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| {{redirect|Poisson|other persons and things bearing this name}}
| | For stress related prostatitis, doctors would recommend different kinds of physical therapy. So to keep things simple, I have put together a short list for you: the top 5 causes for yeast infections. In fact, I discovered that it not only kills yeast infections, but it makes a nice all-purpose ear cleaner. Even though Diflucan has been known to be a treatment that remedies yeast infection it can also interrupt the embyonic formation. Cloves can be employed for the region to aid alleviate the itching and burning induce by yeast infection. <br><br>Make sure you get adequate sleep and continue with regular exercise as that will definitely help in the healing process. Unlike over the counter treatments and doctors prescriptions, natural cures work with your body. Probiotics should be included in your diet if you get recurrent episodes of Candidiasis. However, it's still important to know what the most common symptoms are and what you can do to alleviate the pain and discomfort associated with them. In extreme cases systemic Candidiasis may even be fatal. <br><br>You can also have your doctor or other healthcare provider order a test for you from a place like Genova Diagnostics who have excellent tests for food allergies, candida (yeast infection), etc. Fill the bath tub with warm water and add either a cup of vinegar or a tea spoon of baking soda for every quarter of a gallon, mix well and douche in that. This means eating the right foods and adopting a healthy lifestyle. Of course, on the surface the contention that a yeast infection can kill you may sound like some sort of alarmist propaganda from the manufacturer of some sort of yeast infection suppository, cream or pill. There are a number of triggers for yeast infections, ranging from antibiotics to pregnancy to stress, but there are some things you can do to help reduce the risk of getting a yeast infection such as keeping the genital area cool and dry by wearing cotton underwear and loose-fitting clothes, and changing out of wet or damp clothes as soon as possible. <br><br>Another reason why prostatitis is commonly ignored is because there is not much awareness about it. Sometimes, even low vitamin A, increase in the carotene level, or abnormally high cholesterol could indicate hypothyroidism. * These supplements increase the presence of beneficial bacteria in your body that help keep yeast from over-growing. The yeast take over and wipe out the healthy bacteria in the gut so that yeast is the predominate organism. The Candida fungus which is responsible for the occurrence of the infection is naturally present in our body making us prone to the infection. <br><br>There are some exceptions though, you'll want to add some of these foods which will help kill off yeast. It will cure the eye wrinkles and the under eye dark circles. Even women who are yeast infection experts can sometimes mistake one for Vaginitis so consult with your physician if you think you may have it. The home remedies for yeast infections can help you get rid of your infection. A test that seems to be at least as accurate, plus its easy and free, is the following spit test.<br><br>Here is more info regarding treatment of yeast infection - [http://www.naturalcureyeastinfection.info/sitemap/ please click the following article], stop by our web site. |
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| {{Infobox scientist
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| |name = Siméon Poisson
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| |image = Simeon_Poisson.jpg
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| |image_size = 200px
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| |caption = Siméon Denis Poisson (1781-1840)
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| |birth_date = {{Birth date|1781|6|21|df=yes}}
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| |birth_place = [[Pithiviers]], [[Orléanais]], [[Kingdom of France]]<br>(present-day [[Loiret]], [[France]])
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| |death_date = {{Death date and age|1840|4|25|1781|6|21|df=yes}}
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| |death_place = [[Sceaux, Hauts-de-Seine]], [[July Monarchy|Kingdom of France]]
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| |nationality = [[France]]
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| |fields = [[Mathematics]]
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| |workplaces = [[École Polytechnique]]<br>[[Bureau des Longitudes]]<br>[[Faculte des Sciences|Faculté des Sciences]]<br>[[École Spéciale Militaire de Saint-Cyr|École de Saint-Cyr]]
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| |alma_mater = [[École Polytechnique]]
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| |doctoral_advisor = [[Joseph-Louis Lagrange]]<br>[[Pierre-Simon Laplace]]
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| |academic_advisors =
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| |doctoral_students = [[Michel Chasles]]<br>[[Peter Gustav Lejeune Dirichlet]]<br>[[Joseph Liouville]]
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| |notable_students = [[Nicolas Léonard Sadi Carnot]]
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| |known_for = [[Poisson process]]<br>[[Poisson equation]]<br>[[Poisson kernel]]<br>[[Poisson distribution]]<br>[[Poisson bracket]]<br>[[Poisson algebra]]<br>[[Poisson regression]]<br>[[Poisson summation formula]]<br>[[Arago spot|Poisson's spot]]<br>[[Poisson's ratio]]<br>[[Most probable number|Poisson zeros]]<br>{{nowrap|[[Conway–Maxwell–Poisson distribution]]}}<br>[[Euler–Poisson–Darboux equation]]
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| |awards =
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| |religion = Unknown, [[Agnostic]]<ref>{{cite book|title=Classical Probability in the Enlightenment|year=1995|publisher=Princeton University Press|isbn=9780691006444|author=Lorraine Daston|accessdate=10 July 2012|page=381|quote=Poisson's understanding of causes, both natural and moral, was totally agnostic.}}</ref>
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| }}
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| {{Classical mechanics|cTopic=Scientists}}
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| '''Siméon Denis Poisson''' ({{IPA-fr|si.me.ɔ̃ də.ni pwa.sɔ̃|lang}}; 21 June 1781 – 25 April 1840), was a [[France|French]] [[mathematician]], [[geometer]], and [[physicist]]. He obtained many important results, but within the elite [[Académie des Sciences]] he also was the final leading opponent of the [[wave theory of light]] and was proven wrong on that matter by [[Augustin-Jean Fresnel]].
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| ==Biography==
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| Poisson was born in [[Pithiviers]], [[Loiret]], the son of soldier Siméon Poisson.
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| In 1798, he entered the [[École Polytechnique]] in [[Paris]] as first in his year, and immediately began to attract the notice of the professors of the school, who left him free to make his own decisions as to what he would study. In 1800, less than two years after his entry, he published two memoirs, one on [[Étienne Bézout]]'s method of elimination, the other on the number of [[integral]]s of a [[finite difference]] equation. The latter was examined by [[Sylvestre Lacroix|Sylvestre-François Lacroix]] and [[Adrien-Marie Legendre]], who recommended that it should be published in the ''Recueil des savants étrangers,'' an unprecedented honour for a youth of eighteen. This success at once procured entry for Poisson into scientific circles. [[Joseph Louis Lagrange]], whose lectures on the theory of functions he attended at the École Polytechnique, recognized his talent early on, and became his friend (the [[Mathematics Genealogy Project]] lists Lagrange as his advisor, but this may be an approximation); while [[Pierre-Simon Laplace]], in whose footsteps Poisson followed, regarded him almost as his son. The rest of his career, till his death in [[Sceaux, Hauts-de-Seine|Sceaux]] near Paris, was nearly occupied by the composition and publication of his many works and in fulfilling the duties of the numerous educational positions to which he was successively appointed.
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| Immediately after finishing his studies at the École Polytechnique, he was appointed ''[[répétiteur]]'' (teaching assistant) there, a position which he had occupied as an amateur while still a pupil in the school; for his schoolmates had made a custom of visiting him in his room after an unusually difficult lecture to hear him repeat and explain it. He was made deputy professor (''professeur suppléant'') in 1802, and, in 1806 full professor succeeding [[Jean Baptiste Joseph Fourier]], whom [[Napoleon]] had sent to [[Grenoble]]. In 1808 he became [[astronomer]] to the [[Bureau des Longitudes]]; and when the [[Faculte des Sciences|Faculté des Sciences]] was instituted in 1809 he was appointed professor of [[rational mechanics]] (''professeur de mécanique rationelle''). He went on to become a member of the Institute in 1812, examiner at the military school (''École Militaire'') at [[École Spéciale Militaire de Saint-Cyr|Saint-Cyr]] in 1815, graduation examiner at the École Polytechnique in 1816, councillor of the university in 1820, and geometer to the Bureau des Longitudes succeeding Pierre-Simon Laplace in 1827.
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| In 1817, he married Nancy de Bardi and with her he had four children. His father, whose early experiences had led him to hate aristocrats, bred him in the stern creed of the First Republic. Throughout the Revolution, the Empire, and the following restoration, Poisson was not interested in politics, concentrating on mathematics. He was appointed to the dignity of [[baron]] in 1821; but he neither took out the diploma or used the title. In March 1818, he was elected a [[Fellow of the Royal Society]]<ref>{{cite web|url=http://www2.royalsociety.org/DServe/dserve.exe?dsqIni=Dserve.ini&dsqApp=Archive&dsqCmd=Show.tcl&dsqDb=Persons&dsqPos=0&dsqSearch=%28Surname%3D%27poisson%27%29|title= Library and Archive Catalogue|publisher=The Royal Society|accessdate= 4 October 2010}}</ref> and in 1823 a foreign member of the [[Royal Swedish Academy of Sciences]]. The [[July Revolution|revolution of July 1830]] threatened him with the loss of all his honours; but this disgrace to the government of [[Louis-Philippe of France|Louis-Philippe]] was adroitly averted by [[François Jean Dominique Arago]], who, while his "revocation" was being plotted by the council of ministers, procured him an invitation to dine at the Palais Royal, where he was openly and effusively received by the citizen king, who "remembered" him. After this, of course, his degradation was impossible, and seven years later he was made a [[peer of France]], not for political reasons, but as a representative of French [[science]].
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| As a teacher of mathematics Poisson is said to have been extraordinarily successful, as might have been expected from his early promise as a ''répétiteur'' at the École Polytechnique. As a scientific worker, his productivity has rarely if ever been equalled. Notwithstanding his many official duties, he found time to publish more than three hundred works, several of them extensive treatises, and many of them memoirs dealing with the most abstruse branches of pure mathematics, [[applied mathematics]], [[mathematical physics]], and rational mechanics. ([[François Arago|Arago]] attributed to him the quote, "Life is good for only two things: doing mathematics and teaching it."<ref>[[François Arago]] (1786 - 1853) attributed to Poisson the quote: "La vie n'est bonne qu'à deux choses: à faire des mathématiques et à les professer." (Life is good for only two things: to do mathematics and to teach it.) See: J.-A. Barral, ed., ''Oeuvres complétes de François Arago ...'', vol. II (Paris, France: Gide et J. Baudry, 1854), [http://books.google.com/books?id=MRIPAAAAQAAJ&pg=PA662#v=onepage&q&f=false page 662].</ref>)
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| A list of Poisson's works, drawn up by himself, is given at the end of Arago's biography. All that is possible is a brief mention of the more important ones. It was in the application of mathematics to physics that his greatest services to science were performed. Perhaps the most original, and certainly the most permanent in their influence, were his memoirs on the theory of [[electricity]] and [[magnetism]], which virtually created a new branch of mathematical physics.
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| Next (or in the opinion of some, first) in importance stand the memoirs on [[celestial dynamics|celestial mechanics]], in which he proved himself a worthy successor to Pierre-Simon Laplace. The most important of these are his memoirs ''Sur les inégalités séculaires des moyens mouvements des planètes'', ''Sur la variation des constantes arbitraires dans les questions de mécanique'', both published in the ''Journal'' of the École Polytechnique (1809); ''Sur la libration de la lune'', in ''Connaissances des temps'' (1821), etc.; and ''Sur le mouvement de la terre autour de son centre de gravité'', in ''Mémoires de l'Académie'' (1827), etc. In the first of these memoirs, Poisson discusses the famous question of the stability of the planetary [[orbit]]s, which had already been settled by Lagrange to the first degree of approximation for the disturbing forces. Poisson showed that the result could be extended to a second approximation, and thus made an important advance in [[planetary theory]]. The memoir is remarkable inasmuch as it roused Lagrange, after an interval of inactivity, to compose in his old age one of the greatest of his memoirs, entitled ''Sur la théorie des variations des éléments des planètes, et en particulier des variations des grands axes de leurs orbites''. So highly did he think of Poisson's memoir that he made a copy of it with his own hand, which was found among his papers after his death. Poisson made important contributions to the theory of attraction.
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| His name is one of the [[List of the 72 names on the Eiffel Tower|72 names inscribed on the Eiffel Tower]].
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| ==Contributions==
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| Poisson's well-known correction of Laplace's second order [[partial differential equation]] for [[potential]]:
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| : <math> \nabla^2 \phi = - 4 \pi \rho \; </math>
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| today named after him [[Poisson's equation]] or the [[potential theory]] equation, was first published in the ''Bulletin de la société philomatique'' (1813). If a function of a given point ρ = 0, we get [[Laplace's equation]]:
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| : <math> \nabla^2 \phi = 0 \; .</math>
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| In 1812 Poisson discovered that Laplace's equation is valid only outside of a solid. A rigorous proof for masses with variable density was first given by [[Carl Friedrich Gauss]] in 1839. Both equations have their equivalents in [[vector calculus|vector algebra]]. Poisson's equation for the [[Laplace operator|divergence of the gradient]] of a [[scalar field]], φ in 3-dimensional space is:
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| : <math> \nabla^2 \phi = \rho (x, y, z) \; .</math>
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| Consider for instance Poisson's equation for surface [[electrical potential]], Ψ as a function of the density of [[electrical charge|electric charge]], ρ<sub>e</sub> at a particular point:
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| : <math> \nabla^2 \Psi = {\partial ^2 \Psi\over \partial x^2 } +
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| {\partial ^2 \Psi\over \partial y^2 } +
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| {\partial ^2 \Psi\over \partial z^2 } =
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| - {\rho_{e} \over \varepsilon \varepsilon_{0}} \; .</math>
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| The distribution of a charge in a [[fluid]] is unknown and we have to use the [[Poisson-Boltzmann equation]]: | |
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| :<math> \nabla^2 \Psi = {n_{0} e \over \varepsilon \varepsilon_{0}}
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| \left( e^{e\Psi (x,y,z)/k_{B}T} -
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| e^{-e\Psi (x,y,z)/ k_{B}T} \right), \; </math>
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| which in most cases cannot be solved analytically. In [[coordinates (elementary mathematics)|polar coordinate]]s the Poisson-Boltzmann equation is:
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| :<math> {1\over r^{2}} {d\over dr} \left( r^{2} {d\Psi \over dr} \right) =
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| {n_{0} e \over \varepsilon \varepsilon_{0}}
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| \left( e^{e\Psi (r) / k_{B}T} - e^{-e\Psi (r) / k_{B}T} \right) \; </math>
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| which also cannot be solved analytically. If a [[Field (mathematics)|field]], φ is not [[scalar field|scalar]], the Poisson equation is valid, as can be for example in 4-dimensional [[Minkowski space]]:
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| :<math> \sqrt \phi_{ik} = \rho (x, y, z, ct) \; . </math>
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| If ρ(''x'', ''y'', ''z'') is a [[continuous function]] and if for ''r''→ ∞ (or if a point 'moves' to [[Extended real number line|infinity]]) a function φ goes to 0 fast enough, a solution of Poisson's equation is the [[Newtonian potential]] of a function ρ(''x'', ''y'', ''z''):
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| :<math> \phi_M = - {1\over 4 \pi} \int {\rho (x, y, z)\, dv \over r} \; </math>
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| where ''r'' is a distance between a volume element ''dv'' and a point ''M''. The integration runs over the whole space.
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| Another "Poisson's integral" is the solution for the [[Green function]] for Laplace's equation with Dirichlet condition over a circular disk:
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| :<math> \phi(\xi \eta) = {1\over 4 \pi} \int _0^{2\pi}
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| {R^2 - \rho^2\over R^2 + \rho^2 - 2R \rho \cos (\psi - \chi) } \phi
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| (\chi)\, d \chi \; </math>
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| where
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| :<math> \xi = \rho \cos \psi, \; </math>
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| :<math>\quad \eta = \rho \sin \psi, \; </math>
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| :φ is a boundary condition holding on the disk's boundary.
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| In the same manner, we define the Green function for the Laplace equation with Dirichlet condition, ∇² φ = 0 over a sphere of radius ''R''. This time the Green function is:
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| :<math> G(x,y,z;\xi,\eta,\zeta) = {1\over r} - {R\over r_1 \rho} \; , </math>
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| where
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| :<math> \rho = \sqrt {\xi^2 + \eta^2 + \zeta^2} </math> is the distance of a point (ξ, η, ζ) from the center of a sphere,
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| ''r'' is the distance between points (''x'', ''y'', ''z'') and (ξ, η, ζ), and
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| ''r''<sub>1</sub> is the distance between the point (''x'', ''y'', ''z'') and the point (''R''ξ/ρ, ''R''η/ρ, ''R''ζ/ρ), symmetrical to the point (ξ, η, ζ).
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| Poisson's integral now has a form:
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| :<math> \phi(\xi, \eta, \zeta) = {1\over 4 \pi} \int\!\!\!\int_S {R^2 -
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| \rho^2 \over R r^3} \phi\, ds \; . </math>
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| Poisson's two most important memoirs on the subject are ''Sur l'attraction des sphéroides'' (Connaiss. ft. temps, 1829), and ''Sur l'attraction d'un ellipsoide homogène'' (Mim. ft. l'acad., 1835). In concluding our selection from his physical memoirs, we may mention his memoir on the theory of waves (Mém. ft. l'acad., 1825).
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| In [[pure mathematics]], his most important works were his series of memoirs on [[definite integral]]s and his discussion of [[Fourier series]], the latter paving the way for the classic researches of [[Peter Gustav Lejeune Dirichlet]] and [[Bernhard Riemann]] on the same subject; these are to be found in the ''Journal'' of the École Polytechnique from 1813 to 1823, and in the ''Memoirs de l'Académie'' for 1823. He also studied [[Fourier integral]]s. We may also mention his essay on the [[calculus of variations]] (''Mem. de l'acad.,'' 1833), and his memoirs on the probability of the mean results of observations (''Connaiss. d. temps,'' 1827, &c). The [[Poisson distribution]] in [[probability theory]] is named after him.
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| In his ''Traité de mécanique'' (2 vols. 8vo, 1811 arid 1833), which was written in the style of Laplace and Lagrange and was long a standard work, he showed many novelties such as an explicit usage of [[momentum|momenta]]:
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| :<math> p_i = {\partial T\over {\partial q_i\over \partial t}},</math>
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| which influenced the work of [[William Rowan Hamilton|Hamilton]] and [[Carl Gustav Jakob Jacobi|Jacobi]].
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| Besides his many memoirs, Poisson published a number of treatises, most of which were intended to form part of a great work on mathematical physics, which he did not live to complete. Among these may be mentioned
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| * ''Nouvelle théorie de l'action capillaire'' (4to, 1831);
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| * ''Théorie mathématique de la chaleur'' (4to, 1835);
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| * Supplement to the same (4to, 1837);
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| * ''Recherches sur la probabilité des jugements en matières criminelles et matière civile'' (4to, 1837), all published at Paris.
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| A translation of Poisson's [http://books.google.com/books?id=lksn7QwUZsQC&dq=Poisson+mechanics&as_brr=1&hl=en Treatise on Mechanics] was published in London in 1842.
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| In 1815 Poisson studied integrations along paths in the complex plane. In 1831 he derived the [[Navier-Stokes equations]] independently of [[Claude-Louis Navier]].
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| ==Flawed views on the wave theory of light==
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| Poisson, despite his brilliance, had surprising hubris on the [[wave theory of light]]. He was a member of the academic "old guard" at the [[Académie française]], who were staunch believers in the [[particle theory of light]] who were alarmed at the wave theory of light's increasing acceptance. In 1818, the Académie française set their prize as [[diffraction]], being certain that a particle theorist would win it. Poisson, relying on intuition rather than mathematics or scientific experiment, ridiculed participant and civil engineer [[Augustin-Jean Fresnel]] when he submitted a thesis explaining diffraction derived from analysis of both the [[Huygens–Fresnel principle]] and [[Young's double slit experiment]].
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| <ref name="fresnel1868">{{Citation | |
| | last = Fresnel | first = A.J.
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| | year =1868
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| | title = OEuvres Completes 1
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| | publisher = Imprimerie impériale
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| | publication-place = Paris
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| | url = http://books.google.com/books/about/%C5%92uvres_compl%C3%A8tes_d_Augustin_Fresnel_Th.html?id=3QgAAAAAMAAJ
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| }}</ref>
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| Poisson studied Fresnel's theory in detail and of course looked for a way to prove it wrong, as he was a dogmatic supporter of the particle-theory of light. Poisson thought that he had found a flaw when he argued that a consequence of Fresnel’s theory was that there would exist an on-axis bright spot in the shadow of a circular obstacle blocking a [[point source]] of light, where there should be complete darkness according to the particle-theory of light. Fresnel's theory could not be true, Poisson declared, surely this result was absurd. (The Poisson spot is not easily observed in every-day situations, because most everyday sources of light are not good point sources.)
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| However, the head of the committee, [[François Arago|Dominique-François-Jean Arago]], and who incidentally later became Prime Minister of France, did not have the hubris of Poisson and decided it was necessary to perform the experiment in more detail. He molded a 2-mm metallic disk to a glass plate with wax.
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| <ref name="fresnel1868_arago">{{Citation
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| | last = Fresnel | first = A.J.
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| | year =1868
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| | title = OEuvres Completes 1
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| | publisher = Imprimerie impériale
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| | publication-place = Paris
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| | page = 369
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| | url = http://books.google.com/books/about/%C5%92uvres_compl%C3%A8tes_d_Augustin_Fresnel_Th.html?id=3QgAAAAAMAAJ
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| }}</ref> To everyone's surprise he succeeded in observing the predicted spot, which convinced most scientists of the wave-nature of light. In the end Fresnel won the competition, much to Poisson's chagrin.
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| After that, the corpuscular theory of light was vanquished, not to be heard of again, in a very different form, till the 20th century developed [[wave-particle duality]]. Arago later noted that the diffraction bright spot (which later became known as both the [[Arago spot]] and the Poisson spot) had already been observed by [[Joseph-Nicolas Delisle]]
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| <ref name="fresnel1868_arago"/> and [[Giacomo F. Maraldi]]
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| <ref name="maraldi1723">{{Citation
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| | last = Maraldi | first = G.F.
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| | year = 1723
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| | title = 'Diverses expèriences d'optique' in Mémoires de l’Académie Royale des Sciences
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| | publisher = Imprimerie impériale
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| | page = 111
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| | url = http://gallica.bnf.fr/ark:/12148/bpt6k3592w/f300.image.langFR
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| }}</ref> a century earlier.
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| ==See also==
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| {{Wikiquote}}
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| *[[List of things named after Siméon Denis Poisson]]
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| ==References==
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| {{reflist}}
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| * {{MacTutor Biography|id=Poisson}}
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| * {{MathGenealogy|id=17865}}
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| *{{1911}}
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| {{Copley Medallists 1801-1850}}
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| {{Use dmy dates|date=September 2010}}
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| {{Authority control|PND=116261293|LCCN=n/83/239440|VIAF=22241140}}
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| {{Persondata<!-- Metadata: see [[Wikipedia:Persondata]] -->
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| |NAME=Poisson, Siméon Denis
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| |ALTERNATIVE NAMES=
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| |SHORT DESCRIPTION=Mathematician, geometer and physicist
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| |DATE OF BIRTH=1781-06-21
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| |PLACE OF BIRTH=Pithiviers, Loiret, France
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| |DATE OF DEATH=1840-04-25
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| |PLACE OF DEATH=Sceaux, Hauts-de-Seine, France
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| }}
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| {{DEFAULTSORT:Poisson, Simeon}}
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| [[Category:1781 births]]
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| [[Category:1840 deaths]]
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| [[Category:People from Pithiviers]]
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| [[Category:19th-century French mathematicians]]
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| [[Category:École Polytechnique alumni]]
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| [[Category:Fellows of the Royal Society]]
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| [[Category:French agnostics]]
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| [[Category:French mathematicians]]
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| [[Category:Mathematical analysts]]
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| [[Category:Members of the French Academy of Sciences]]
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| [[Category:Members of the Royal Swedish Academy of Sciences]]
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| [[Category:Peers of France]]
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| [[Category:Probability theorists]]
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| [[Category:Recipients of the Copley Medal]]
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