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Nagata Dimension
Nagata may refer to: People * Nagata (surname), a family name of Japanese and Fijian origin Places * Mount Nagata, a mountain in Antarctica * Nagata-ku, Kobe, a ward in the city of Kobe * Nagata Shrine, a Shinto shrine in Nagata-ku * Nagata Station (other), a number of Japanese railway stations Mathematics * Nagata–Biran conjecture, an algebraic formula * Nagata dimension or Assouad-Nagata dimension, a notion of dimension for metric spaces * Nagata ring, an integral domain in algebra * Nagata–Smirnov metrization theorem characterizes when a topological space is metrizable * Nagata's compactification theorem, an algebraic formula * Nagata's conjecture, an algebraic formula * Nagata's conjecture on curves, an algebraic formula Other uses * Nagata Acoustics, a Japanese consultancy, specialising in concert halls * ''Nagata Maru The was a Japanese cargo ship owned by Nippon Yusen Kaisha, Tokyo. The ship entered service in 1937. The name ''Nagata Maru'' derives ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nagata (surname)
Nagata is a surname which can be either of Japanese (written: 永田 or 長田) or Fijian origin. Notable people with the surname include: * Akira Nagata (born 1985), Japanese vocalist and actor * Alipate Nagata, Fijian politician * Anna Nagata (born 1982), Japanese actress * Apisai Nagata, Fijian rugby union footballer *Hidejirō Nagata (1876–1943), politician and cabinet minister in the Empire of Japan * Hideo Nagata (1885–1949), Japanese poet and playwright * Hiroko Nagata (1945–2011), Japanese leftist radical *Hiroshi Nagata (1907–1961), Japanese field hockey player * Hisayasu Nagata (1969–2009), Japanese politician * Hisayoshi Nagata (born 1962), Japanese former water polo player * Jun-iti Nagata (1925–2007), Japanese mathematician * Kabi Nagata (born 1987), Japanese manga artist *Katsuhiko Nagata (born 1973), Japanese Olympic wrestler and mixed martial artist *Kazuhiko Nagata (born 1964), Japanese engineer, driver, and entrepreneur (Top Secret) *Linda Nagata (born ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Explorers Range
Explorers Range () is a large mountain range in the Bowers Mountains of Victoria Land, Antarctica, extending from Mount Bruce in the north to Carryer Glacier and McLin Glacier in the south. Exploration and naming The Explorers Range was named by the New Zealand Antarctic Place-Names Committee (NZ-APC) for the northern party of New Zealand Geological Survey Antarctic Expedition (NZGSAE), 1963–64, whose members carried out a topographical and geological survey of the area. The names of several party members are assigned to features in and about this range. Location The Explorers Range is south of the Stuhlinger Ice Piedmont, Cape Cheetham and Gannutz Glacier. The Rennick Glacier flows north to the sea along its western side. Glaciers originating in the northern Explorer Range that flow into this glacier include, from north to south, Arruiz Glacier, Alvarez Glacier and Sheehan Glacier. Ob' Bay is to the east of the northern part of the range, which is fed by glaciers ori ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nagata-ku, Kobe
is one of 9 wards of Kobe, Japan. It has an area of 11.46 km2, and a population of 96,072 (2018). This region suffered the largest number of casualties in the Great Hanshin earthquake The Great Hanshin Earthquake (, ) occurred on January 17, 1995, at 05:46:53 JST in the southern part of Hyōgo Prefecture, Japan, including the region of Hanshin. It measured 6.9 on the moment magnitude scale and had a maximum intensity of 7 o .... Demographics In recent years Nagata-ku's overall population has been decreasing, but the number of foreign residents has been increasing. Nagata-ku now has the largest Korean and Vietnamese communities in Kobe. Education West Kobe Korean Elementary School ( 西神戸朝鮮初級学校), a North Korean school, is in the ward. The South Korean government maintains the Korean Education Center (, ) in this ward. References External links Official website of Nagata-ku, Kobe Wards of Kobe {{Hyogo-geo-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nagata Shrine
is a Shinto shrine in Nagata-ku, Kobe, Japan. At Nagata, Kotoshironushi-no-Okami is enshrined. The shrine is associated with Amaterasu, who is said to have told Empress Jingū that a shrine was wanted at Nagata. History According to the ''Nihon Shoki'', Nagata was founded by Empress Jingū at the beginning of the 3rd century along with Hirota Shrine. In 2001, the shrine celebrated its 1,800 years of history. From 1871 through 1946, the Nagata was officially designated one of the , meaning that it stood in the second tier of government supported shrines which were especially venerated by the imperial family. Festivals and events An autumn matsuri in October is a special day ('' en'nichi'') for the ''kami'' Kotoshironushi. A '' setsubun'' observance in February is the ''Tsuina-shiki Shinji,'' which engages hopes for safety in the home and averting misfortune. This Shinto purification ritual is designated as an intangible cultural heritage event. The elaborate ceremony is a p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nagata Station (other)
Nagata Station is the name of eight train stations in Japan: * Nagata Station (Saitama) (永田駅) - in Fukaya, Saitama, on the Chichibu Main Line * Nagata Station (Chiba) (永田駅) - in Oamishirasato, Sanbu District, Chiba, on the JR East Sotobo Line * Nagata Station (Osaka) (長田駅) - in Higashiosaka, Osaka, on the Osaka Municipal Subway Chuo Line and the Kintetsu Keihanna Line * Nagata Station (Kobe Municipal Subway) (長田駅) - in Nagata-ku, Kobe, on the Kobe Municipal Subway Seishin-Yamate Line, * Nagata Station (Shintetsu) is a railway station in Nagata-ku, Kobe, Hyōgo Prefecture, Japan. Lines *Kobe Electric Railway , often called , is a Japanese private railway company in Kobe and surrounding cities. It is a subsidiary of Hankyu Hanshin Toho Group. Lines ... (長田駅) - in Nagata-ku, Kobe, on the Kobe Electric Railway Arima Line * Kosoku Nagata Station (高速長田駅) - in Nagata-ku, Kobe, on the Hanshin Railway Kobe Kosoku Line, close to Nagata St ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nagata–Biran Conjecture
In mathematics, the Nagata–Biran conjecture, named after Masayoshi Nagata and Paul Biran, is a generalisation of Nagata's conjecture on curves to arbitrary polarised surfaces. Statement Let ''X'' be a smooth algebraic surface and ''L'' be an ample line bundle In mathematics, a distinctive feature of algebraic geometry is that some line bundles on a projective variety can be considered "positive", while others are "negative" (or a mixture of the two). The most important notion of positivity is that of ... on ''X'' of degree ''d''. The Nagata–Biran conjecture states that for sufficiently large ''r'' the Seshadri constant satisfies : \varepsilon(p_1,\ldots,p_r;X,L) = . References *. *. See in particular page 3 of the pdf. Algebraic surfaces Conjectures {{algebraic-geometry-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nagata Dimension
Nagata may refer to: People * Nagata (surname), a family name of Japanese and Fijian origin Places * Mount Nagata, a mountain in Antarctica * Nagata-ku, Kobe, a ward in the city of Kobe * Nagata Shrine, a Shinto shrine in Nagata-ku * Nagata Station (other), a number of Japanese railway stations Mathematics * Nagata–Biran conjecture, an algebraic formula * Nagata dimension or Assouad-Nagata dimension, a notion of dimension for metric spaces * Nagata ring, an integral domain in algebra * Nagata–Smirnov metrization theorem characterizes when a topological space is metrizable * Nagata's compactification theorem, an algebraic formula * Nagata's conjecture, an algebraic formula * Nagata's conjecture on curves, an algebraic formula Other uses * Nagata Acoustics, a Japanese consultancy, specialising in concert halls * ''Nagata Maru The was a Japanese cargo ship owned by Nippon Yusen Kaisha, Tokyo. The ship entered service in 1937. The name ''Nagata Maru'' derives ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nagata Ring
In commutative algebra, an N-1 ring is an integral domain A whose integral closure in its quotient field is a finitely generated A- module. It is called a Japanese ring (or an N-2 ring) if for every finite extension L of its quotient field K, the integral closure of A in L is a finitely generated A-module (or equivalently a finite A-algebra). A ring is called universally Japanese if every finitely generated integral domain over it is Japanese, and is called a Nagata ring, named for Masayoshi Nagata, or a pseudo-geometric ring if it is Noetherian and universally Japanese (or, which turns out to be the same, if it is Noetherian and all of its quotients by a prime ideal are N-2 rings). A ring is called geometric if it is the local ring of an algebraic variety or a completion of such a local ring, but this concept is not used much. Examples Fields and rings of polynomials or power series in finitely many indeterminates over fields are examples of Japanese rings. Another important exa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nagata–Smirnov Metrization Theorem
In topology, the Nagata–Smirnov metrization theorem characterizes when a topological space In mathematics, a topological space is, roughly speaking, a Geometry, geometrical space in which Closeness (mathematics), closeness is defined but cannot necessarily be measured by a numeric Distance (mathematics), distance. More specifically, a to ... is metrizable. The theorem states that a topological space X is metrizable if and only if it is regular, Hausdorff and has a countably locally finite (that is, -locally finite) basis. A topological space X is called a regular space if every non-empty closed subset C of X and a point p not contained in C admit non-overlapping open neighborhoods. A collection in a space X is countably locally finite (or -locally finite) if it is the union of a countable family of locally finite collections of subsets of X. Unlike Urysohn's metrization theorem, which provides only a sufficient condition for metrizability, this theorem provides both a ne ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nagata's Compactification Theorem
In algebraic geometry, Nagata's compactification theorem, introduced by , implies that every abstract variety can be embedded in a complete variety, and more generally shows that a separated and finite type morphism to a Noetherian scheme ''S'' can be factored into an open immersion followed by a proper morphism. Nagata's original proof used the older terminology of Zariski–Riemann spaces and valuation theory, which sometimes made it hard to follow. Deligne showed, in unpublished notes expounded by Conrad, that Nagata's proof can be translated into scheme theory and that the condition that ''S'' is Noetherian can be replaced by the much weaker condition that ''S'' is quasi-compact and quasi-separated. gave another scheme-theoretic proof of Nagata's theorem. An important application of Nagata's theorem is in defining the analogue in algebraic geometry of cohomology with compact support, or more generally higher direct image functors with proper support. The idea is that given ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nagata's Conjecture
In algebra, Nagata's conjecture states that Nagata's automorphism of the polynomial ring ''k'' 'x'',''y'',''z''is wild. The conjecture was proposed by and proved by . Nagata's automorphism is given by :\phi(x,y,z) = (x-2\Delta y-\Delta^2z, y+\Delta z, z), where \Delta = xz+y^2. For the inverse, let (a,b,c)=\phi(x,y,z) Then z=c and \Delta= b^2+ac. With this y=b-\Delta c and x=a+2\Delta y+\Delta^2 z. References * *{{Citation , last1=Umirbaev , first1=Ualbai U. , last2=Shestakov , first2=Ivan P. , title=The tame and the wild automorphisms of polynomial rings in three variables , doi=10.1090/S0894-0347-03-00440-5 , mr=2015334 , year=2004 , journal=Journal of the American Mathematical Society The ''Journal of the American Mathematical Society'' (''JAMS''), is a quarterly peer-reviewed mathematical journal published by the American Mathematical Society. It was established in January 1988. Abstracting and indexing This journal is abs ... , issn=0894-0347 , volume=1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nagata's Conjecture On Curves
In mathematics, the Nagata conjecture on curves, named after Masayoshi Nagata, governs the minimal degree required for a plane algebraic curve to pass through a collection of very general points with prescribed multiplicities. History Nagata arrived at the conjecture via work on the 14th problem of Hilbert, which asks whether the invariant ring of a linear group action on the polynomial ring over some field is finitely generated. Nagata published the conjecture in a 1959 paper in the American Journal of Mathematics, in which he presented a counterexample to Hilbert's 14th problem. Statement :Nagata Conjecture. Suppose are very general points in and that are given positive integers. Then for any curve in that passes through each of the points with multiplicity must satisfy ::\deg C > \frac\sum_^r m_i. The condition is necessary: The cases and are distinguished by whether or not the anti-canonical bundle on the blowup of at a collection of points is nef. In the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
