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Painlevé Equations
Painlevé, a surname, may refer to: __NOTOC__ People * Jean Painlevé (1902–1989), French film director, actor, translator, animator, son Paul * Paul Painlevé (1863–1933), French mathematician and politician, twice Prime Minister of France Mathematics * Painlevé conjecture, a conjecture about singularities in the n-body problem by Paul Painlevé * Painlevé paradox, a paradox in rigid-body dynamics by Paul Painlevé * Painlevé transcendents In mathematics, Painlevé transcendents are solutions to certain nonlinear second-order ordinary differential equations in the complex plane with the Painlevé property (the only movable singularities are poles), but which are not generally solvabl ..., ordinary differential equation solutions discovered by Paul Painlevé Other * French aircraft carrier ''Painlevé'', a planned ship named in honor of Paul Painlevé {{DEFAULTSORT:Painleve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jean Painlevé
Jean Painlevé (20 November 1902 – 2 July 1989) was a photographer and filmmaker who specialized in underwater fauna. He was the son of mathematician and twice prime minister of France Paul Painlevé. Upbringing A few days after Painlevé was born, his mother, Marguerite Petit de Villeneuve, died from complications arising from an infection contracted during childbirth. Painlevé, an only son, was raised by his father's sister Marie, a widow. In the ''Lycée Louis Le Grand'', he was a poor and inattentive student who preferred to skip classes and go to the '' Jardin d'Acclimatation'' where he was assisting the guard in taking care of the animals. Painlevé later wrote: "In high school, my classmates hated me. They hated people in the margins, such as Vigo, son of the anarchist Almereyda, or Pierre Merle, son of , director of atirical weekly''Merle Blanc'' ("White Blackbird"). Me, I was the son of a ''Boche'' (" Kraut)", that Painlevé who had fought for Sarrail, solit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paul Painlevé
Paul Painlevé (; 5 December 1863 – 29 October 1933) was a French mathematician and statesman. He served twice as Prime Minister of the Third Republic: 12 September – 13 November 1917 and 17 April – 22 November 1925. His entry into politics came in 1906 after a professorship at the Sorbonne that began in 1892. His first term as prime minister lasted only nine weeks but dealt with weighty issues, such as the Russian Revolution, the American entry into the war, the failure of the Nivelle Offensive, quelling the French Army Mutinies and relations with the British. In the 1920s as Minister of War he was a key figure in building the Maginot Line. In his second term as prime minister he dealt with the outbreak of rebellion in Syria's Jabal Druze in July 1925 which had excited public and parliamentary anxiety over the general crisis of France's empire. Biography Early life Painlevé was born in Paris. Brought up within a family of skilled artisans (his father was a draughtsma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Painlevé Conjecture
In physics, the Painlevé conjecture is a theorem about singularities among the solutions to the ''n''-body problem: there are noncollision singularities for ''n'' ≥ 4. The theorem was proven for ''n'' ≥ 5 in 1988 by Jeff Xia and for n=4 in 2014 by Jinxin Xue. Background and statement Solutions (\mathbf,\mathbf) of the ''n''-body problem \dot = M^\mathbf,\; \dot = \nabla U(\mathbf) (where M are the masses and U denotes the gravitational potential) are said to have a singularity if there is a sequence of times t_n converging to a finite t^* where \nabla U\left(\mathbf\left(t_n\right)\right) \rightarrow \infty. That is, the forces and accelerations become infinite at some finite point in time. A ''collision singularity'' occurs if \mathbf(t) tends to a definite limit when t \rightarrow t^*, t [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Painlevé Paradox
In rigid-body dynamics, the Painlevé paradox (also called frictional paroxysms by Jean Jacques Moreau) is the paradox that results from inconsistencies between the contact and Coulomb models of friction. It is named for former French prime minister and mathematician Paul Painlevé. To demonstrate the paradox, a hypothetical system is constructed where analysis of the system requires assuming the direction of the frictional force. Using that assumption, the system is solved. However, once the solution is obtained, the final direction of motion is determined to contradict the assumed direction of the friction force, leading to a paradox. This result is due to a number of discontinuities in the behavior of rigid bodies and the discontinuities inherent in the Coulomb friction law, especially when dealing with large coefficients of friction. There exist, however, simple examples which prove that the Painlevé paradoxes can appear even for small, realistic friction. Explanations Si ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Painlevé Transcendents
In mathematics, Painlevé transcendents are solutions to certain nonlinear second-order ordinary differential equations in the complex plane with the Painlevé property (the only movable singularities are poles), but which are not generally solvable in terms of elementary functions. They were discovered by , , , and . History Painlevé transcendents have their origin in the study of special functions, which often arise as solutions of differential equations, as well as in the study of isomonodromic deformations of linear differential equations. One of the most useful classes of special functions are the elliptic functions. They are defined by second order ordinary differential equations whose singularities have the Painlevé property: the only movable singularities are poles. This property is rare in nonlinear equations. Poincaré and L. Fuchs showed that any first order equation with the Painlevé property can be transformed into the Weierstrass elliptic function or the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
