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Raphael Høegh-Krohn
Jan Raphael Høegh-Krohn (10 February 1938 – 24 January 1988) was a Norwegian mathematician. He finished his Ph.D. in 1966, titled ''On Partly Gentle Perturbation with Application to Perturbation by Annihilation-Creation Operator,'' under the supervision of Kurt Friedrichs at the New York University. He authored over 150 papers and is known for the discovery of a fundamental duality in relativistic quantum statistical mechanics Quantum statistical mechanics is statistical mechanics applied to quantum mechanical systems. In quantum mechanics a statistical ensemble (probability distribution over possible quantum states) is described by a density operator ''S'', which is a ... by representing the basic correlation functions in terms of a certain stochastic process, now known as the Høegh-Krohn process. Books * Albeverio, Sergio; Gesztesy, Friedrich; Høegh-Krohn, Raphael; Holden, Helge: Solvable models in quantum mechanics. Texts and Monographs in Physics. Springer-Verlag, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ã…lesund
Ålesund () sometimes spelled Aalesund in English, is a municipality in Møre og Romsdal County, Norway. It is part of the traditional district of Sunnmøre and the centre of the Ålesund Region. The town of Ålesund is the administrative centre of Ålesund Municipality, as well as the principal shipping town of the Sunnmøre district. The town is a sea port and is noted for its concentration of Art Nouveau architecture. Although sometimes internationally spelled by its older name ''Aalesund'', this spelling is obsolete in Norwegian. However, the local football club Aalesunds FK still carries that spelling, having been founded before the official change. The municipality is the 184th largest by area out of the 356 municipalities in Norway. Ålesund is the 13th most populous municipality in Norway with a population of 67,114. The municipality's population density is and its population has increased by 9.9% over the previous 10-year period. General information In 1793, t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Norwegian People
Norwegians ( no, nordmenn) are a North Germanic ethnic group and nation native to Norway, where they form the vast majority of the population. They share a common culture and speak the Norwegian language. Norwegians are descended from the Norse of the Early Middle Ages who formed a unified Kingdom of Norway in the 9th century. During the Viking Age, Norwegians and other Norse peoples conquered, settled and ruled parts of the British Isles, the Faroe Islands, Iceland and Greenland. Norwegians are closely related to other North Germanic peoples and descendants of the Norsemen such as Danes, Swedes, Icelanders and the Faroe Islanders, as well as groups such as the Scots whose nation they significantly settled and left a lasting impact in. The Norwegian language is part of the larger Scandinavian dialect continuum of generally mutually intelligible languages in Scandinavia. Norwegian people and their descendants are found in migrant communities worldwide, notably in the Un ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
New York University
New York University (NYU) is a private research university in New York City. Chartered in 1831 by the New York State Legislature, NYU was founded by a group of New Yorkers led by then-Secretary of the Treasury Albert Gallatin. In 1832, the non-denominational all-male institution began its first classes near City Hall based on a curriculum focused on a secular education. The university moved in 1833 and has maintained its main campus in Greenwich Village surrounding Washington Square Park. Since then, the university has added an engineering school in Brooklyn's MetroTech Center and graduate schools throughout Manhattan. NYU has become the largest private university in the United States by enrollment, with a total of 51,848 enrolled students, including 26,733 undergraduate students and 25,115 graduate students, in 2019. NYU also receives the most applications of any private institution in the United States and admission is considered highly selective. NYU is organized int ... [...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 points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kurt Friedrichs
Kurt Otto Friedrichs (September 28, 1901 – December 31, 1982) was a noted German-American mathematician. He was the co-founder of the Courant Institute at New York University, and a recipient of the National Medal of Science. Biography Friedrichs was born in Kiel, Schleswig-Holstein on September 28, 1901. His family soon moved to Düsseldorf, where he grew up. He attended several different universities in Germany studying the philosophical works of Heidegger and Husserl, but finally decided that mathematics was his real calling. During the 1920s, Friedrichs pursued this field in Göttingen, which had a renowned Mathematical Institute under the direction of Richard Courant. Courant became a close colleague and lifelong friend of Friedrichs. In 1931, Friedrichs became a full professor of mathematics at the Technische Hochschule in Braunschweig. In early February 1933, a few days after Hitler became the Chancellor of Germany, Friedrichs met and immediately fell in love with a yo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Helge Holden
Helge Holden (born 28 September 1956) is a Norwegian mathematician working in the field of differential equations and mathematical physics. He was Praeses of the Royal Norwegian Society of Sciences and Letters from 2014 to 2016. He earned the dr.philos. degree at the University of Oslo in 1985. The title of his dissertation with Raphael Høegh-Krohn was ''Point Interactions and the Short-Range Expansion. A Solvable Model in Quantum Mechanics and Its Approximation''. He was appointed professor at the Norwegian Institute of Technology (now: the Norwegian University of Science and Technology ) in 1991. His research interests are Differential equations, mathematical physics (in particular hyperbolic conservation laws and completely integrable systems), Stochastic analysis, and flow in porous media. In 2014 he became Chairman of the board of the Abel Prize fund. He was elected Secretary General of the International Mathematical Union (IMU) for the period 2019–2022. Awards and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Statistical Mechanics
Quantum statistical mechanics is statistical mechanics applied to quantum mechanical systems. In quantum mechanics a statistical ensemble (probability distribution over possible quantum states) is described by a density operator ''S'', which is a non-negative, self-adjoint, trace-class operator of trace 1 on the Hilbert space ''H'' describing the quantum system. This can be shown under various mathematical formalisms for quantum mechanics. One such formalism is provided by quantum logic. Expectation From classical probability theory, we know that the expectation of a random variable ''X'' is defined by its distribution D''X'' by : \mathbb(X) = \int_\mathbb \lambda \, d \, \operatorname_X(\lambda) assuming, of course, that the random variable is integrable or that the random variable is non-negative. Similarly, let ''A'' be an observable of a quantum mechanical system. ''A'' is given by a densely defined self-adjoint operator on ''H''. The spectral measure of ''A'' defined ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sergio Albeverio
Sergio Albeverio (born 17 January 1939) is a Swiss mathematician and mathematical physicist working in numerous fields of mathematics and its applications. In particular he is known for his work in probability theory, analysis (including infinite dimensional, non-standard, and stochastic analysis), mathematical physics, and in the areas algebra, geometry, number theory, as well as in applications, from natural to social-economic sciences. He initiated (with Raphael Høegh-Krohn) a systematic mathematical theory of Feynman path integrals and of infinite dimensional Dirichlet forms and associated stochastic processes (with applications particularly in quantum mechanics, statistical mechanics and quantum field theory). He also gave essential contributions to the development of areas such as ''p''-adic functional and stochastic analysis as well as to the singular perturbation theory for differential operators. Other important contributions concern constructive quantum field the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fritz Gesztesy
Friedrich "Fritz" Gesztesy (born 5 November 1953 in Austria) is a well-known Austrian-American mathematical physicist and Professor of Mathematics at Baylor University, known for his important contributions in spectral theory, functional analysis, nonrelativistic quantum mechanics (particularly, Schrödinger operators), ordinary and partial differential operators, and completely integrable systems (soliton equations). He has authored more than 270 publications on mathematics and physics. Career After studying physics at the University of Graz, he continued with his PhD in theoretical physics. The title of his dissertation 1976 with Heimo Latal and Ludwig Streit was ''Renormalization, Nelson's symmetry and energy densities in a field theory with quadratic interaction''. After working at the Institut for Theoretical Physics of the University of Graz (1977–82) and several stays abroad at the Bielefeld University (Alexander von Humboldt Scholarship 1980–81 and 1983–84) and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jens Erik Fenstad
Jens Erik Fenstad (15 April 1935 – 13 April 2020) was a Norwegian mathematician. Fenstad graduated as ''mag.scient.'' from the University of Oslo in 1959, and worked as a research fellow there and at University of California, Berkeley, UC Berkeley. He was a professor at the University of Oslo from 1968 to 2003, except for the years 1989 to 1993, when he was vice rector (''prorektor''). On 29 May 1998 Fensted received an Honorary degree, honorary doctorate from the Faculty of Science and Technology at Uppsala University, Sweden. He served in the Executive Committee of the DLMPST, Division for Logic, Methodology and Philosophy of Science of the International Union of History and Philosophy of Science as Treasurer from 1975 to 1983 and as President from 1991 to 1995. He chaired the Norwegian Mathematical Society and the World Commission on Ethics (COMEST) of the UNESCO, and co-founded the Abel Prize. He has also edited the journal ''Nordisk Matematisk Tidsskrift''. He was a membe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Non-standard Analysis
The history of calculus is fraught with philosophical debates about the meaning and logical validity of fluxions or infinitesimal numbers. The standard way to resolve these debates is to define the operations of calculus using epsilon–delta procedures rather than infinitesimals. Nonstandard analysis instead reformulates the calculus using a logically rigorous notion of infinitesimal numbers. Nonstandard analysis originated in the early 1960s by the mathematician Abraham Robinson. He wrote: ... the idea of infinitely small or ''infinitesimal'' quantities seems to appeal naturally to our intuition. At any rate, the use of infinitesimals was widespread during the formative stages of the Differential and Integral Calculus. As for the objection ... that the distance between two distinct real numbers cannot be infinitely small, Gottfried Wilhelm Leibniz argued that the theory of infinitesimals implies the introduction of ideal numbers which might be infinitely small or infinitely ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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