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Extensions
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 Fields ... [...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] |
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] |
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 (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] |
Extensions (Ahmad Jamal Album)
''Extensions'' is an album by American jazz pianist Ahmad Jamal featuring performances recorded in 1965 and released on the Argo label.Ahmad Jamal discography accessed May 18, 2012 Critical reception awarded the album 3 stars.Allmusic Reviewaccessed May 18, 20121 Track listing # "Extensions" (Ahmad Jamal) – 13:10 # "Dance to the Lady" () – 5:50 # "This Terr ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extensible Cardinal
In mathematics, extendible cardinals are large cardinals introduced by , who was partly motivated by reflection principles. Intuitively, such a cardinal represents a point beyond which initial pieces of the universe of sets start to look similar, in the sense that each is elementarily embeddable into a later one. Definition For every ordinal ''η'', a cardinal κ is called η-extendible if for some ordinal ''λ'' there is a nontrivial elementary embedding ''j'' of ''V''κ+η into ''V''λ, where ''κ'' is the critical point of ''j'', and as usual ''Vα'' denotes the ''α''th level of the von Neumann hierarchy. A cardinal ''κ'' is called an extendible cardinal if it is ''η''-extendible for every nonzero ordinal ''η'' (Kanamori 2003). Variants and relation to other cardinals A cardinal ''κ'' is called ''η-C(n)''-extendible if there is an elementary embedding ''j'' witnessing that ''κ'' is ''η''-extendible (that is, ''j'' is elementary from ''Vκ+η'' to some ''Vλ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extension By Definitions
In mathematical logic, more specifically in the proof theory of first-order theories, extensions by definitions formalize the introduction of new symbols by means of a definition. For example, it is common in naive set theory to introduce a symbol \emptyset for the set which has no member. In the formal setting of first-order theories, this can be done by adding to the theory a new constant \emptyset and the new axiom \forall x(x\notin\emptyset), meaning "for all ''x'', ''x'' is not a member of \emptyset". It can then be proved that doing so adds essentially nothing to the old theory, as should be expected from a definition. More precisely, the new theory is a conservative extension of the old one. Definition of relation symbols ''Let'' T be a first-order theory and \phi(x_1,\dots,x_n) a formula of T such that x_1, ..., x_n are distinct and include the variables free in \phi(x_1,\dots,x_n). Form a new first-order theory T' from T by adding a new n-ary relation symbol R, the logical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mystic Moods Orchestra
The Mystic Moods Orchestra was a group known for mixing orchestral pop, environmental sounds, and pioneering recording techniques. It was created by audiophile Brad Miller. The first Mystic Moods Orchestra album, ''One Stormy Night'', was released in 1966 through the label Philips. Throughout the rest of the 1960s and 1970s, the group continued to release similar styled recordings and their recordings continued to be reissued throughout the 1980s and 1990s. History Brad Miller was born in Burbank, California, and had developed an interest in railroading in his teens. After a few years of hanging around railyards and learning all the lore of steam and diesel engines, he decided to record the sounds of some of the last steam locomotives operating on a major rail line. Eventually, around 1958, he and his friend, Jim Connella, formed a company called Mobile Fidelity Records and started cutting records from these field recordings, which they released through railroading magazines and mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Joint
A joint or articulation (or articular surface) is the connection made between bones, ossicles, or other hard structures in the body which link an animal's skeletal system into a functional whole.Saladin, Ken. Anatomy & Physiology. 7th ed. McGraw-Hill Connect. Webp.274/ref> They are constructed to allow for different degrees and types of movement. Some joints, such as the knee, elbow, and shoulder, are self-lubricating, almost frictionless, and are able to withstand compression and maintain heavy loads while still executing smooth and precise movements. Other joints such as sutures between the bones of the skull permit very little movement (only during birth) in order to protect the brain and the sense organs. The connection between a tooth and the jawbone is also called a joint, and is described as a fibrous joint known as a gomphosis. Joints are classified both structurally and functionally. Classification The number of joints depends on if sesamoids are included, age of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extension (anatomy)
Motion, the process of movement, is described using specific anatomical terms. Motion includes movement of organs, joints, limbs, and specific sections of the body. The terminology used describes this motion according to its direction relative to the anatomical position of the body parts involved. Anatomists and others use a unified set of terms to describe most of the movements, although other, more specialized terms are necessary for describing unique movements such as those of the hands, feet, and eyes. In general, motion is classified according to the anatomical plane it occurs in. ''Flexion'' and ''extension'' are examples of ''angular'' motions, in which two axes of a joint are brought closer together or moved further apart. ''Rotational'' motion may occur at other joints, for example the shoulder, and are described as ''internal'' or ''external''. Other terms, such as ''elevation'' and ''depression'', describe movement above or below the horizontal plane. Many anatomic ... [...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, 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] |
