of its vertices * Canonical ring, a graded ring associated to an algebraic variety * Canonical injection, in set theory * Canonical representative, in set theory a standard member of each element of a set partition Differential geometry * Canonical one-fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Canon (basic Principle)
The term canon derives from the Greek (), meaning "rule", and thence via Latin and Old French into English. The concept in English usage is very broad: in a general sense it refers to being one (adjectival) or a group (noun) of official, authentic or approved rules or laws, particularly ecclesiastical; or group of official, authentic, or approved literary or artistic works, such as the literature of a particular author, of a particular genre, or a particular group of religious scriptural texts; or similarly, one or a body of rules, principles, or standards accepted as axiomatic and universally binding in a religion, or a field of study or art. Examples This principle of grouping has led to more specific uses of the word in different contexts, such as the Biblical canon (which a particular religious community regards as authoritative) and thence to literary canons (of a particular "body of literature in a particular language, or from a particular culture, period, genre"). W.C Sa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Canonical One-form
In mathematics, the tautological one-form is a special 1-form defined on the cotangent bundle T^Q of a manifold Q. In physics, it is used to create a correspondence between the velocity of a point in a mechanical system and its momentum, thus providing a bridge between Lagrangian mechanics with Hamiltonian mechanics (on the manifold Q). The exterior derivative of this form defines a symplectic form giving T^Q the structure of a symplectic manifold. The tautological one-form plays an important role in relating the formalism of Hamiltonian mechanics and Lagrangian mechanics. The tautological one-form is sometimes also called the Liouville one-form, the Poincaré one-form, the canonical one-form, or the symplectic potential. A similar object is the canonical vector field on the tangent bundle. To define the tautological one-form, select a coordinate chart U on T^*Q and a canonical coordinate system on U. Pick an arbitrary point m \in T^*Q. By definition of cotangent bundle, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Canonical Model
A canonical model is a design pattern used to communicate between different data formats. Essentially: create a data model which is a superset of all the others ("canonical"), and create a "translator" module or layer to/from which all existing modules exchange data with other modules. The individual modules can then be considered endpoints on an intelligent bus; the bus centralises all the data-translation intelligence. A form of enterprise application integration, it is intended to reduce costs and standardize on agreed data definitions associated with integrating business systems. A canonical model is any model that is canonical in nature, i.e. a model which is in the simplest form possible based on a standard, application integration (EAI) solution. Most organizations also adopt a set of standards for message structure and content (message payload). The desire for consistent message payload results in the construction of an enterprise or business domain canonical model c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Canonical Link Element
A canonical link element is an HTML element that helps webmasters prevent duplicate content issues in search engine optimization by specifying the "canonical" or "preferred" version of a web page. It is described in RFC 6596, which went live in April 2012. Purpose A major problem for search engines is to determine the original source for documents that are available on multiple URLs. Content duplication can happen in many ways, including: * Duplication due to -parameters * Duplication with multiple URLs due to CMS * Duplication due to accessibility on different hosts/protocols * Duplication due to print versions of websites Duplicate content issues occur when the same content is accessible from multiple URLs. For example, would be considered by search engines to be an entirely different page from , even though both URLs may reference the same content. In February 2009, Google, Yahoo and Microsoft announced support for the canonical link element, which can be inserted into t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Canonical Huffman Code
In computer science and information theory, a canonical Huffman code is a particular type of Huffman code with unique properties which allow it to be described in a very compact manner. Data compressors generally work in one of two ways. Either the decompressor can infer what codebook the compressor has used from previous context, or the compressor must tell the decompressor what the codebook is. Since a canonical Huffman codebook can be stored especially efficiently, most compressors start by generating a "normal" Huffman codebook, and then convert it to canonical Huffman before using it. In order for a symbol code scheme such as the Huffman code to be decompressed, the same model that the encoding algorithm used to compress the source data must be provided to the decoding algorithm so that it can use it to decompress the encoded data. In standard Huffman coding this model takes the form of a tree of variable-length codes, with the most frequent symbols located at the top of th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Microcanonical Ensemble
In statistical mechanics, the microcanonical ensemble is a statistical ensemble that represents the possible states of a mechanical system whose total energy is exactly specified. The system is assumed to be isolated in the sense that it cannot exchange energy or particles with its environment, so that (by conservation of energy) the energy of the system does not change with time. The primary macroscopic variables of the microcanonical ensemble are the total number of particles in the system (symbol: ), the system's volume (symbol: ), as well as the total energy in the system (symbol: ). Each of these is assumed to be constant in the ensemble. For this reason, the microcanonical ensemble is sometimes called the ensemble. In simple terms, the microcanonical ensemble is defined by assigning an equal probability to every microstate whose energy falls within a range centered at . All other microstates are given a probability of zero. Since the probabilities must add up to 1, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Grand Canonical Ensemble
In statistical mechanics, the grand canonical ensemble (also known as the macrocanonical ensemble) is the statistical ensemble that is used to represent the possible states of a mechanical system of particles that are in thermodynamic equilibrium (thermal and chemical) with a reservoir. The system is said to be open in the sense that the system can exchange energy and particles with a reservoir, so that various possible states of the system can differ in both their total energy and total number of particles. The system's volume, shape, and other external coordinates are kept the same in all possible states of the system. The thermodynamic variables of the grand canonical ensemble are chemical potential (symbol: ) and absolute temperature (symbol: . The ensemble is also dependent on mechanical variables such as volume (symbol: which influence the nature of the system's internal states. This ensemble is therefore sometimes called the ensemble, as each of these three quantities ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Canonical Transformation
In Hamiltonian mechanics, a canonical transformation is a change of canonical coordinates that preserves the form of Hamilton's equations. This is sometimes known as form invariance. It need not preserve the form of the Hamiltonian itself. Canonical transformations are useful in their own right, and also form the basis for the Hamilton–Jacobi equations (a useful method for calculating conserved quantities) and Liouville's theorem (itself the basis for classical statistical mechanics). Since Lagrangian mechanics is based on generalized coordinates, transformations of the coordinates do not affect the form of Lagrange's equations and, hence, do not affect the form of Hamilton's equations if we simultaneously change the momentum by a Legendre transformation into P_i=\frac. Therefore, coordinate transformations (also called point transformations) are a ''type'' of canonical transformation. However, the class of canonical transformations is much broader, since the old generalized ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Canonical Conjugate Variables
Conjugate variables are pairs of variables mathematically defined in such a way that they become Fourier transform duals, or more generally are related through Pontryagin duality. The duality relations lead naturally to an uncertainty relation—in physics called the Heisenberg uncertainty principle—between them. In mathematical terms, conjugate variables are part of a symplectic basis, and the uncertainty relation corresponds to the symplectic form. Also, conjugate variables are related by Noether's theorem, which states that if the laws of physics are invariant with respect to a change in one of the conjugate variables, then the other conjugate variable will not change with time (i.e. it will be conserved). Examples There are many types of conjugate variables, depending on the type of work a certain system is doing (or is being subjected to). Examples of canonically conjugate variables include the following: * Time and frequency: the longer a musical note is sustained, the m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Canonical Theory
Joel E. Keizer (31 August, 1942 - 16 May, 1999) was an American biologist and university professor. He is principally known for his work in non-equilibrium thermodynamics and mathematical modelling of cellular phenomena, in particular human production of insulin. Canonical theory Canonical theory is a molecular theory developed by Keizer and coworkers which claims to explain many physical, chemical, and biological processes in an unified and canonical way. Ronald F. Fox and Keizer showed the application of the canonical theory to chaos. Keizer used the canonical form for the first formulation of statistical thermodynamics valid in far from equilibrium regimes, where the Onsager reciprocal relations and the Albert Einstein formula for the fluctuations do not work. Keizer also provided fluctuating generalizations of the Boltzmann equation and of hydrodynamics (fluctuating hydrodynamics). The applications of his work to biology are the reason that he was considered as one of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Canonical Stress–energy Tensor
The adjective canonical is applied in many contexts to mean "according to the canon" the standard, rule or primary source that is accepted as authoritative for the body of knowledge or literature in that context. In mathematics, "canonical example" is often used to mean "archetype". Science and technology * Canonical form, a natural unique representation of an object, or a preferred notation for some object Mathematics * * Canonical coordinates, sets of coordinates that can be used to describe a physical system at any given point in time * Canonical map, a morphism that is uniquely defined by its main property * Canonical polyhedron, a polyhedron whose edges are all tangent to a common sphere, whose center is the average of its vertices * Canonical ring, a graded ring associated to an algebraic variety * Canonical injection, in set theory * Canonical representative, in set theory a standard member of each element of a set partition Differential geometry * Canonical one-form, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Canonical Quantum Gravity
In physics, canonical quantum gravity is an attempt to quantize the canonical formulation of general relativity (or canonical gravity). It is a Hamiltonian formulation of Einstein's general theory of relativity. The basic theory was outlined by Bryce DeWitt in a seminal 1967 paper, and based on earlier work by Peter G. Bergmann using the so-called canonical quantization techniques for constrained Hamiltonian systems invented by Paul Dirac. Dirac's approach allows the quantization of systems that include gauge symmetries using Hamiltonian techniques in a fixed gauge choice. Newer approaches based in part on the work of DeWitt and Dirac include the Hartle–Hawking state, Regge calculus, the Wheeler–DeWitt equation and loop quantum gravity. Canonical quantization In the Hamiltonian formulation of ordinary classical mechanics the Poisson bracket is an important concept. A "canonical coordinate system" consists of canonical position and momentum variables that satisfy canoni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
