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David Eugene Muller
David Eugene Muller (November 2, 1924 – April 27, 2008) was an American mathematician and computer scientist. He was a professor of mathematics and computer science at the University of Illinois (1953–92), after which he became an emeritus professor, and was an adjunct professor of mathematics at the New Mexico State University (1995–2008). Muller received his BS in 1947 and his PhD in 1951 in physics from Caltech; an honorary PhD was conferred by the University of Paris in 1989. He was the inventor of the Muller C-element (or Muller C-gate), a device used to implement asynchronous circuitry in digital computers. He also co-invented the Reed–Muller codes. He discovered the codes, and Irving S. Reed proposed the majority logic decoding for the first time. Furthermore, he invented Muller automata, an automaton model for infinite words. In geometric group theory Muller is known for the Muller–Schupp theorem, joint with Paul Schupp, characterizing finitely generat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brackets
A bracket is either of two tall fore- or back-facing punctuation marks commonly used to isolate a segment of text or data from its surroundings. They come in four main pairs of shapes, as given in the box to the right, which also gives their names, that vary between British English, British and American English. "Brackets", without further qualification, are in British English the ... marks and in American English the ... marks. Other symbols are repurposed as brackets in specialist contexts, such as International Phonetic Alphabet#Brackets and transcription delimiters, those used by linguists. Brackets are typically deployed in symmetric pairs, and an individual bracket may be identified as a "left" or "right" bracket or, alternatively, an "opening bracket" or "closing bracket", respectively, depending on the Writing system#Directionality, directionality of the context. In casual writing and in technical fields such as computing or linguistic analysis of grammar, brackets ne ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometric Group Theory
Geometric group theory is an area in mathematics devoted to the study of finitely generated groups via exploring the connections between algebraic properties of such groups and topological and geometric properties of spaces on which these groups can act non-trivially (that is, when the groups in question are realized as geometric symmetries or continuous transformations of some spaces). Another important idea in geometric group theory is to consider finitely generated groups themselves as geometric objects. This is usually done by studying the Cayley graphs of groups, which, in addition to the graph structure, are endowed with the structure of a metric space, given by the so-called word metric. Geometric group theory, as a distinct area, is relatively new, and became a clearly identifiable branch of mathematics in the late 1980s and early 1990s. Geometric group theory closely interacts with low-dimensional topology, hyperbolic geometry, algebraic topology, computational group ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leningrad
Saint Petersburg, formerly known as Petrograd and later Leningrad, is the List of cities and towns in Russia by population, second-largest city in Russia after Moscow. It is situated on the Neva, River Neva, at the head of the Gulf of Finland on the Baltic Sea. The city had a population of 5,601,911 residents as of 2021, with more than 6.4 million people living in the Saint Petersburg metropolitan area, metropolitan area. Saint Petersburg is the List of European cities by population within city limits, fourth-most populous city in Europe, the List of cities and towns around the Baltic Sea, most populous city on the Baltic Sea, and the world's List of northernmost items#Cities and settlements, northernmost city of more than 1 million residents. As the former capital of the Russian Empire, and a Ports of the Baltic Sea, historically strategic port, it is governed as a Federal cities of Russia, federal city. The city was founded by Tsar Peter the Great on 27 May 1703 on the s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Berlin
Berlin ( ; ) is the Capital of Germany, capital and largest city of Germany, by both area and List of cities in Germany by population, population. With 3.7 million inhabitants, it has the List of cities in the European Union by population within city limits, highest population within its city limits of any city in the European Union. The city is also one of the states of Germany, being the List of German states by area, third smallest state in the country by area. Berlin is surrounded by the state of Brandenburg, and Brandenburg's capital Potsdam is nearby. The urban area of Berlin has a population of over 4.6 million and is therefore the most populous urban area in Germany. The Berlin/Brandenburg Metropolitan Region, Berlin-Brandenburg capital region has around 6.2 million inhabitants and is Germany's second-largest metropolitan region after the Rhine-Ruhr region, as well as the List of EU metropolitan areas by GDP, fifth-biggest metropolitan region by GDP in the European Union. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
London Mathematical Society
The London Mathematical Society (LMS) is one of the United Kingdom's Learned society, learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh Mathematical Society and the Operational Research Society (ORS). History The Society was established on 16 January 1865, the first president being Augustus De Morgan. The earliest meetings were held in University College London, University College, but the Society soon moved into Burlington House, Piccadilly. The initial activities of the Society included talks and publication of a journal. The LMS was used as a model for the establishment of the American Mathematical Society in 1888. Mary Cartwright was the first woman to be President of the LMS (in 1961–62). The Society was granted a royal charter in 1965, a century after its foundation. In 1998 the Society moved from rooms in Burlington House into De Morgan House (named after t ... [...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 became the first president while Fiske became secretary. The society soon decided to publish a journal, but ran into some resistance over 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 influentia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The University Of Texas
The University of Texas at Austin (UT Austin, UT, or Texas) is a public university, public research university in Austin, Texas, United States. Founded in 1883, it is the flagship institution of the University of Texas System. With 53,082 students as of fall 2023, it is also the largest institution in the system. The university is a major center for academic research, with research expenditures totaling $1.06 billion for the 2023 fiscal year. It joined the Association of American Universities in 1929. The university houses seven museums and seventeen libraries, including the Lyndon Baines Johnson Library and Museum, Lyndon B. Johnson Presidential Library and the Blanton Museum of Art, and operates various auxiliary research facilities, such as the J. J. Pickle Research Campus and McDonald Observatory. UT Austin's athletics constitute the Texas Longhorns. The Longhorns have won four NCAA Division I National Football Championships, six NCAA Division I National Baseball Champions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jessie Marie Jacobs Muller Offermann
Jessie Marie Jacobs Muller Offermann (1890–1954) was an American mathematician who also made contributions to the field of genetics. Jessie M. Jacobs completed her undergraduate degree at McPherson College. After a year spent teaching high school she was awarded one of the first two fellowships to study graduate-level mathematics at the University of Kansas, where she earned her master's degree in 1916. She earned her Ph.D. in mathematics from the University of Illinois at Urbana–Champaign in 1919 under the supervision of Arthur Byron Coble. She became an associate professor at Rockford College and then, in 1920, an instructor at the University of Texas at Austin,. Biography on p.470-472 of thSupplementary MaterialaAMS/ref> where she also edited the ''Texas Mathematics Teachers' Bulletin''. Her tenure at the university, along with that of colleague Goldie Printis Horton, is recognized by an annual lecture series.. While at the University of Texas, she met geneticist Hermann Jos ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hermann Joseph Muller
Hermann Joseph Muller (December 21, 1890 – April 5, 1967) was an American geneticist who was awarded the 1946 Nobel Prize in Physiology or Medicine, "for the discovery that mutations can be induced by X-rays". Muller warned of long-term dangers of radioactive fallout from nuclear war and nuclear testing, which resulted in greater public scrutiny of these practices. Early life Muller was born in New York City, the son of Frances (Lyons) and Hermann Joseph Muller Sr., an artisan who worked with metals. Muller was a third-generation American whose father's ancestors were originally Catholic and came to the United States from Koblenz. His mother's family was of mixed Jewish (descended from Spanish and Portuguese Jews) and Anglican background, and had come from Britain. Among his first cousins was Alfred Kroeber (Kroeber was Ursula Le Guin's father) and first cousins once removed was Herbert J. Muller. As an adolescent, Muller attended a Unitarian church and considered himsel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Word Problem For Groups
A word is a basic element of language that carries meaning, can be used on its own, and is uninterruptible. Despite the fact that language speakers often have an intuitive grasp of what a word is, there is no consensus among linguists on its definition and numerous attempts to find specific criteria of the concept remain controversial. Different standards have been proposed, depending on the theoretical background and descriptive context; these do not converge on a single definition. Some specific definitions of the term "word" are employed to convey its different meanings at different levels of description, for example based on phonological, grammatical or orthographic basis. Others suggest that the concept is simply a convention used in everyday situations. The concept of "word" is distinguished from that of a morpheme, which is the smallest unit of language that has a meaning, even if it cannot stand on its own. Words are made out of at least one morpheme. Morphemes can ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Context-free Language
In formal language theory, a context-free language (CFL), also called a Chomsky type-2 language, is a language generated by a context-free grammar (CFG). Context-free languages have many applications in programming languages, in particular, most arithmetic expressions are generated by context-free grammars. Background Context-free grammar Different context-free grammars can generate the same context-free language. Intrinsic properties of the language can be distinguished from extrinsic properties of a particular grammar by comparing multiple grammars that describe the language. Automata The set of all context-free languages is identical to the set of languages accepted by pushdown automata, which makes these languages amenable to parsing. Further, for a given CFG, there is a direct way to produce a pushdown automaton for the grammar (and thereby the corresponding language), though going the other way (producing a grammar given an automaton) is not as direct. Examples An e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Free Group
In mathematics, the free group ''F''''S'' over a given set ''S'' consists of all words that can be built from members of ''S'', considering two words to be different unless their equality follows from the group axioms (e.g. ''st'' = ''suu''−1''t'' but ''s'' ≠ ''t''−1 for ''s'',''t'',''u'' ∈ ''S''). The members of ''S'' are called generators of ''F''''S'', and the number of generators is the rank of the free group. An arbitrary group ''G'' is called free if it is isomorphic to ''F''''S'' for some subset ''S'' of ''G'', that is, if there is a subset ''S'' of ''G'' such that every element of ''G'' can be written in exactly one way as a product of finitely many elements of ''S'' and their inverses (disregarding trivial variations such as ''st'' = ''suu''−1''t''). A related but different notion is a free abelian group; both notions are particular instances of a free object from universal algebra. As such, free groups are defined by their universal property. History ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
