Joseph Liouville (2129 bytes)
1: '''Joseph Liouville''' (born [[March 24]] [[1809]], died [[September ...
3: Liouville graduated from the [[École Polytechnique]] in 182...
5: ...e Galois]] which appeared in his journal in 1846. Liouville was also involved in politics for some time, and ...
7: ... is a second "[[Liouville's theorem (Hamiltonian)|Liouville's theorem]]" in Hamiltonian dynamics.
9: [[Category:1809 births|Liouville, Joseph]]

Liouville (crater) (1008 bytes)
20: |[[Joseph Liouville]]
22: '''Liouville''' is a small [[lunar]] impact [[crater]] that is...

Liouville function (1458 bytes)
1: [[sv:Liouvilles lambda-funktion]]
2: ...noted by λ(''n'') and named after [[Joseph Liouville]], is an important [[function (mathematics)|funct...
10: ...ave Ω(1)=0 and therefore λ(1)=1. The Liouville function satisfies the identity:
15: The Liouville function is related to the [[Riemann zeta functio...

Liouville number (7281 bytes)
1: In [[number theory]], a '''Liouville number''' is a [[real number]] ''x'' with the pro...
5: A Liouville number can then be approximated "quite closely" b...
7: It is relatively easily proven that if ''x'' is a Liouville number, ''x'' is [[irrational number | irrational...
13: In [[1844]], [[Joseph Liouville]] showed that numbers of with this property are n...
19: ...iouville's constant'''. Liouville's constant is a Liouville number; if we define ''p''_''n'' and ''...

Liouville equation (1829 bytes)
1: The '''Liouville equation''' is the most important equation of [[S...
14: (See [[Liouville's theorem (Hamiltonian)]] for further discussion ...
31: Another way to write down the Liouville Equation is
39: The Liouville Equation is a [[continuity equation]] for the [[p...
42: ...ville equation (differential geometry)]], [[Sturm-Liouville equation]].

Liouville's theorem (380 bytes)
1: '''Liouville's theorem''' has various meanings:
3: *In [[complex analysis]], see [[Liouville's theorem (complex analysis)]].
4: *In [[Hamiltonian mechanics]], see [[Liouville's theorem (Hamiltonian)]].
5: *In [[number theory]], the theorem that any [[Liouville number]] is [[Transcendental number|transcendenta...

Liouville-Neumann series (990 bytes)
1: In [[mathematics]], the '''[[Liouville]]-Neumann series''' is an [[infinite series]] def...

Sturm-Liouville theory (10705 bytes)
1: ...Charles Francois Sturm]] (1803-1855) and [[Joseph Liouville]] (1809-1882), is a second-order linear [[differe...
9: '''Sturm-Liouville theory''' is important in applied mathematics, wh...
11: == Sturm-Liouville form ==
14: is said to be in Sturm-Liouville form. The function ''w'' is known as the weight f...
19: can easily be put into Sturm-Liouville form, since ''D''(1-''x''²)=-2''x'', s...

Riemann-Liouville differintegral (2486 bytes)
13: The '''Riemann-Liouville differintegral''' (RL) is the simplest and easies...
15: === Constructing the Riemann-Liouville differintegral ===
16: We first introduce the ''Riemann-Liouville fractional integral'', which is a straightforward...

Liouville's theorem (Hamiltonian) (6261 bytes)
1: ...ouville's theorem''' (also sometimes known as the Liouville equation) is a key theorem in [[statistical mecha...
4: ...her being in the field of complex analysis (see [[Liouville's theorem (complex analysis)]].

Liouville's theorem (complex analysis) (2134 bytes)
2: '''Liouville's theorem''' in [[complex analysis]] states that ...
4: Liouville's theorem can be used to give an elegant short pr...
21: See also [[Joseph Liouville]].
23: [[de:Satz von Liouville]]
24: [[fr:Théorème de Liouville]]

Joseph K. (950 bytes)
1: ...daptation of ''[[The Trial (movie)|The Trial]]'', Joseph K. is played by [[Anthony Perkins]].

Joseph II (169 bytes)
1: '''Joseph II''' may refer to either:
3: *[[Joseph II, Holy Roman Emperor]]
4: *[[Joseph II of Constantinople | Joseph II, Orthodox Patriarch]] of Constantinople

Joseph I (148 bytes)
1: There have been two monarchs named '''Joseph I'''
3: *[[Joseph I, Holy Roman Emperor]] (1678-1711)
4: *[[Joseph I of Portugal]] (1750-1777)

Joseph (1602 bytes)
1: '''Joseph''' (יוסף, [[Standard Hebr...
3: * [[Joseph (Hebrew Bible)|Joseph]], son of [[Jacob]], is a character in the [[Book...
4: **''[[Joseph and the Amazing Technicolor Dreamcoat]]'' is a wo...
5: ...eh]] (taken from the same [[Joseph (Hebrew Bible)|Joseph]] who wore the coat of many colours).
6: * [[Saint Joseph]] of Nazareth is a character from the [[New Testa...

Joseph J. Fern (2757 bytes)
1: [[Image:josephjfern.jpg|thumb|108px|Joseph J. Fern was the first Mayor of Honolulu.]]
3: '''Joseph James Fern''' ([[August 25]], [[1872]] - [[Februa...
14: ...aiheku'i Alapai with whom he had twelve children: Joseph James, Mary K., Nancy K., George, Kaipo, Elizabet...
19: [[Category:1872 births|Fern, Joseph J.]]
20: [[Category:1920 deaths|Fern, Joseph J.]]

Joseph Wright (267 bytes)
1: '''Joseph Wright''' may refer to:
2: *[[Joseph Wright of Derby]] ([[1734]] — [[1797]]), En...
3: *[[Joseph Wright (art director)]] Academy awards 1942 & 196...
4: *[[Joseph Wright (rower)]] Toronto Argomauts, [[Rowing at t...

Joseph Guillemot (2319 bytes)
1: '''Joseph Guillemot''' ([[October 1]], [[1899]] – [[M...
3: Born in [[Le Dorat]], France, Joseph Guillemot's lungs were severely damaged by [[must...
11: Joseph Guillemot, a pack a day cigarette smoker, died in...
13: [[Category:1899 births|Guillemot, Joseph]]
14: [[Category:1975 deaths|Guillemot, Joseph]]

Joseph W. Barr (2031 bytes)
1: '''Joseph Walker Barr''' ([[January 17]], [[1918]]–[[...
22: .../jwbarr.html US Treasury - Biography of Secretary Joseph W. Barr]
24: [[Category:1918 births|Barr, Joseph W.]]
25: [[Category:1996 deaths|Barr, Joseph W.]]
26: [[Category:U.S. Secretaries of the Treasury|Barr, Joseph W.]]

Joseph Spencer (2090 bytes)
1: '''Joseph Spencer''' ([[1714]]–[[1789]]) was an Ameri...
16: [[Category:1714 births|Spencer, Joseph]]
17: [[Category:1789 deaths|Spencer, Joseph]]
18: [[Category:Continental Army generals|Spencer, Joseph]]
19: [[Category:Continental Congressmen|Spencer, Joseph]]

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