Information: - The EuroHockey Nations Championship is an international men's and women's field hockey competition organised by the European Hockey Federation (EHF) for the top eight European national teams. It is the top division of the EuroHockey Nations Championships. - England is a country that is part of the United Kingdom. It shares land borders with Scotland to the north and Wales to the west. The Irish Sea lies northwest of England and the Celtic Sea lies to the southwest. England is separated from continental Europe by the North Sea to the east and the English Channel to the south. The country covers five-eighths of the island of Great Britain (which lies in the North Atlantic) in its centre and south; and includes over 100 smaller islands such as the Isles of Scilly, and the Isle of Wight. - Manchester is a major city and metropolitan borough in Greater Manchester, England, with a population of 514,414 . It lies within the United Kingdom's second-most populous urban area, with a population of 2.55 million. Manchester is fringed by the Cheshire Plain to the south, the Pennines to the north and east and an arc of towns with which it forms a continuous conurbation. The local authority is Manchester City Council. - The 2007 EuroHockey Nations Championship for men is the 11th edition of EuroHockey Nations Championship field hockey championship. It was held in Manchester, England from August 19 to August 26, 2007. Netherlands defeated Spain to win their third title, while Belgium upset Germany to secure the last automatic berth for 2008 Summer Olympic Games. - Field hockey is a team sport of the hockey family. The earliest origins of the sport date back to the Middle Ages in England, Scotland, France and the Netherlands. The game can be played on a grass field or a turf field as well as an indoor board surface. Each team plays with eleven players, including the goalie. Players use sticks made out of wood, carbon fibre, fibre glass or a combination of carbon fibre and fibre glass in different quantities (with the higher carbon fibre stick being more expensive and less likely to break) to hit a round, hard, plastic ball. The length of the stick depends on the player's individual height. Only one end of the stick is allowed to be used. Goalies often have a different kind of stick, however they can also use an ordinary field hockey stick. The specific goal-keeping sticks have another curve at the end of the stick, this is to give them more surface area to save the ball. The uniform consists of shin guards, shoes, shorts, a mouth guard and a jersey. Today, the game is played globally, with particular popularity throughout Western Europe, the Indian subcontinent, Southern Africa, Australia, New Zealand, Argentina, and parts of the United States (such as Mississippi, Alabama, Florida, Kentucky, Massachusetts, and Pennsylvania). Field Hockey is the national sport of India and Pakistan. The term "field hockey" is used primarily in Canada and the United States where ice hockey is more popular. In Sweden the term landhockey is used. - The 2005 Men 's EuroHockey Nations Trophy was the first ever edition of the EuroHockey Nations Championship for '' B '' - nations . It was held in Rome , Italy from September 11 to September 17 , 2005 . The number one and two were promoted to the '' A '' - level , the 2007 Men 's EuroHockey Nations Championship , while the number seven and eight were relegated to the '' C '' - level , the 2007 Men 's EuroHockey Nations Challenge . - The European Hockey Federation is a European sports federation for field hockey, based in Brussels. It is the umbrella organisation for all European national federations and organises the Euro Hockey League. Marijke Fleuren was elected as president on August 22, 2011. After reading the paragraphs above, choose the best answer for the entity that related to '2005 men's eurohockey nations trophy' with the relationship of 'sport'. Choices: - field hockey - hockey - sport - united kingdom
field hockey

Information: - A mathematician is someone who uses an extensive knowledge of mathematics in his/her work, typically to solve mathematical problems. - Jacques Dixmier ( born 1924 ) is a French mathematician . He worked on operator algebras , especially C * - algebras , and wrote several of the standard reference books on them , and introduced the Dixmier trace and the Dixmier mapping . He received his Ph.D. in 1949 from the University of Paris , and his students include Alain Connes . In 1949 upon the initiative of Jean - Pierre Serre and Pierre Samuel , Dixmier became a member of Bourbaki , in which he made essential contributions to the Bourbaki volume on Lie algebras . After retiring as professor emeritus from the University of Paris VI , he spent five years at the Institut des Hautes Etudes Scientifiques . Often there is made the erroneous claim that Dixmier originated the name von Neumann algebra for the operator algebras introduced by John von Neumann , but Dixmier said in an interview that the name originated from a proposal by Jean Dieudonne . Dixmier was an invited speaker at the International Congress of Mathematicians in 1966 at Moscow with talk Espace dual d'une algebre , ou d'un groupe localement compact and again in 1978 at Helsinki with talk Algebres enveloppantes . - Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear functions defined on these spaces and respecting these structures in a suitable sense. The historical roots of functional analysis lie in the study of spaces of functions and the formulation of properties of transformations of functions such as the Fourier transform as transformations defining continuous, unitary etc. operators between function spaces. This point of view turned out to be particularly useful for the study of differential and integral equations. - The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space. It extends the methods of vector algebra and calculus from the two-dimensional Euclidean plane and three-dimensional space to spaces with any finite or infinite number of dimensions. A Hilbert space is an abstract vector space possessing the structure of an inner product that allows length and angle to be measured. Furthermore, Hilbert spaces are complete: there are enough limits in the space to allow the techniques of calculus to be used. - A mathematical problem is a problem that is amenable to being represented, analyzed, and possibly solved, with the methods of mathematics. This can be a real-world problem, such as computing the orbits of the planets in the solar system, or a problem of a more abstract nature, such as Hilbert's problems.<br> It can also be a problem referring to the nature of mathematics itself, such as Russell's Paradox. - Mathematics (from Greek "mathma", knowledge, study, learning) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics. - In mathematics, the Dixmier trace, introduced by , is a non-normal trace on a space of linear operators on a Hilbert space larger than the space of trace class operators. Dixmier traces are examples of singular traces. - In functional analysis, an operator algebra is an algebra of continuous linear operators on a topological vector space with the multiplication given by the composition of mappings. Although it is usually classified as a branch of functional analysis, it has direct applications to representation theory, differential geometry, quantum statistical mechanics, quantum information, and quantum field theory. After reading the paragraphs above, choose the best answer for the entity that related to 'jacques dixmier' with the relationship of 'field of work'. Choices: - algebra - computing - mathematical analysis - mathematician - mathematics
mathematical analysis