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Garside Element
In mathematics, a Garside element is an element of an algebraic structure such as a monoid that has several desirable properties. Formally, if ''M'' is a monoid, then an element Δ of ''M'' is said to be a Garside element if the set of all right divisors of Δ, :\, is the same set as the set of all left divisors of Δ, :\, and this set generates ''M''. A Garside element is in general not unique: any power of a Garside element is again a Garside element. Garside monoid and Garside group A Garside monoid is a monoid with the following properties: * Finitely generated and atomic; * Cancellative; * The partial order relations of divisibility are lattices; * There exists a Garside element. A Garside monoid satisfies the Ore condition for multiplicative sets and hence embeds in its group of fractions: such a group is a Garside group. A Garside group is biautomatic and hence has soluble word problem and conjugacy problem. Examples of such groups include braid gro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting poin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Braid Group
A braid (also referred to as a plait) is a complex structure or pattern formed by interlacing two or more strands of flexible material such as textile yarns, wire, or hair. The simplest and most common version is a flat, solid, three-stranded structure. More complex patterns can be constructed from an arbitrary number of strands to create a wider range of structures (such as a fishtail braid, a five-stranded braid, rope braid, a French braid and a waterfall braid). The structure is usually long and narrow with each component strand functionally equivalent in zigzagging forward through the overlapping mass of the others. It can be compared with the process of weaving, which usually involves two separate perpendicular groups of strands (warp and weft). Historically, the materials used have depended on the indigenous plants and animals available in the local area. During the Industrial Revolution, mechanized braiding equipment was invented to increase production. The braiding t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Annales Scientifiques De L'École Normale Supérieure
''Annales Scientifiques de l'École Normale Supérieure'' is a French scientific journal of mathematics published by the Société Mathématique de France. It was established in 1864 by the French chemist Louis Pasteur and published articles in mathematics, physics, chemistry Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that covers the Chemical element, elements that make up matter to the chemical compound, compounds made of atoms, molecules and ions ..., biology, and geology. In 1900, it became a purely mathematical journal. It is published with help of the Centre national de la recherche scientifique. Its web site is hosted by the mathematics department of the École Normale Supérieure. External links * Archive(1864–2013) Mathematics journals Publications established in 1864 Multilingual journals Multidisciplinary scientific journals Société Mathématique de France academic journals ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Benson Farb
Benson Stanley Farb (born October 25, 1967) is an American mathematician at the University of Chicago. His research fields include geometric group theory and low-dimensional topology. Early life A native of Norristown, Pennsylvania, Farb earned his bachelor's degree from Cornell University. In 1994, he obtained his doctorate from Princeton University, under supervision of William Thurston. Career Farb has advised over 40 students, including Pallavi Dani, Kathryn Mann, Dan Margalit, Karin Melnick and Andrew Putman. In 2012 Farb became a fellow of the American Mathematical Society. In 2014 he was an invited speaker at the International Congress of Mathematicians in Seoul, speaking in the section on Topology. He was elected to the American Academy of Arts and Sciences in 2021. Books *Reviews of ''A Primer on Mapping Class Groups'' * * * * Personal life Farb married Amie Wilkinson Amie Wilkinson (born 1968) is an American mathematician and Professor of Mathematics ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Mayors Of Oxford
The earliest recorded Mayor of Oxford in England was Laurence Kepeharm (1205–1207?). On 23 October 1962 the city was granted the honour of electing a Lord Mayor. Notable figures who have been Lord Mayor of Oxford include J. N. L. Baker (1964–65), Air-Vice-Marshal William Foster MacNeece Foster (1966–67) and Olive Gibbs (1974–75 and 1981–82). List of notable Mayors List of Lord Mayors References People from Oxford Local government in Oxford Oxford Mayors In many countries, a mayor is the highest-ranking official in a Municipal corporation, municipal government such as that of a city or a town. Worldwide, there is a wide variance in local laws and customs regarding the powers and responsibilities ... Oxford mayors {{England-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magdalen College School, Oxford
Magdalen College School (MCS) is a public school (English independent day school) in Oxford, England, for boys aged seven to eighteen and for girls in the sixth form. It was founded by William Waynflete about 1480 as part of Magdalen College, Oxford. In 2010 '' The Good Schools Guide'' described the school as having "A comfortable mix of brains, brawn and artistic flair but demanding and challenging too. Not what you might expect a boys' public school to look like or feel like." The school was named Independent School of the Year by ''The Sunday Times'' in 2004, and 2008, being the first boys' school to attain this accolade twice. The school is run by a headmaster, known since the foundation of the school simply as "the Master" and controlled by a Board of Governors, who appoint the Master. It has both a senior school and a junior school. The Senior School has six houses, each headed by a housemaster selected from the senior members of the teaching staff, of whom there ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Patrick Dehornoy
Patrick Dehornoy (11 September 1952 – 4 September 2019) was a mathematician at the University of Caen Normandy who worked on set theory and group theory. Early life and education Dehornoy was born on 11 September 1952 in Rouen, France. He graduated from the Lycée Pierre-Corneille in 1971. He studied at the École normale supérieure from 1971 to 1975 and completed his Ph.D. in 1978 at the University of Paris, with a thesis written under the direction of Kenneth Walter McAloon. Career Dehornoy was a researcher at the French National Centre for Scientific Research (CNRS) from 1975 to 1982. He was at the University of Caen Normandy as a Professor from 1983 to 2017 and as an Emeritus Professor from 2017 until his death. From 2009 to 2013, he was an adjunct scientific director of the ' (INSMI) at the CNRS. Dehornoy died on 4 September 2019 in Villejuif, France at the age of 66. Research Dehornoy found one of the first applications of large cardinals to algebra by con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proceedings Of The London Mathematical Society
The London Mathematical Society (LMS) is one of the United Kingdom's 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, 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 the society's first president), at 57 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Artin Group Of Finite Type
Artin may refer to: * Artin (name), a surname and given name, including a list of people with the name ** Artin, a variant of Harutyun, an Armenian given name * 15378 Artin, a main-belt asteroid See also {{disambiguation, surname ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Artin Group
Artin may refer to: * Artin (name), a surname and given name, including a list of people with the name ** Artin, a variant of Harutyun Harutyun ( hy, Հարություն and in Western Armenian Յարութիւն) also spelled Haroutioun, Harutiun and its variants Harout, Harut and Artin is a common male Armenian name; it means resurrection in Armenian. People with the name H ..., an Armenian given name * 15378 Artin, a main-belt asteroid See also {{disambiguation, surname ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conjugacy Problem
In abstract algebra, the conjugacy problem for a group ''G'' with a given presentation is the decision problem of determining, given two words ''x'' and ''y'' in ''G'', whether or not they represent conjugate elements of ''G''. That is, the problem is to determine whether there exists an element ''z'' of ''G'' such that :y = zxz^.\,\! The conjugacy problem is also known as the transformation problem. The conjugacy problem was identified by Max Dehn in 1911 as one of the fundamental decision problems in group theory; the other two being the word problem and the isomorphism problem. The conjugacy problem contains the word problem as a special case: if ''x'' and ''y'' are words, deciding if they are the same word is equivalent to deciding if xy^ is the identity, which is the same as deciding if it's conjugate to the identity. In 1912 Dehn gave an algorithm that solves both the word and conjugacy problem for the fundamental groups of closed orientable two-dimensional manifolds of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Structure
In mathematics, an algebraic structure consists of a nonempty set ''A'' (called the underlying set, carrier set or domain), a collection of operations on ''A'' (typically binary operations such as addition and multiplication), and a finite set of identities, known as axioms, that these operations must satisfy. An algebraic structure may be based on other algebraic structures with operations and axioms involving several structures. For instance, a vector space involves a second structure called a field, and an operation called ''scalar multiplication'' between elements of the field (called '' scalars''), and elements of the vector space (called '' vectors''). Abstract algebra is the name that is commonly given to the study of algebraic structures. The general theory of algebraic structures has been formalized in universal algebra. Category theory is another formalization that includes also other mathematical structures and functions between structures of the same type (homo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
