Ques: Information: - The city of Larvik was established as a municipality on 1 January 1838 (see formannskapsdistrikt). The city of Stavern, and the rural municipalities of Brunlanes, Hedrum, and Tjlling were merged into the municipality of Larvik on January 1, 1988. - Brunlanes is a parish and former municipality within Larvik municipality in Vestfold county, Norway. - Tjlling is a former municipality in Vestfold county, Norway. Tjlling was established as a municipality January 1, 1838 (see formannskapsdistrikt). Together with Brunlanes, Stavern and Hedrum, it was merged into Larvik on January 1, 1988. Location. Tjlling has a long coastline with many fine beaches and coves . Tjlling is also known as a popular holiday area. People from other parts of the country often spend their summer vacations there. Popular tourist sites include Ula and Kjerringvik. The coastline is a beautiful area; during the last Ice Age, this was where the end of the glacier polished the granite rocks, making them smooth and without any sharp edges. Boat lovers often travel the fjords and spend time on the islands. History. Tjlling is the site of one of the oldest Viking Era settlement within Scandinavia. Kaupang was a big trading centre for the Vikings. There have been several earlier archaeological surveys and excavations at Kaupang. In 1867 Antiquarian Nicolay Nicolaysen mapped one of the grave-fields around the former town and excavated 79 grave mounds. He uncovered a cremation cemetery, largely dated to the 10th century. Charlotte Blindheim (1917-2005) started excavating in 1947 and completed her last publication in 1999. In 1997, Dagfinn Skre and his associates from the University of Oslo undertook a new program of work at Kaupang followed by a large excavation that ran over three years, from 2000 till 2002. Most recently it has been the site of post-excavation work conducted by the University of Oslo. - History. The introduction of self-government in rural districts was a major political change. The Norwegian farm culture ("bondekultur") that emerged came to serve as a symbol of nationalistic resistance to the forced union with Sweden. The legislation of 1837 gave both the towns and the rural areas the same institutions: a minor change for the town, but a major advance for the rural communities. The significance of this legislation is hailed by a nationalistic historian, Ernst Sars: - Anne Rygh Pedersen ( born 28 June 1967 in Larvik ) is a Norwegian politician for the Labour Party . She served in the position of deputy representative to the Norwegian Parliament from Vestfold during the term 2001 -- 2005 . Rygh Pedersen was the county mayor of Vestfold 2003 -- 2005 . When the second cabinet Stoltenberg assumed office following the 2005 elections , she was appointed State Secretary in the Ministry of Justice and the Police . Rygh Pedersen resigned om February 9 , 2007 . She now lives in Tnsberg and has a son . - Hedrum is a parish and the site of a historic church in Vestfold county, Norway. History. The parish of Hedrum was established as a municipality on January 1 1838 (see formannskapsdistrikt). Small parts of Hedrum were transferred to the city of Larvik in 1855, 1875, 1937 and 1948. Border adjustments between Hedrum and the neighboring municipalities Andebu, Tjlling and Siljan also took place. Hedrum was incorporated into the enlarged Larvik municipality on January 1, 1988. Before the merger Hedrum had a population of 10,449. Given the information above, choose from the list below the object entity that exhibits the relation 'country of citizenship' with the subject 'anne rygh pedersen'. Choices: - norway - sweden
Ans: norway

Ques: 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. Given the information above, choose from the list below the object entity that exhibits the relation 'field of work' with the subject 'jacques dixmier'. Choices: - algebra - computing - mathematical analysis - mathematician - mathematics
Ans:
mathematical analysis