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Laurent Schwartz
Laurent-Moïse Schwartz (; 5 March 1915 – 4 July 2002) was a French mathematician. He pioneered the theory of Distribution (mathematics), distributions, which gives a well-defined meaning to objects such as the Dirac delta function. He was awarded the Fields Medal in 1950 for his work on the theory of distributions. For several years he taught at the École polytechnique. Biography Family Laurent Schwartz came from a Jewish family of Alsace, Alsatian origin, with a strong scientific background: his father was a well-known surgeon, his uncle Robert Debré (who contributed to the creation of UNICEF) was a famous Pediatrics, pediatrician, and his great-uncle-in-law, Jacques Hadamard, was a famous mathematician. During his training at Lycée Louis-le-Grand to enter the École Normale Supérieure, he fell in love with Marie-Hélène Schwartz, Marie-Hélène Lévy, daughter of the probabilist Paul Lévy (mathematician), Paul Lévy who was then teaching at the École polytechniqu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paris
Paris () is the Capital city, capital and List of communes in France with over 20,000 inhabitants, largest city of France. With an estimated population of 2,048,472 residents in January 2025 in an area of more than , Paris is the List of cities in the European Union by population within city limits, fourth-most populous city in the European Union and the List of cities proper by population density, 30th most densely populated city in the world in 2022. Since the 17th century, Paris has been one of the world's major centres of finance, diplomacy, commerce, culture, Fashion capital, fashion, and gastronomy. Because of its leading role in the French art, arts and Science and technology in France, sciences and its early adoption of extensive street lighting, Paris became known as the City of Light in the 19th century. The City of Paris is the centre of the ÃŽle-de-France region, or Paris Region, with an official estimated population of 12,271,794 inhabitants in January 2023, or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Henri Hogbe Nlend
Henri Hogbe Nlend (born 23 December 1939) is a Cameroonian mathematician, university professor, former government minister and presidential candidate. Biography Henri Hogbe Nlend was a professor at the University of Yaoundé, and at the University of Bordeaux. In 1976, at a meeting of the International Mathematical Union it was decided to form an African Mathematical Union. Hogbe Nlend was elected as its first president, a post he held until 1986.[International Handbook of Mathematics Education], Alan J. Bishop, , accessed 1 August 2008 The AMU was partially funded from another organization in Paris, which was also chaired by Hogbe Nlend. It is said that he was good at raising funds and that meetings were held twice a year. Hogbe Nlend was a candidate in the 1997 Cameroonian presidential election, presidential election held on 12 October 1997, which was boycotted by the major opposition parties, and placed second, although he received only 2.9% of the vote. The winning candidate, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
École Polytechnique
(, ; also known as Polytechnique or l'X ) is a ''grande école'' located in Palaiseau, France. It specializes in science and engineering and is a founding member of the Polytechnic Institute of Paris. The school was founded in 1794 by mathematician Gaspard Monge during the French Revolution and was militarized under Napoleon I in 1804. It is still supervised by the Ministry of Armed Forces (France), French Ministry of Armed Forces. Originally located in the Latin Quarter, Paris, Latin Quarter in central Paris, the institution moved to Palaiseau in 1976, in the Paris-Saclay, Paris-Saclay technology cluster. French engineering students undergo initial military training and have the status of paid Aspirant, officer cadets. The school has also been awarding doctorates since 1985, masters since 2005 and bachelors since 2017. Most Polytechnique engineering graduates go on to become top executives in companies, senior civil servants, military officers, or researchers. List of É ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dirac Delta Function
In mathematical analysis, the Dirac delta function (or distribution), also known as the unit impulse, is a generalized function on the real numbers, whose value is zero everywhere except at zero, and whose integral over the entire real line is equal to one. Thus it can be Heuristic, represented heuristically as \delta (x) = \begin 0, & x \neq 0 \\ , & x = 0 \end such that \int_^ \delta(x) dx=1. Since there is no function having this property, modelling the delta "function" rigorously involves the use of limit (mathematics), limits or, as is common in mathematics, measure theory and the theory of distribution (mathematics), distributions. The delta function was introduced by physicist Paul Dirac, and has since been applied routinely in physics and engineering to model point masses and instantaneous impulses. It is called the delta function because it is a continuous analogue of the Kronecker delta function, which is usually defined on a discrete domain and takes values ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theory
A theory is a systematic and rational form of abstract thinking about a phenomenon, or the conclusions derived from such thinking. It involves contemplative and logical reasoning, often supported by processes such as observation, experimentation, and research. Theories can be scientific, falling within the realm of empirical and testable knowledge, or they may belong to non-scientific disciplines, such as philosophy, art, or sociology. In some cases, theories may exist independently of any formal discipline. In modern science, the term "theory" refers to Scientific theory, scientific theories, a well-confirmed type of explanation of nature, made in a way Consistency, consistent with the scientific method, and fulfilling the Scientific theory#Characteristics of theories, criteria required by modern science. Such theories are described in such a way that scientific tests should be able to provide Empirical evidence, empirical support for it, or Empirical evidence, empirical contradi ... [...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, mathematical structure, structure, space, Mathematical model, models, and mathematics#Calculus and analysis, change. History One of the earliest known mathematicians was Thales of Miletus (); 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's theorem. The number of known mathematicians grew when Pythagoras of Samos () 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 math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fields Medal
The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of Mathematicians, International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years. The name of the award honours the Canadian mathematician John Charles Fields. The Fields Medal is regarded as one of the highest honors a mathematician can receive, and has been list of prizes known as the Nobel or the highest honors of a field, described as the Nobel Prize of Mathematics, although there are several major differences, including frequency of award, number of awards, age limits, monetary value, and award criteria. According to the annual Academic Excellence Survey by Academic Ranking of World Universities, ARWU, the Fields Medal is consistently regarded as the top award in the field of mathematics worldwide, and in another reputation survey conducted by IREG Observatory on Academic Ranking and Excellence, IR ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cylinder Set Measure
In mathematics, cylinder set measure (or promeasure, or premeasure, or quasi-measure, or CSM) is a kind of prototype for a Measure (mathematics), measure on an infinite-dimensional vector space. An example is the Gaussian cylinder set measure on Hilbert space. Cylinder set measures are in general not measures (and in particular need not be Sigma additivity, countably additive but only Sigma additivity, finitely additive), but can be used to define measures, such as the Classical Wiener space#Classical Wiener measure, classical Wiener measure on the set of continuous paths starting at the origin in Euclidean space. This is done in the construction of the abstract Wiener space where one defines a cylinder set Gaussian measure on a separable Hilbert space and chooses a Banach space in such a way that the cylindrical measure becomes σ-additive on the cylindrical algebra. The terminology is not always consistent in the literature. Some authors call cylinder set measures just cylinder m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schwartz–Bruhat Function
In mathematics, a Schwartz–Bruhat function, named after Laurent Schwartz and François Bruhat, is a complex valued function on a locally compact abelian group, such as the adeles, that generalizes a Schwartz function on a real vector space. A tempered distribution is defined as a continuous linear functional on the space of Schwartz–Bruhat functions. Definitions *On a real vector space \mathbb^n, the Schwartz–Bruhat functions are just the usual Schwartz functions (all derivatives rapidly decreasing) and form the space \mathcal(\mathbb^n). *On a torus, the Schwartz–Bruhat functions are the smooth functions. *On a sum of copies of the integers, the Schwartz–Bruhat functions are the rapidly decreasing functions. *On an elementary group (i.e., an abelian locally compact group that is a product of copies of the reals, the integers, the circle group, and finite groups), the Schwartz–Bruhat functions are the smooth functions all of whose derivatives are rapidly decreasing. * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schwartz Space
In mathematics, Schwartz space \mathcal is the function space of all functions whose derivatives are rapidly decreasing. This space has the important property that the Fourier transform is an automorphism on this space. This property enables one, by duality, to define the Fourier transform for elements in the dual space \mathcal^* of \mathcal, that is, for tempered distributions. A function in the Schwartz space is sometimes called a Schwartz function. Schwartz space is named after French mathematician Laurent Schwartz. Definition Let \mathbb be the set of non-negative integers, and for any n \in \mathbb, let \mathbb^n := \underbrace_ be the ''n''-fold Cartesian product. The ''Schwartz space'' or space of rapidly decreasing functions on \mathbb^n is the function space\mathcal \left(\mathbb^n, \mathbb\right) := \left \,where C^(\mathbb^n, \mathbb) is the function space of smooth functions from \mathbb^n into \mathbb, and\, f\, _:= \sup_ \left, \boldsymbol^\boldsymbol (\ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schwartz Kernel Theorem
In mathematics, the Schwartz kernel theorem is a foundational result in the theory of generalized functions, published by Laurent Schwartz in 1952. It states, in broad terms, that the generalized functions introduced by Schwartz (Schwartz distributions) have a two-variable theory that includes all reasonable bilinear forms on the space \mathcal of test functions. The space \mathcal itself consists of smooth functions of compact support. Statement of the theorem Let X and Y be open sets in \mathbb^n. Every distribution k \in \mathcal'(X \times Y) defines a continuous linear map K \colon \mathcal(Y) \to \mathcal'(X) such that for every u \in \mathcal(X), v \in \mathcal(Y). Conversely, for every such continuous linear map K, there exists one and only one distribution k \in \mathcal'(X \times Y) such that () holds. The distribution k is the kernel of the map K. Note Given a distribution k \in \mathcal'(X \times Y), one can always write the linear map K informally as :Kv = \int_ k( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
