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Topic: Poincar

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Henri Poincar

The Poincar Conjecture

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	Congettura di Poincarè: Tutte le informazioni su Congettura di Poincarè su Encyclopedia.it (Site not responding. Last check: 2007-10-21)
		Purtroppo si accorse molto presto di essere in errore dato che riuscì a creare una varietà chiamata spazio dodecaedrico di Poincare, che era omologo con una sfera a 3 D pur non avendone tutte le proprietà topologiche.
		Sotto le condizioni di Poincaré il quesito può essere posto anche nel seguente modo "ogni anello deve potersi contrarre fino a formare un punto".
		Questo indusse i matematici più famosi a essere molto cauti negli annunci legati alla congettura di Poincaré dato che errori a volte molto sottili rendevano le dimostrazioni inutili.
	www.encyclopedia.it /c/co/congettura_di_poincare_1.html (881 words)

	Jules Henri Poincaré [Internet Encyclopedia of Philosophy]
		Poincaré sketched a preliminary version of the special theory of relativity and stated that the velocity of light is a limit velocity and that mass depends on speed.
		However, Poincaré found that the evolution of such a system is often chaotic in the sense that a small perturbation in the initial state such as a slight change in one body's initial position might lead to a radically different later state than would be produced by the unperturbed system.
		Poincaré argues that this reasoning is a vicious circle, for it relies upon the principle of complete induction, whose consistency we have to prove.
	www.utm.edu /research/iep/p/poincare.htm (3565 words)

	Henri Poincaré - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-10-21)
		Poincaré was interested in the way his mind worked; he studied his habits and gave a talk about his observations in 1908 at the Institute of General Psychology in Paris.
		Poincaré made many contributions to different fields of applied mathematics such as: celestial mechanics, fluid mechanics, optics, electricity, telegraphy, capillarity, elasticity, thermodynamics, potential theory, quantum theory, theory of relativity and cosmology.
		Poincaré had the opposite philosophical views of Bertrand Russell and Gottlob Frege, who believed that mathematics were a branch of logic.
	en.wikipedia.org /wiki/Henri_Poincar%c3%a9 (2519 words)

	Poincare
		Poincaré was a scientist preoccupied by many aspects of mathematics, physics and philosophy, and he is often described as the last universalist in mathematics.
		Poincaré realised that indeed he had made an error and Mittag-Leffler made strenuous efforts to prevent the publication of the incorrect version of the memoir.
		Poincaré was absolutely correct, however, in his criticism of those like Russell who wished to axiomatise mathematics were doomed to failure.
	www-groups.dcs.st-and.ac.uk /~history/Mathematicians/Poincare.html (3075 words)

	PlanetMath: Poincaré, Jules Henri
		Poincaré had the opposite philosophical views of Bertrand Rusell and Gottlob Fredge who believed that mathematics were a branch of logic.
		Poincaré's first area of interest in mathematics was the Fuchsian function that he named after the mathematician Lazarus Fuch because Fuch was known for being a good teacher and done alot of research in differential equations and in the theory of functions.
		Poincaré contributed to the field of algebraic topology and published Analysis situs in 1895 which was the first real systematic look at topology.
	planetmath.org /encyclopedia/JulesHenriPoincare.html (2227 words)

	Poincaré, Raymond on Encyclopedia.com (Site not responding. Last check: 2007-10-21)
		During World War I, Poincaré called on (1917) Georges Clemenceau to form a new cabinet, despite his personal hatred of the man. After the war Poincaré called for harsh punishment of Germany and for adequate guarantees of French security.
		In the face of Germany's failure to pay the heavy reparations assigned by the peace treaty, Poincaré sent French troops to occupy the Ruhr in 1923.
		To deal with the financial situation, Poincaré pursued an extreme deflationary policy, balancing the budget and securing (1928) the stabilization of the franc at one fifth of its former value.
	www.encyclopedia.com /html/P/PoincarR1.asp (563 words)

	Time [Internet Encyclopedia of Philosophy]
		Although his actual proof was shown to depend on some probability theory and not merely on Newton's laws of motion, his treatment of entropy as being basically a statistical concept was broadly accepted, as was his claim that time's arrow is to be explained in terms of entropy increase.
		Poincaré's recurrence theorem in statistical mechanics says every isolated dynamical system will eventually return to a state as close to the initial state as we might wish.
		The problem raised by Poincaré is less of a problem for Boltzmann's treatment of time's arrow than is the Loschmidt Problem.
	www.iep.utm.edu /t/time.htm (15789 words)

	[No title]
		The difficulty in passing from 3-d to 4-d comes from the highter dimension of the Poincar\'{e} group (passing from 7 to 10 dimensions) and from the non-integrability of some kernels.
		Thus from theorem 5, $c$ is the interaction kernel in the centre-of-mass frame of a continuous unitary representation of the Poincar\'{e} group.
		The Poincar\'{e} representation describing one particle of mass $m>0$ without spin in given by the following lemma (which is essentially given in [21]).
	mpej.unige.ch /mp_arc/papers/98-305 (5398 words)

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