Joseph Liouville

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The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Liouville, Joseph


Born Mar. 24, 1809, in St. Orner; died Sept. 8, 1882, in Paris. French mathematician. Member of the Paris Academy of Sciences (1839).

Liouville was a professor at the Ecole Polytechnique (from 1833) and the Collège de France (from 1839). He constructed the theory of elliptic functions, which he viewed as doubly periodic functions of a complex variable. He also studied the boundary-value problem for second-order linear differential equations (the Sturm-Liouville problem). Liouville proved the existence of transcendental numbers and gave an actual construction of such numbers. He established a fundamental theorem in mechanics (Liouville’s theorem) on the integration of the canonical equations of dynamics.


“Discours, prononcés aux funérailles de M. Liouville.” Comptes rendus hébdomadaires des séances de l’Académie des Sciences de Paris, 1882, vol. 95, pp. 467–71.
Synge, J. L. Classical Dynamics. Moscow, 1963. (Translated from English.)
The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
References in periodicals archive ?
On the other hand, Riemann and Liouville have extended traditional integral in order to obtain its fractional model.
The quoted conversation of the two famous mathematicians evoked interest among the researchers and the theory of noninteger orders was further developed, generalized, and formulated by famous mathematicians such as Riemann, Liouville, L Euler, Letnikov, Grunwald, Marchuad, Weyl, Riesz, Caputo, Abel, and others; see, for example, [36].
A real number [xi] is called a Liouville number, if there exist infinitely many rational numbers [([p.sub.n]/[q.sub.n]).sub.n[greater than or equal to]1], with [q.sub.n] [greater than or equal to] 1 and such that
Saarloos[3] shown that the density function (mass, momentum and energy fields) obeys a Liouville equation for hydrodynamics ideal fluid.
where ([sub.a][D.sup.[alpha]]) and ([sub.a][D.sup.[beta]]) are Riemann Liouville fractional derivatives of order [alpha] and [beta], respectively, f, g : [a, b] [right arrow] R are given continuous functions and a, b, B are given real constants.
Para tal, partimos da equacao de Liouville e, assumindo a validade de outras duas equacoes, chegamos a equacao de Schrodinger.
On variations of the Liouville constant which are also Liouville numbers Diego MARQUES and Carlos Gustavo MOREIRA Communicated by Masaki KASHIWARA, M.J.A.
In the last years, the inverse nodal problem and fractional calculus for Sturm Liouville problem has been studied by several authors Browne and Sleeman (1996), Yang (1997), Cheng et al.
Recollection of the role of Liouville in the history of the elliptic functions
A class of spinning magnetic brane in (n + 1)-dimensional EBId gravity with Liouville type potential which produces a longitudinal nonlinear electromagnetic field was presented in [56].