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Möbius Inversion
Moebius, Möbius or Mobius may refer to: People * August Ferdinand Möbius (1790–1868), German mathematician and astronomer * Theodor Möbius (1821–1890), German philologist * Karl Möbius (1825–1908), German zoologist and ecologist * Paul Julius Möbius (1853–1907), German neurologist * Dieter Moebius (1944–2015), German/Swiss musician * Mark Mobius (born 1936), emerging markets investments pioneer * Jean Giraud (1938–2012), French comics artist who used the pseudonym Mœbius Fictional characters * Mobius M. Mobius, a character in Marvel Comics * Mobius, also known as the Anti-Monitor, a supervillain in DC Comics Mathematics * Möbius energy, a particular knot energy * Möbius strip, an object with one surface and one edge * Möbius function, an important multiplicative function in number theory and combinatorics ** Möbius transform, transform involving the Möbius function ** Möbius inversion formula, in number theory * Möbius transformation, a particular rati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Möbius Inversion Formula
In mathematics, the classic Möbius inversion formula is a relation between pairs of arithmetic functions, each defined from the other by sums over divisors. It was introduced into number theory in 1832 by August Ferdinand Möbius. A large generalization of this formula applies to summation over an arbitrary locally finite partially ordered set, with Möbius' classical formula applying to the set of the natural numbers ordered by divisibility: see incidence algebra. Statement of the formula The classic version states that if and are arithmetic functions satisfying : g(n)=\sum_f(d)\quad\textn\ge 1 then :f(n)=\sum_\mu(d)g\left(\frac\right)\quad\textn\ge 1 where is the Möbius function and the sums extend over all positive divisors of (indicated by d \mid n in the above formulae). In effect, the original can be determined given by using the inversion formula. The two sequences are said to be Möbius transforms of each other. The formula is also correct if and are funct ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
August Ferdinand Möbius
August Ferdinand Möbius (, ; ; 17 November 1790 – 26 September 1868) was a German mathematician and theoretical astronomer. Early life and education Möbius was born in Schulpforta, Electorate of Saxony, and was descended on his mother's side from religious reformer Martin Luther. He was home-schooled until he was 13, when he attended the college in Schulpforta in 1803, and studied there, graduating in 1809. He then enrolled at the University of Leipzig, where he studied astronomy under the mathematician and astronomer Karl Mollweide.August Ferdinand Möbius, The MacTutor History of Mathematics archive History.mcs.st-andrews.ac.uk. Retrieved on 2017-04-26. In 1813, he began to study astronomy under mathematician |
Möbius–Kantor Graph
In the mathematical field of graph theory, the Möbius–Kantor graph is a symmetric bipartite cubic graph with 16 vertices and 24 edges named after August Ferdinand Möbius and Seligmann Kantor. It can be defined as the generalized Petersen graph ''G''(8,3): that is, it is formed by the vertices of an octagon, connected to the vertices of an eight-point star in which each point of the star is connected to the points three steps away from it. Möbius–Kantor configuration asked whether there exists a pair of polygons with ''p'' sides each, having the property that the vertices of one polygon lie on the lines through the edges of the other polygon, and vice versa. If so, the vertices and edges of these polygons would form a projective configuration. For ''p'' = 4 there is no solution in the Euclidean plane, but found pairs of polygons of this type, for a generalization of the problem in which the points and edges belong to the complex projective plane. That is, in Kantor's so ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sonic The Hedgehog
is a Japanese video game series and media franchise created by Sega. The franchise follows Sonic, an anthropomorphic blue hedgehog who battles the evil Doctor Eggman, a mad scientist. The main ''Sonic the Hedgehog'' games are platformers mostly developed by Sonic Team; other games, developed by various studios, include spin-offs in the racing, fighting, party and sports genres. The franchise also incorporates printed media, animations, feature films, and merchandise. Sega developed the first ''Sonic'' game, released in 1991 for the Sega Genesis, to compete with Nintendo's mascot Mario. Its success helped Sega become one of the leading video game companies during the fourth generation of video game consoles in the early 1990s. Sega Technical Institute developed the next three ''Sonic'' games, plus the spin-off ''Sonic Spinball'' (1993). A number of ''Sonic'' games were also developed for Sega's 8-bit consoles, the Master System and Game Gear. After a hiatus during the unsuc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
New Vegas
''Fallout: New Vegas'' is a 2010 action role-playing game developed by Obsidian Entertainment and published by Bethesda Softworks. It was announced in April 2009 and released for Microsoft Windows, PlayStation 3, and Xbox 360 on October 19, 2010. A spin-off of the main ''Fallout'' series, the game is set in a post-apocalyptic open world environment that encompasses a region consisting of parts of Arizona, California, and Nevada. It is set in a world that deviated onto an alternate timeline thanks to Atomic Age technology, which eventually led to a global nuclear apocalypse in the year 2077 in an event referred to as "The Great War", caused by a major conflict between the U.S. and China over natural resources. The main story of ''New Vegas'' takes place in the year 2281, four years after the events of ''Fallout 3'' and 204 years after the bombs fell. It is not a direct sequel, but does feature the return of several elements found in ''Fallout 2''. Players take control of a chara ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fallout New Vegas
''Fallout: New Vegas'' is a 2010 action role-playing game developed by Obsidian Entertainment and published by Bethesda Softworks. It was announced in April 2009 and released for Microsoft Windows, PlayStation 3, and Xbox 360 on October 19, 2010. A spin-off of the main ''Fallout'' series, the game is set in a post-apocalyptic open world environment that encompasses a region consisting of parts of Arizona, California, and Nevada. It is set in a world that deviated onto an alternate timeline thanks to Atomic Age technology, which eventually led to a global nuclear apocalypse in the year 2077 in an event referred to as "The Great War", caused by a major conflict between the U.S. and China over natural resources. The main story of ''New Vegas'' takes place in the year 2281, four years after the events of ''Fallout 3'' and 204 years after the bombs fell. It is not a direct sequel, but does feature the return of several elements found in ''Fallout 2''. Players take control of a char ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Starcraft II
''StarCraft II'' is a military science fiction video game created by Blizzard Entertainment as a sequel to the successful ''StarCraft'' video game released in 1998. Set in a fictional future, the game centers on a galactic struggle for dominance among the various fictional races of StarCraft. ''StarCraft II'' single-player campaign is split into three installments, each of which focuses on one of the three races: '' StarCraft II: Wings of Liberty'' (released 2010), ''Heart of the Swarm'' (2013) and ''Legacy of the Void'' (2015). A final campaign pack called '' StarCraft II: Nova Covert Ops'' was released in 2016. ''StarCraft II'' multi-player gameplay spawned a separate e-sports competition that later drew interest from companies other than Blizzard, and attracted attention in South Korea and elsewhere, similar to the original ''StarCraft'' e-sports. Since 2017, ''StarCraft II'' multi-player mode, co-op mode and the first single-player campaign have been free-to-play. Story ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shattered Skies
Shattered may refer to: Books * ''Shattered'' (Casey book), a 2010 non-fiction book: true-crime account of pregnant mother's murder * ''Shattered'' (Francis novel), a 2000 novel by Dick Francis: glassblower seeks videotape following death of jockey * ''Shattered'' (Koontz novel), a 1973 novel by Dean Koontz: family on road trip pursued by psychopath * ''Shattered'' (Walters novel), a 2006 novel by Eric Walters: spoiled teen put to work in a soup kitchen * ''Shattered'', a 2014 novel by Kevin Hearne: urban fantasy in the Iron Druid universe * '' Shattered: Inside Hillary Clinton's Doomed Campaign'', a 2017 non-fiction book by Amie Parnes and Jonathan Allen Film and TV * ''Shattered'' (1921 film), a German silent film * ''Shattered'' (1972 film), a British film directed by Alastair Reid, most commonly known as ''Something to Hide'' * ''Shattered'' (1991 film), an American film directed by Wolfgang Petersen * ''Shattered'' (2007 film), a Canadian film directed by Mike Bar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Legacy Of Kain
''Legacy of Kain'' is a series of dark fantasy action-adventure video games primarily developed by Crystal Dynamics and formerly published by Eidos Interactive, then Square Enix Europe after 2009. The first title, '' Blood Omen: Legacy of Kain'', was created by Silicon Knights in association with Crystal Dynamics, but, after a legal battle, Crystal Dynamics retained the rights to the game's intellectual property, and continued its story with four sequels. To date, five games comprise the series, all initially developed for video game consoles and later ported to Microsoft Windows. Focusing on the eponymous character of Kain, a vampire antihero, each title features action, exploration and puzzle-solving, with some role-playing game elements. The series takes place in the fictional land of Nosgoth—a gothic fantasy setting—and revolves around Kain's quest to defy his fate and restore balance to the world. '' Legacy of Kain: Soul Reaver'' introduced another antihero protagoni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Command & Conquer
''Command & Conquer'' (''C&C'') is a real-time strategy (RTS) video game franchise, first developed by Westwood Studios. The first game was one of the earliest of the RTS genre, itself based on Westwood Studios' influential strategy game ''Dune II'' and introducing trademarks followed in the rest of the series. This includes full-motion video cutscenes with an ensemble cast to progress the story, as opposed to digitally in-game rendered cutscenes. Westwood Studios was taken over by Electronic Arts in 1998 and closed down in 2003. The studio and some of its members were absorbed into EA Los Angeles, which continued development on the series. History After Westwood Studios developed the critically acclaimed ''Dune II'', ''Computer Gaming World'' reported in 1993 that the company would not use the ''Dune'' license for Westwood's next strategy game "mostly because the programmers are tired of sand". The magazine stated that it would have "new terrain and enemies", and that "the des ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Xenoblade Chronicles 3
''Xenoblade Chronicles 3'' is a 2022 action role-playing game developed by Monolith Soft and published by Nintendo for the Nintendo Switch. Released on July 29, it is the fourth installment of the open-world ''Xenoblade Chronicles'' franchise, and the eighth main entry in the '' Xeno'' series. ''Xenoblade Chronicles 3'' depicts the consequences of the worlds featured in ''Xenoblade Chronicles'' and ''Xenoblade Chronicles 2,'' and concludes the trilogy's overall narrative. The development team wanted to develop a story-driven game in the style of the first two entries in the series, while featuring content and combat gameplay from previous ''Xeno'' entries. The game was announced February 9th, 2022, and released July 29th the same year. Like the first two entries, the game was localized by Nintendo of Europe. In gameplay, the game is similar in story writing, but very different to previous entries in mechanics. The game takes place in Aionios, where two warring nations, Keves and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mobius Final Fantasy
was an episodic role-playing video game developed and published by Square Enix for iOS, Android (operating system), Android, and Microsoft Windows. It was released in Japan in June 2015, and released internationally in August 2016. The player controls Warrior of Light (Wol), a man who wakes with amnesia in the world of Palamecia, and must help conquer the dark forces attacking its people. The game features gameplay elements from previous ''Final Fantasy'' titles, including leveling, exploration via standard navigation and fast-travel systems, and turn-based combat tied to a job system. Common themes were also drawn from the original ''Final Fantasy (video game), Final Fantasy'' title, such as "warriors of light" and their fight against chaos and darkness. The game, which began development in early 2014, was developed around the concept of a mobile game on a similar level to a home console game and "a rich gaming experience, anytime, anywhere". This prompted skepticism from both in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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