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Wolfgang Haken
Wolfgang Haken (June 21, 1928 – October 2, 2022) was a German American mathematician who specialized in topology, in particular 3-manifolds. Biography Haken was born in Berlin, Germany. His father was Werner Haken, a physicist who had Max Planck as a doctoral thesis advisor. In 1953, Haken earned a Ph.D. degree in mathematics from Christian-Albrechts-Universität zu Kiel (Kiel University) and married Anna-Irmgard von Bredow, who earned a Ph.D. degree in mathematics from the same university in 1959. In 1962, they left Germany so he could accept a position as visiting professor at the University of Illinois at Urbana-Champaign. He became a full professor in 1965, retiring in 1998. In 1976, together with colleague Kenneth Appel at the University of Illinois at Urbana-Champaign, Haken solved the four-color theorem. They proved that any two-dimensional map, with certain limitations, can be filled in with four colors without any adjacent “countries” sharing the same color. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Berlin
Berlin ( , ) is the capital and largest city of Germany by both area and population. Its 3.7 million inhabitants make it the European Union's most populous city, according to population within city limits. One of Germany's sixteen constituent states, Berlin is surrounded by the State of Brandenburg and contiguous with Potsdam, Brandenburg's capital. Berlin's urban area, which has a population of around 4.5 million, is the second most populous urban area in Germany after the Ruhr. The Berlin-Brandenburg capital region has around 6.2 million inhabitants and is Germany's third-largest metropolitan region after the Rhine-Ruhr and Rhine-Main regions. Berlin straddles the banks of the Spree, which flows into the Havel (a tributary of the Elbe) in the western borough of Spandau. Among the city's main topographical features are the many lakes in the western and southeastern boroughs formed by the Spree, Havel and Dahme, the largest of which is Lake Müggelsee. Due to its l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tautology (logic)
In mathematical logic, a tautology (from el, ταυτολογία) is a formula or assertion that is true in every possible interpretation. An example is "x=y or x≠y". Similarly, "either the ball is green, or the ball is not green" is always true, regardless of the colour of the ball. The philosopher Ludwig Wittgenstein first applied the term to redundancies of propositional logic in 1921, borrowing from rhetoric, where a tautology is a repetitive statement. In logic, a formula is satisfiable if it is true under at least one interpretation, and thus a tautology is a formula whose negation is unsatisfiable. In other words, it cannot be false. It cannot be untrue. Unsatisfiable statements, both through negation and affirmation, are known formally as contradictions. A formula that is neither a tautology nor a contradiction is said to be Contingency (philosophy), logically contingent. Such a formula can be made either true or false based on the values assigned to its propositi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unknotting Problem
In mathematics, the unknotting problem is the problem of algorithmically recognizing the unknot, given some representation of a knot, e.g., a knot diagram. There are several types of unknotting algorithms. A major unresolved challenge is to determine if the problem admits a polynomial time algorithm; that is, whether the problem lies in the complexity class P. Computational complexity First steps toward determining the computational complexity were undertaken in proving that the problem is in larger complexity classes, which contain the class P. By using normal surfaces to describe the Seifert surfaces of a given knot, showed that the unknotting problem is in the complexity class NP. claimed the weaker result that unknotting is in AM ∩ co-AM; however, later they retracted this claim. In 2011, Greg Kuperberg proved that (assuming the generalized Riemann hypothesis) the unknotting problem is in co-NP, and in 2016, Marc Lackenby provided an unconditional proof ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wolfgang Haken With Marshall Pangilinan
Wolfgang is a German male given name traditionally popular in Germany, Austria and Switzerland. The name is a combination of the Old High German words ''wolf'', meaning "wolf", and ''gang'', meaning "path", "journey", "travel". Besides the regular "wolf", the first element also occurs in Old High German as the combining form "-olf". The earliest reference of the name being used was in the 8th century. The name was also attested as "Vulfgang" in the Reichenauer Verbrüderungsbuch in the 9th century. The earliest recorded famous bearer of the name was a tenth-century Saint Wolfgang of Regensburg. Due to the lack of conflict with the pagan reference in the name with Catholicism, it is likely a much more ancient name whose meaning had already been lost by the tenth century. Grimm (''Teutonic Mythology'' p. 1093) interpreted the name as that of a hero in front of whom walks the "wolf of victory". A Latin gloss by Arnold of St Emmeram interprets the name as ''Lupambulus''.E. F ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs. The society is one of the four parts of the Joint Policy Board for Mathematics and a member of the Conference Board of the Mathematical Sciences. History The AMS was founded in 1888 as the New York Mathematical Society, the brainchild of Thomas Fiske, who was impressed by the London Mathematical Society on a visit to England. John Howard Van Amringe was the first president and Fiske became secretary. The society soon decided to publish a journal, but ran into some resistance, due to concerns about competing with the American Journal of Mathematics. The result was the ''Bulletin of the American Mathematical Society'', with Fiske as editor-in-chief. The de facto journal, as intended, was influential in in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fulkerson Prize
The Fulkerson Prize for outstanding papers in the area of discrete mathematics is sponsored jointly by the Mathematical Optimization Society (MOS) and the American Mathematical Society (AMS). Up to three awards of $1,500 each are presented at each (triennial) International Symposium of the MOS. Originally, the prizes were paid out of a memorial fund administered by the AMS that was established by friends of the late Delbert Ray Fulkerson to encourage mathematical excellence in the fields of research exemplified by his work. The prizes are now funded by an endowment administered by MPS. Winners SourceMathematical Optimization Society* 1979: ** Richard M. Karp for classifying many important NP-complete problems. ** Kenneth Appel and Wolfgang Haken for the four color theorem. ** Paul Seymour for generalizing the max-flow min-cut theorem to matroids. * 1982: ** D.B. Judin, Arkadi Nemirovski, Leonid Khachiyan, Martin Grötschel, László Lovász and Alexander Schrijver for the e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
International Mathematical Union
The International Mathematical Union (IMU) is an international non-governmental organization devoted to international cooperation in the field of mathematics across the world. It is a member of the International Science Council (ISC) and supports the International Congress of Mathematicians. Its members are national mathematics organizations from more than 80 countries. The objectives of the International Mathematical Union (IMU) are: promoting international cooperation in mathematics, supporting and assisting the International Congress of Mathematicians (ICM) and other international scientific meetings/conferences, acknowledging outstanding research contributions to mathematics through the awarding of scientific prizes, and encouraging and supporting other international mathematical activities, considered likely to contribute to the development of mathematical science in any of its aspects, whether pure, applied, or educational. The IMU was established in 1920, but dissolved in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Invited Address At The International Congress Of Mathematicians
This is a list of International Congresses of Mathematicians Plenary and Invited Speakers. Being invited to talk at an International Congress of Mathematicians has been called "the equivalent, in this community, of an induction to a hall of fame." The current list of Plenary and Invited Speakers presented here is based on the ICM's post-WW II terminology, in which the one-hour speakers in the morning sessions are called "Plenary Speakers" and the other speakers (in the afternoon sessions) whose talks are included in the ICM published proceedings are called "Invited Speakers". In the pre-WW II congresses the Plenary Speakers were called "Invited Speakers". By congress year 1897, Zürich * Jules Andrade * Léon Autonne *Émile Borel * N. V. Bougaïev *Francesco Brioschi *Hermann Brunn *Cesare Burali-Forti *Charles Jean de la Vallée Poussin *Gustaf Eneström *Federigo Enriques *Gino Fano * Zoel García de Galdeano * Francesco Gerbaldi *Paul Gordan *Jacques Hadamard * Adolf Hurwitz ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hermann Haken
Hermann Haken (born 12 July 1927) is physicist and professor emeritus in theoretical physics at the University of Stuttgart. He is known as the founder of synergetics. He is a cousin of the mathematician Wolfgang Haken, who proved the Four color theorem. He is a nephew of Werner Haken, a doctoral student of Max Planck. Biography After his studies in mathematics and physics in Halle (Saale) and Erlangen, receiving his PhD in mathematics in 1951 at the University of Erlangen and being guest lecturer at universities in the UK and US, Haken was appointed as a full professor in theoretical physics at the University of Stuttgart. His research has been in non linear optics (his specialities are laser physics, particle physics, statistical physics and group theory). Haken developed his institute in a relatively short time to be an international centre for laser theory, starting in 1960 when Theodore Maiman built the first experimental laser. The interpretation of the laser princip ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electric Violin
An electric violin is a violin equipped with an electronic output of its sound. The term most properly refers to an instrument intentionally made to be electrified with built-in pickups, usually with a solid body. It can also refer to a violin fitted with an electric pickup of some type, although "amplified violin" or "electro-acoustic violin" are more accurate then. History Electrically amplified violins have been used in one form or another since the 1920s; jazz and blues artist Stuff Smith is generally credited as being one of the first performers to adapt pickups and amplifiers to violins. The Electro Stringed Instrument Corporation, National String Instrument Corporation and Vega Company sold electric violins in the 1930s and 1940s; Fender advertised an electric violin in 1958 (first production model pictured at the head of this page) but withdrew it at the point of production. After Fender was bought by CBS, the electric violin went into production in 1969 until 1975. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continuum Fingerboard
The Continuum Fingerboard or Haken Continuum is a music performance controller and synthesizer developed by Lippold Haken, a professor of Electrical and Computer Engineering at the University of Illinois, and sold by Haken Audio, located in Champaign, Illinois. The Continuum Fingerboard was initially developed from 1983 to 1998 at the CERL Sound Group at the University of Illinois, to control sound-producing algorithms on the Platypus audio signal processor and the Kyma/Capybara workstation. In 1999, the first Continuum Fingerboard was commercially sold. Until 2008, the Continuum Fingerboard provided IEEE-1394 (FireWire) connections to control a Kyma sound design workstation, as well as MIDI connections to control a MIDI synthesizer module. More recently, the Continuum Fingerboard generates audio directly in addition to providing MIDI connections for MIDI modules, software synthesizers, and Kyma (the IEEE-1394 connection that was present on earlier models has been removed). ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Master Theorem (analysis Of Algorithms)
In the analysis of algorithms, the master theorem for divide-and-conquer recurrences provides an asymptotic analysis (using Big O notation) for recurrence relations of types that occur in the analysis of many divide and conquer algorithms. The approach was first presented by Jon Bentley, Dorothea Blostein (née Haken), and James B. Saxe in 1980, where it was described as a "unifying method" for solving such recurrences. The name "master theorem" was popularized by the widely used algorithms textbook ''Introduction to Algorithms'' by Cormen, Leiserson, Rivest, and Stein. Not all recurrence relations can be solved with the use of this theorem; its generalizations include the Akra–Bazzi method. Introduction Consider a problem that can be solved using a recursive algorithm such as the following: procedure p(input ''x'' of size ''n''): if ''n'' 1). Crucially, a and b must not depend on n. The theorem below also assumes that, as a base case for the recurrence, T(n)=\Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
