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Arnaud Denjoy
Arnaud Denjoy (; 5 January 1884 – 21 January 1974) was a French mathematician. Biography Denjoy was born in Auch, Gers. His contributions include work in harmonic analysis and differential equations. His integral was the first to be able to integrate all derivatives. Among his students is Gustave Choquet. He is also known for the more general broad Denjoy integral, or Khinchin integral. Denjoy was an Invited Speaker of the ICM with talk ''Sur une classe d'ensembles parfaits en relation avec les fonctions admettant une dérivée seconde généralisée'' in 1920 at Strasbourg and with talk ''Les equations differentielles periodiques'' in 1950 at Cambridge, Massachusetts. In 1931 he was the president of the Société Mathématique de France. In 1942 he was elected a member of the Académie des sciences and was its president in 1962. Denjoy married in 1923 and was the father of three sons. He died in Paris in 1974. He was an atheist with a strong interest in philosophy, psy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Auch
Auch (; oc, label= Gascon, Aush ) is a commune in southwestern France. Located in the region of Occitanie, it is the capital of the Gers department. Auch is the historical capital of Gascony. Geography Localization Hydrography The River Gers flows through the town. Transportation Auch is well connected to nearby cities and towns such as Agen, Toulouse and Tarbes by Routes Nationales and by train to Toulouse. Climate History and population Auch is a very ancient town, whose settlement was noted by the Romans during their conquest of the area in the . At that time, it was settled by an Aquitanian tribe known to the Romans as the Ausci. Their name for the town was Climberrum" or Elimberris. This has been tentatively etymologized from the Iberian ''iltir'' ("town, oppidum") and a cognate of the Basque ''berri'' ("new"), although another Iberian settlement in Granada recorded by the Romans as "Iliberi" probably had no contact with proto-Basque speaking peoples ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harmonic Analysis
Harmonic analysis is a branch of mathematics concerned with the representation of Function (mathematics), functions or signals as the Superposition principle, superposition of basic waves, and the study of and generalization of the notions of Fourier series and Fourier transforms (i.e. an extended form of Fourier analysis). In the past two centuries, it has become a vast subject with applications in areas as diverse as number theory, representation theory, signal processing, quantum mechanics, tidal analysis and neuroscience. The term "harmonics" originated as the Ancient Greek word ''harmonikos'', meaning "skilled in music". In physical eigenvalue problems, it began to mean waves whose frequencies are Multiple (mathematics), integer multiples of one another, as are the frequencies of the Harmonic series (music), harmonics of music notes, but the term has been generalized beyond its original meaning. The classical Fourier transform on R''n'' is still an area of ongoing research, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Denjoy–Young–Saks Theorem
In mathematics, the Denjoy–Young–Saks theorem gives some possibilities for the Dini derivatives of a function that hold almost everywhere. proved the theorem for continuous functions, extended it to measurable function In mathematics and in particular measure theory, a measurable function is a function between the underlying sets of two measurable spaces that preserves the structure of the spaces: the preimage of any measurable set is measurable. This is in di ...s, and extended it to arbitrary functions. and give historical accounts of the theorem. Statement If ''f'' is a real valued function defined on an interval, then with the possible exception of a set of measure 0 on the interval, the Dini derivatives of ''f'' satisfy one of the following four conditions at each point: *''f'' has a finite derivative *''D''+''f'' = ''D''–''f'' is finite, ''D''−''f'' = ∞, ''D''+''f'' = –∞. *''D''−''f'' = ''D''+''f'' is finite, ''D''+''f'' = ∞, ''D''–''f'' = –∠... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Denjoy–Riesz Theorem
In topology, the Denjoy–Riesz theorem states that every compact set of totally disconnected points in the Euclidean plane can be covered by a continuous image of the unit interval, without self-intersections (a Jordan arc). Definitions and statement A topological space is zero-dimensional according to the Lebesgue covering dimension if every finite open cover has a refinement that is also an open cover by disjoint sets. A topological space is totally disconnected if it has no nontrivial connected subsets; for points in the plane, being totally disconnected is equivalent to being zero-dimensional. The Denjoy–Riesz theorem states that every compact totally disconnected subset of the plane is a subset of a Jordan arc. History credits the result to publications by Frigyes Riesz in 1906, and Arnaud Denjoy in 1910, both in '' Comptes rendus de l'Académie des sciences''. As describe,. Riesz actually gave an incorrect argument that every totally disconnected set in the plane is a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Denjoy–Luzin–Saks Theorem
In mathematics, the Denjoy–Luzin–Saks theorem states that a function of generalized bounded variation in the restricted sense has a derivative In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). Derivatives are a fundamental tool of calculus. F ... almost everywhere, and gives further conditions of the set of values of the function where the derivative does not exist. N. N. Luzin and A. Denjoy proved a weaker form of the theorem, and later strengthened their theorem. References * Theorems in analysis {{mathanalysis-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Denjoy–Luzin Theorem
In mathematics, the Denjoy–Luzin theorem, introduced independently by and states that if a trigonometric series converges absolutely on a set of positive measure, then the sum of its coefficients In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series, or an expression; it is usually a number, but may be any expression (including variables such as , and ). When the coefficients are themselves var ... converges absolutely, and in particular the trigonometric series converges absolutely everywhere. References * * * Fourier series Theorems in analysis {{mathanalysis-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Denjoy Integral (other)
The Denjoy integral in mathematics can refer to two closely related integrals connected to the work of Arnaud Denjoy: * the ''narrow'' Denjoy integral, or just Denjoy integral, also known as Henstock–Kurzweil integral, * the (more general) ''wide'' Denjoy integral, or Khinchin integral. {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Denjoy Theorem (other)
{{mathdab ...
In mathematics, Denjoy's theorem may refer to several theorems proved by Arnaud Denjoy, including * Denjoy–Carleman theorem * Denjoy–Koksma inequality * Denjoy–Luzin theorem * Denjoy–Luzin–Saks theorem * Denjoy–Riesz theorem * Denjoy–Wolff theorem * Denjoy–Young–Saks theorem * Denjoy's theorem on rotation number In mathematics, the Denjoy theorem gives a sufficient condition for a diffeomorphism of the circle to be topologically conjugate to a diffeomorphism of a special kind, namely an irrational rotation. proved the theorem in the course of his topolog ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Académie Des Sciences
The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research. It was at the forefront of scientific developments in Europe in the 17th and 18th centuries, and is one of the earliest Academies of Sciences. Currently headed by Patrick Flandrin (President of the Academy), it is one of the five Academies of the Institut de France. History The Academy of Sciences traces its origin to Colbert's plan to create a general academy. He chose a small group of scholars who met on 22 December 1666 in the King's library, near the present-day Bibliothèque Nationals, and thereafter held twice-weekly working meetings there in the two rooms assigned to the group. The first 30 years of the Academy's existence were relatively informal, since no statutes had as yet been laid down for the institution. In contrast to its British ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Société Mathématique De France
Lactalis is a French multinational dairy products corporation, owned by the Besnier family and based in Laval, Mayenne, France. The company's former name was Besnier SA. Lactalis is the largest dairy products group in the world, and is the second largest food products group in France, behind Danone. It owns brands such as Parmalat, Président, Siggi's Dairy, Skånemejerier, Rachel's Organic, and Stonyfield Farm. History André Besnier started a small cheesemaking company in 1933 and launched its ''Président'' brand of Camembert in 1968. In 1990, it acquired Group Bridel (2,300 employees, 10 factories, fourth-largest French dairy group) with a presence in 60 countries. In 1992, it acquired United States cheese company Sorrento. In 1999, ''la société Besnier'' became ''le groupe Lactalis'' owned by Belgian holding company BSA International SA. In 2006, they bought Italian group Galbani, and in 2008, bought Swiss cheesemaker Baer. They bought Italian group Parmalat in a 2011 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
International Congress Of Mathematicians
The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be renamed as the IMU Abacus Medal), the Carl Friedrich Gauss Prize, Gauss Prize, and the Chern Medal are awarded during the congress's opening ceremony. Each congress is memorialized by a printed set of Proceedings recording academic papers based on invited talks intended to be relevant to current topics of general interest. Being List of International Congresses of Mathematicians Plenary and Invited Speakers, invited to talk at the ICM has been called "the equivalent ... of an induction to a hall of fame". History Felix Klein and Georg Cantor are credited with putting forward the idea of an international congress of mathematicians in the 1890s.A. John Coleman"Mathematics without borders": a book review ''CMS Notes'', vol 31, no. 3, April 1999 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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