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Torus (other)
A torus, pl. tori, is a type of surface. Torus may also refer to: Music * ''Torus'' (album), a 2013 album by Sub Focus *''Torus'', a 2017 EP by Merzbow (Masami Akita) Science and technology Architecture * A semicircular molding – see Molding (decorative)#Types Astrophysics *Three-torus model of the universe, a model for describing the shape of the universe Biology * Receptacle (botany), the thickened part of a stem from which the flower and fruit parts grow * Sagittal keel, or sagittal torus, a structure found in crania * Torus, a structure of the xylem Mathematics * Torus knot * Algebraic torus * Umbilic torus * Genus-2 surface, also called "double torus" * Maximal torus * Clifford torus Medicine * Torus palatinus, a bony growth on the palate * Torus mandibularis, a bony growth on the mandible * Torus tubarius, the base of the opening of Eustachian tube into the nasopharynx * Torus fracture, a term used in radiology to describe an incomplete fracture ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Torus
In geometry, a torus (plural tori, colloquially donut or doughnut) is a surface of revolution generated by revolving a circle in three-dimensional space about an axis that is coplanar with the circle. If the axis of revolution does not touch the circle, the surface has a ring shape and is called a torus of revolution. If the axis of revolution is tangent to the circle, the surface is a horn torus. If the axis of revolution passes twice through the circle, the surface is a spindle torus. If the axis of revolution passes through the center of the circle, the surface is a degenerate torus, a double-covered sphere. If the revolved curve is not a circle, the surface is called a ''toroid'', as in a square toroid. Real-world objects that approximate a torus of revolution include swim rings, inner tubes and ringette rings. Eyeglass lenses that combine spherical and cylindrical correction are toric lenses. A torus should not be confused with a '' solid torus'', which is formed by r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maximal Torus
In the mathematical theory of compact Lie groups a special role is played by torus subgroups, in particular by the maximal torus subgroups. A torus in a compact Lie group ''G'' is a compact, connected, abelian Lie subgroup of ''G'' (and therefore isomorphic to the standard torus T''n''). A maximal torus is one which is maximal among such subgroups. That is, ''T'' is a maximal torus if for any torus ''T''′ containing ''T'' we have ''T'' = ''T''′. Every torus is contained in a maximal torus simply by dimensional considerations. A noncompact Lie group need not have any nontrivial tori (e.g. R''n''). The dimension of a maximal torus in ''G'' is called the rank of ''G''. The rank is well-defined since all maximal tori turn out to be conjugate. For semisimple groups the rank is equal to the number of nodes in the associated Dynkin diagram. Examples The unitary group U(''n'') has as a maximal torus the subgroup of all diagonal matrices. That is, : T = \left\. ''T'' is clearl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Torus (housing Association)
Torus (officially Torus62 Ltd, a Community Benefit Society no 7973) is a housing association in North West England. Torus is the parent organisation of Liverpool Mutual Homes, Helena Partnerships (in St Helens) and Golden Gates Housing Trust (in Warrington). Liverpool Liverpool Mutual Homes is a tenant-led housing association in Merseyside Merseyside ( ) is a metropolitan and ceremonial county in North West England, with a population of 1.38 million. It encompasses both banks of the Mersey Estuary and comprises five metropolitan boroughs: Knowsley, St Helens, Sefton, Wi ... The housing association manages more than 15,000 homes across the county, all of which were either previously owned by Liverpool City Council or are new developments. The main offices of the organisation are based on Old Haymarket, Liverpool. St Helens Helena Housing Ltd formed in 2001 to manage housing owned by St Helens Metropolitan Borough Council. Warrington Golden Gates was owned by Warr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Joint European Torus
The Joint European Torus, or JET, is an operational magnetically confined plasma physics experiment, located at Culham Centre for Fusion Energy in Oxfordshire, UK. Based on a tokamak design, the fusion research facility is a joint European project with a main purpose of opening the way to future nuclear fusion grid energy. At the time of its design JET was larger than any comparable machine. JET was built with the hope of reaching ''scientific breakeven'' where the fusion energy gain factor ''Q'' =1.0. It began operation in 1983 and spent most of the next decade increasing its performance in a lengthy series of experiments and upgrades. In 1991 the first experiments including tritium were made, making JET the first reactor in the world to run on the production fuel of a 50–50 mix of tritium and deuterium. It was also decided to add a divertor design to JET, which occurred between 1991 and 1993. Performance was significantly improved, and in 1997 JET set the record for the cl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Torus (nuclear Physics)
A tokamak (; russian: токамáк; otk, 𐱃𐰸𐰢𐰴, Toḳamaḳ) is a device which uses a powerful magnetic field to confine plasma in the shape of a torus. The tokamak is one of several types of magnetic confinement devices being developed to produce controlled thermonuclear fusion power. , it was the leading candidate for a practical fusion reactor. Tokamaks were initially conceptualized in the 1950s by Soviet physicists Igor Tamm and Andrei Sakharov, inspired by a letter by Oleg Lavrentiev. The first working tokamak was attributed to the work of Natan Yavlinsky on the T-1 in 1958. It had been demonstrated that a stable plasma equilibrium requires magnetic field lines that wind around the torus in a helix. Devices like the z-pinch and stellarator had attempted this, but demonstrated serious instabilities. It was the development of the concept now known as the safety factor (labelled ''q'' in mathematical notation) that guided tokamak development; by arranging th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Torus Fracture
A Torus fracture, also known as a buckle fracture is the most common fracture in children. It is a common occurrence following a fall, as the wrist absorbs most of the impact and compresses the bony cortex on one side and remains intact on the other, creating a bulging effect. As the bulge is only on one side of the bone, this injury is can be classified as an incomplete fracture. The compressive force is provided by the trabeculae and is longitudinal to the axis of the long bone. The word "torus" originates from the Latin word "protuberance." Signs and symptoms Torus fractures are low risk and may cause acute pain. As the bone buckles (or crushes), instead of breaking, they are a stable injury as there is no displacement of the bone. This mechanism is analogous to the crumple zones in cars. As with other fractures, the site of fracture may be tender to touch and cause a sharp pain if pressure is exerted on the injured area. Risk factors Physical activities or sports such as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Torus Tubarius
The base of the cartilaginous portion of the Eustachian tube (auditory tube) lies directly under the mucous membrane of the nasal part of the pharynx, where it forms an elevation or cushion, the torus tubarius or torus of the auditory tube, behind the pharyngeal orifice of the tube. The torus tubarius is very close to the tubal tonsil, which is sometimes also called the ''tonsil of (the) torus tubarius''. Two folds run posteriorly and anteriorly: *posteriorly, the vertical fold of mucous membrane, the salpingopharyngeal fold, stretches from the lower part of the torus tubarius; it contains the Salpingopharyngeus muscle which originates from the superior border of the medial lamina of the cartilage of the auditory tube, and passes downward and blends with the posterior fasciculus of the palatopharyngeus muscle. *anteriorly, the second and smaller fold, the salpingopalatine fold, smaller than the salpingopharyngeal fold, contains some fibers of muscle, called ''salpingopalatine musc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Torus Mandibularis
Torus mandibularis is a bone, bony exostosis, growth in the Human mandible, mandible along the surface nearest to the tongue. Mandibular tori are usually present near the premolars and above the location of the mylohyoid muscle's attachment to the mandible. In 90% of cases, there is a torus on both the left and right sides. The prevalence of mandibular tori ranges from 5-40%. It is less common than bony growths occurring on the palate, known as torus palatinus. Mandibular tori are more common in Asian and Inuit populations, and slightly more common in males. In the United States, the prevalence is 7-10% of the population. It is believed that mandibular tori are caused by several factors. They are more common in early adulthood and are associated with bruxism. The size of the tori may fluctuate throughout life, and in some cases the tori can be large enough to touch each other in the midline of mouth. Consequently, it is believed that mandibular tori are the result of local stresse ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Torus Palatinus
A torus palatinus (pl. tori palatini), or palatal torus (pl. palatal tori), is a bony protrusion on the palate. Palatal tori are usually present on the midline of the hard palate.Neville, B.W., D. Damm, C. Allen, J. Bouquot. ''Oral & Maxillofacial Pathology''. Second edition. 2002. Page 20. . Most palatal tori are less than 2 cm in diameter, but their size can change throughout life. Types Sometimes, the tori are categorized by their appearance. Arising as a broad base and a smooth surface, flat tori are located on the midline of the palate and extend symmetrically to either side. Spindle tori have a ridge located at their midline. Nodular tori have multiple bony growths that each have their own base. Lobular tori have multiple bony growths with a common base. Cause Although some research suggest palatal tori to be an autosomal dominant trait, it is generally believed that palatal tori are caused by several factors. They are more common in early adult life and can increase ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clifford Torus
In geometric topology, the Clifford torus is the simplest and most symmetric flat embedding of the cartesian product of two circles ''S'' and ''S'' (in the same sense that the surface of a cylinder is "flat"). It is named after William Kingdon Clifford. It resides in R4, as opposed to in R3. To see why R4 is necessary, note that if ''S'' and ''S'' each exists in its own independent embedding space R and R, the resulting product space will be R4 rather than R3. The historically popular view that the cartesian product of two circles is an R3 torus in contrast requires the highly asymmetric application of a rotation operator to the second circle, since that circle will only have one independent axis ''z'' available to it after the first circle consumes ''x'' and ''y''. Stated another way, a torus embedded in R3 is an asymmetric reduced-dimension projection of the maximally symmetric Clifford torus embedded in R4. The relationship is similar to that of projecting the edges of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Genus-2 Surface
In mathematics, a genus ''g'' surface (also known as a ''g''-torus or ''g''-holed torus) is a surface formed by the connected sum of ''g'' many tori: the interior of a disk is removed from each of ''g'' many tori and the boundaries of the ''g'' many disks are identified (glued together), forming a ''g''-torus. The genus of such a surface is ''g''. A genus ''g'' surface is a two-dimensional manifold. The classification theorem for surfaces states that every compact connected two-dimensional manifold is homeomorphic to either the sphere, the connected sum of tori, or the connected sum of real projective planes. Definition of genus The genus of a connected orientable surface is an integer representing the maximum number of cuttings along non-intersecting closed simple curves without rendering the resultant manifold disconnected. It is equal to the number of handles on it. Alternatively, it can be defined in terms of the Euler characteristic ''χ'', via the relationship ''χ''&nb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Torus (album)
''Torus'' is the second studio album by British DJ and record producer Sub Focus. The album was released on 30 September 2013, through RAM Records, Mercury Records and Virgin EMI Records. Musical concept and songs ''Torus'' is the geometric name for the shape in Sub Focus' logo. It was originally used on his debut album cover and the shape has played a big part in his live shows as well as in promotion and artwork. The title track was written as an intro to Douwma's live sets, in preparation for a Brixton performance in 2012. He wanted to start his sets with a low tempo and gradually speed up. "Safe in Sound" was one of the earliest tracks to be completed and was written with Seton Daunt and later given the Mary O'Hara sample. "Endorphins" originally had a female vocalist, and was given to several artists but in the end Alex Clare visited Nick's studio to record what would be the final version of the track. "Twilight" was written as an ambient contrast to the club-orientated ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
