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Extension
Extension, extend or extended may refer to: Mathematics Logic or set theory * Axiom of extensionality * Extensible cardinal * Extension (model theory) * Extension (predicate logic), the set of tuples of values that satisfy the predicate * Extension (semantics), the set of things to which a property applies * Extension by definitions * Extensional definition, a definition that enumerates every individual a term applies to * Extensionality Other uses * Extension of a polyhedron, in geometry * Exterior algebra, Grassmann's theory of extension, in geometry * Homotopy extension property, in topology * Kolmogorov extension theorem, in probability theory * Linear extension, in order theory * Sheaf extension, in algebraic geometry * Tietze extension theorem, in topology * Whitney extension theorem, in differential geometry * Group extension, in abstract algebra and homological algebra Music * Extension (music), notes that fit outside the standard range * ''Extended'' (Solar Field ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extensions (The Manhattan Transfer Album)
Extension, extend or extended may refer to: Mathematics Logic or set theory * Axiom of extensionality * Extensible cardinal * Extension (model theory) * Extension (predicate logic), the set of tuples of values that satisfy the predicate * Extension (semantics), the set of things to which a property applies * Extension by definitions * Extensional definition, a definition that enumerates every individual a term applies to * Extensionality Other uses * Extension of a polyhedron, in geometry * Exterior algebra, Grassmann's theory of extension, in geometry * Homotopy extension property, in topology * Kolmogorov extension theorem, in probability theory * Linear extension, in order theory * Sheaf extension, in algebraic geometry * Tietze extension theorem, in topology * Whitney extension theorem, in differential geometry * Group extension, in abstract algebra and homological algebra Music * Extension (music), notes that fit outside the standard range * ''Extended'' (Solar Field ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extensional Definition
In logic, extensional and intensional definitions are two key ways in which the objects, concepts, or referents a term refers to can be defined. They give meaning or denotation to a term. Intensional definition An intensional definition gives meaning to a term by specifying necessary and sufficient conditions for when the term should be used. In the case of nouns, this is equivalent to specifying the properties that an object needs to have in order to be counted as a referent of the term. For example, an intensional definition of the word "bachelor" is "unmarried man". This definition is valid because being an unmarried man is both a necessary condition and a sufficient condition for being a bachelor: it is necessary because one cannot be a bachelor without being an unmarried man, and it is sufficient because any unmarried man is a bachelor.Cook, Roy T. "Intensional Definition". In ''A Dictionary of Philosophical Logic''. Edinburgh: Edinburgh University Press, 2009. 155. This i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extension (Clare Fischer Album)
''Extension'' is the third album by composer/arranger/keyboardist Clare Fischer, and his first for big band, recorded and released in 1963 on the Pacific Jazz Records, Pacific Jazz label, reissued on CD (together with the 1967 LP, ''Songs for Rainy Day Lovers'') in 2002 as ''America the Beautiful'', and, under its original name, in 2012. WorldCat. Retrieved 2013-03-18 According to Ed Beach, disk jockey of the WRVR 106.7 FM New York radio program “Just Jazz,” on this album, all of the solos, except for those of Clare Fischer and tenor saxophonist Jerry Coker, were written out (by Fischer), not improvised. Reception Reviewing the 2012 CD reissue for All About Jazz, Troy Collins calls ''Extension'' Fischer's "masterpiece," representing "a majestic culmination of his concepts, drawing up ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extension, British Columbia
Extension is an unincorporated community near the east coast of southern Vancouver Island, British Columbia. The location off BC Highway 19 is about by road northwest of Victoria, and south of Nanaimo. Discovery Louis Stark, an African American, lived in today's Colvilletown neighbourhood of south Nanaimo. Many suspected foul play when his body was found at the bottom of a cliff in 1895. One theory claimed he had refused to sell his coal rich land to Dunsmuir coal, desperately seeking new sources to replace its nearly exhausted Wellington mine. Another rumour suggested he was the discoverer of the coal seam on the southern slope of Mt. Benson. However, after the death, his close neighbour Ephraim (Edward) Hodgson claimed the credit and reward for the discovery. Murder charges against Hodgson were dropped. The Mt. Benson seam proved to be an extension of the Wellington one being worked by Dunsmuir, and the location was initially called Wellington Extension. Railway Thwarted i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Group Extension
In mathematics, a group extension is a general means of describing a group in terms of a particular normal subgroup and quotient group. If Q and N are two groups, then G is an extension of Q by N if there is a short exact sequence :1\to N\;\overset\;G\;\overset\;Q \to 1. If G is an extension of Q by N, then G is a group, \iota(N) is a normal subgroup of G and the quotient group G/\iota(N) is isomorphic to the group Q. Group extensions arise in the context of the extension problem, where the groups Q and N are known and the properties of G are to be determined. Note that the phrasing "G is an extension of N by Q" is also used by some. Since any finite group G possesses a maximal normal subgroup N with simple factor group G/N, all finite groups may be constructed as a series of extensions with finite simple groups. This fact was a motivation for completing the classification of finite simple groups. An extension is called a central extension if the subgroup N lies in the center o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extensions (McCoy Tyner Album)
''Extensions'' is an album by jazz pianist McCoy Tyner released on the Blue Note label. It was recorded on February 9, 1970 but not released until January of 1973. It has performances by Tyner with alto saxophonist Gary Bartz, tenor saxophonist Wayne Shorter, bassist Ron Carter, drummer Elvin Jones, and features Alice Coltrane playing harp on three of the four tracks. Reception In his AllMusic review Scott Yanow says, "The all-star sextet stretches out on lengthy renditions of four of Tyner's modal originals, and there is strong solo space for the leader and the two saxophonists... Stimulating music". Reviewing the album for jazz.com, Jared Pauley says, "McCoy Tyner finds himself among elite company on ''Extensions.'' Recorded as jazz was entering the fusion period, this is a great example of just how good straight-ahead swing can sound... This performance matches the superb quality of previous Shorter and Tyner albums where members of the Davis and Coltrane groups recorded tog ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extension (George Braith Album)
''Extension'' is the third album by American saxophonist George Braith recorded in 1964 and released on the Blue Note Records, Blue Note label.Blue Note Records discography accessed November 17, 2010 Reception The Allmusic review by Stephen Thomas Erlewine awarded the album 4½ stars and stated "George Braith turned in his strongest record with ''Extension''. Largely freed from the restraints of the dueling horns, Braith is able to explore the outer reaches of his music. He still remains grounded in soul-jazz -- any guitar-organ combo is bound to have soul-jazz roots -- but he pushes the music toward adventurous hard bop, often with rewarding results".Erlewine, S. T. [ Allmusic Review] accessed November 16, 2010 Track li ...
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Extension, Louisiana
Extension is an unincorporated community in Franklin Parish, Louisiana, United States. Its ZIP code is 71243. Notable people Singer and songwriter Richard Berry was born in Extension. He is known for writing one of the world's most recorded songs, "Louie Louie "Louie Louie" is a rhythm and blues song written and composed by American musician Richard Berry in 1955, recorded in 1956, and released in 1957. It is best known for the 1963 hit version by the Kingsmen and has become a standard in pop and r ...." Notes Unincorporated communities in Franklin Parish, Louisiana Unincorporated communities in Louisiana {{Louisiana-geo-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exterior Algebra
In mathematics, the exterior algebra, or Grassmann algebra, named after Hermann Grassmann, is an algebra that uses the exterior product or wedge product as its multiplication. In mathematics, the exterior product or wedge product of vectors is an algebraic construction used in geometry to study areas, volumes, and their higher-dimensional analogues. The exterior product of two vectors u and v, denoted by u \wedge v, is called a bivector and lives in a space called the ''exterior square'', a vector space that is distinct from the original space of vectors. The magnitude of u \wedge v can be interpreted as the area of the parallelogram with sides u and v, which in three dimensions can also be computed using the cross product of the two vectors. More generally, all parallel plane surfaces with the same orientation and area have the same bivector as a measure of their oriented area. Like the cross product, the exterior product is anticommutative, meaning t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extensions (Dave Holland Album)
''Extensions'' is an album by jazz bassist Dave Holland released on the ECM label in 1990. The record is Dave Holland's eighth album to be released on the ECM label. It features two members of his previous quintet— saxophonist Steve Coleman and drummer Marvin "Smitty" Smith—alongside guitarist Kevin Eubanks, in his first appearance on a Holland record. Holland recorded "Processional" again on his later sextet album '' Pass It On''. Reception The Allmusic review by Brian Olewnick awarded the album 4 stars, calling it a "tight and enjoyable quartet date" and "One of his better albums from this period, ''Extensions'' should please any Holland fan, and is an agreeable and non-threatening jumping in point for the curious".Olewnick, BAllmusic Reviewaccessed August 19, 2011. ''Extensions'' was voted Album of the Year (1989) by ''Downbeat Magazine''. Track listing # "Nemesis" (Kevin Eubanks) - 11:31 # "Processional" (Dave Holland) - 7:16 # "Black Hole" (Steve Coleman) - 10:10 # ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extension (geology)
Extensional tectonics is concerned with the structures formed by, and the tectonic processes associated with, the stretching of a planetary body's crust or lithosphere. Deformation styles The types of structure and the geometries formed depend on the amount of stretching involved. Stretching is generally measured using the parameter ''β'', known as the ''beta factor'', where : \beta = \frac \,, ''t''0 is the initial crustal thickness and ''t''1 is the final crustal thickness. It is also the equivalent of the strain parameter ''stretch''. Low beta factor In areas of relatively low crustal stretching, the dominant structures are high to moderate angle normal faults, with associated half grabens and tilted fault blocks. High beta factor In areas of high crustal stretching, individual extensional faults may become rotated to too low a dip to remain active and a new set of faults may be generated. Large displacements may juxtapose syntectonic sediments against metamorphic roc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extension (semantics)
In any of several fields of study that treat the use of signs — for example, in linguistics, logic, mathematics, semantics, semiotics, and philosophy of language — the extension of a concept, idea, or sign consists of the things to which it applies, in contrast with its comprehension or intension, which consists very roughly of the ideas, properties, or corresponding signs that are implied or suggested by the concept in question. In philosophical semantics or the philosophy of language, the 'extension' of a concept or expression is the set of things it extends to, or applies to, if it is the sort of concept or expression that a single object by itself can satisfy. Concepts and expressions of this sort are monadic or "one-place" concepts and expressions. So the extension of the word "dog" is the set of all (past, present and future) dogs in the world: the set includes Fido, Rover, Lassie, Rex, and so on. The extension of the phrase "Wikipedia reader" includes each person ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
