Jacobi symbol (2498 bytes)
1: ...fter the German mathematician [[Carl Gustav Jakob Jacobi]].
4: ...cobi symbol is a generalization of the [[Legendre symbol]] using the [[prime factorization]] of the bottom...
6: ...pha_k}</math>. For any integer ''a'', the Jacobi symbol <math>\left(\frac{a}{n}\right) = \left(\frac{a}{p...
8: ==Properties of the Jacobi symbol==
9: ...e are a number of useful properties of the Jacobi symbol which can be used to speed up calculations. They...

Jacobi (381 bytes)
1: There are several people with the surname '''Jacobi''':
2: * Mathematician [[Carl Gustav Jakob Jacobi]]
3: * American author [[Carl Richard Jacobi]]
4: * Danish author [[Carl Jacobi]]
5: * British actor [[Derek Jacobi]]

Viktor Jacobi (846 bytes)
1: ...omposers, [[Imre Kálmán]] and [[Albert Szirmai]]. Jacobi started his career as "Jakabfi Victor" on Decembe...
5: [[Category:Hungarian composers|Jacobi, Viktor]]
6: [[Category:1883 births|Jacobi, Viktor]]
7: [[Category:1921 deaths|Jacobi, Viktor]]

Jacobi field (5372 bytes)
1: ... of the name, see [[Carl Gustav Jacob Jacobi|Carl Jacobi]].
5: Jacobi fields can be obtained in the following way: Take...
7: is a Jacobi field.
9: ...a Jacobi field if and only if it satisfies the '''Jacobi equation''':
12: ...ete space|complete]] Riemannian manifold, for any Jacobi field there is a family of geodesics <math>\gamma...

Abraham Jacobi (1114 bytes)
1: '''Abraham Jacobi''' ([[May 6]], [[1830]] - [[July 10]], [[1919]]) ...
3: ...soned until he escaped in [[1853]]. Upon release, Jacobi sailed to [[England]] and then to [[New York]].
9: His wife, [[Mary Putnam Jacobi]], was also a physician. She was the first woman ...
13: [[Category:American physicians|Jacobi, Abraham]]
14: [[de:Abraham Jacobi]]

Jacobi identity (470 bytes)
1: The '''[[Carl Gustav Jakob Jacobi|Jacobi]] identity''' is the name for the following equat...
5: ...dentity. But note that an algebra can satisfy the Jacobi identity but yet not be [[anticommutative]].
7: ''See also'': [[Super Jacobi identity]].
11: [[sl:Jacobijeva enakost]]

Carl Jacobi (131 bytes)
1: *[[Carl Gustav Jakob Jacobi]] for the mathematician (1804-1851).
2: *[[Carl Richard Jacobi]] for the author (1908-1997).

Derek Jacobi (2195 bytes)
1: [[Image:DerekJacobi.jpg|right|]]
3: Sir '''Derek George Jacobi''' (born [[October 22]], [[1938]]) is a British [...
5: ...n his [[1965]] film of ''[[Othello]]''. Although Jacobi's name was becoming known and he was increasingly...
7: ...]'s adaptation of the novels of [[Ellis Peters]]. Jacobi has also done the narration for an audio book ver...
9: In the early [[2000s]] Jacobi toured internationally for a production of ''[[Th...

Jacobi (crater) (3810 bytes)
7: eponym=[[Carl Gustav Jakob Jacobi|Karl G. J. Jacobi]]}}
8: '''Jacobi''' is a [[lunar]] [[crater]] that is located in t...
10: ...ces. The larger of the craters on the north rim, 'Jacobi O', forms a member of a chain of craters that for...
12: ...bi E', and 'Jacobi G' form a line to the south of Jacobi crater.
16: ...e side of the crater mid-point that is closest to Jacobi

Euler-Jacobi pseudoprime (3635 bytes)
1: ...mposite]] [[integer]] ''n'' is called an '''Euler-Jacobi pseudoprime''' to base ''a'', if ''a'' and ''n'' ...
5: where (''a''/''n'') is the [[Jacobi symbol]].
7: ...he above equation, as explained in the [[Legendre symbol]] article. The equation can be tested rather quic...
9: ...''/2 bases less than ''n'', ''n'' is not an Euler-Jacobi pseudoprime.
13: The table below gives all Euler-Jacobi pseudoprimes less than 10000 for some prime bases...

Friedrich Heinrich Jacobi (11695 bytes)
1: '''Friedrich Heinrich Jacobi''' ([[January 25]], [[1743]] - [[March 10]], [[18...
3: ...al career. Of a retiring, meditative disposition, Jacobi associated himself at [[Geneva]] mainly with the ...
5: ...financial affairs, and his zeal in social reform. Jacobi kept up his interest in literary and philosophic ...
7: ...t Appendices, 1789) expressed sharply and clearly Jacobi's strenuous objection to a dogmatic system in phi...
9: ... In this writing, and especially in the Appendix, Jacobi came into contact with the critical philosophy, a...

Johann Georg Jacobi (1003 bytes)
1: ...at the cathedral of Halberstadt in 1769, and here Jacobi issued a number of anacreontic [[lyrics]] and [[s...
6: [[Category:1740 births|Jacobi, Johann Georg]]
7: [[Category:1814 deaths|Jacobi, Johann Georg]]
8: [[Category:German poets|Jacobi, Johann Georg]]
9: [[Category:natives of North Rhine-Westphalia|Jacobi, Johann Georg]]

Carl Richard Jacobi (910 bytes)
1: '''Carl Jacobi''' ([[July 10]], [[1908]] - [[August 25]], [[1997...
3: ... he began his writing career in campus magazines. Jacobi died on [[August 25]], [[1997]].
15: Carl Jacobi was also the name of a different author, who live...
17: [[Category:1908 births|Jacobi, Carl Richard]]
18: [[Category:1997 deaths|Jacobi, Carl Richard]]

Moritz von Jacobi (3236 bytes)
1: ...a]]n engineer and physicist born in [[Potsdam]]. Jacobi worked mainly in Russia. He futhered progress in ...
5: .... With financial assistance of [[Czar Nicholas]], Jacobi constructed in [[1839]] a 28 foot electric motor ...
7: ==Jacobi's Law==
21: ... a load such as an electric motor from a battery. Jacobi obtained his [[theorem]] by [[common sense]].
30: ...c.il/~eugeniik/history/jacobi.html Moritz Hermann Jacobi]''". Biosensors & Bioelectronics.

Jacobi triple product (1253 bytes)
1: ...le product''' is a relation that re-expresses the Jacobi [[theta function]], normally written as a series,...
11: This can easily be seen to be a relation on the Jacobi [[theta function]]; taking <math>x=\exp (i\pi\tau...

Carl Gustav Jakob Jacobi (5286 bytes)
1: [[image:Carl_Jacobi.jpg|right|Karl Gustav Jacob Jacobi]]
2: '''Karl Gustav Jacob Jacobi''' ([[Potsdam]] [[December 10]], [[1804]] - [[Ber...
4: ...berg]], and this chair he filled until [[1842]]. Jacobi suffered a breakdown from overwork in [[1843]]. H...
6: ...[[motion equation]]s in [[rotational form]] are [[Jacobi integral|integrable]] only for the three cases of...
8: ...al number theorem]] of [[Pierre de Fermat]]. The Jacobi [[theta function]]s, so frequently applied in the...

Jacobi's elliptic functions (10118 bytes)
1: ...oded. They were introduced by [[Carl Gustav Jakob Jacobi]], around 1830.
4: ...' are called the [[quarter period]]s. The twelve Jacobian elliptic functions are then pq, where p and q a...
6: The Jacobian elliptic functions are then the unique doubly-p...
11: The Jacobian elliptic functions are then the unique elliptic...
31: Equivalently, Jacobi's elliptic functions can be defined in terms of h...

Hamilton-Jacobi-Bellman equation (1316 bytes)
1: '''The Hamilton-Jacobi-Bellman (HJB) equation''' is a [[partial differen...
5: ...is sometimes referred to simply as the ''Hamilton-Jacobi'' equation, when the system contains no stochasti...
7: In Hamiltonian mechanics, the Hamilton-Jacobi-Bellman equation is very close to quantum mechani...

No symbol (2635 bytes)
1: [[Image:No_symbol.png|thumb|150px|right|An example]]
2: ...ed to indicate something is not permitted. The No symbol is usually colored red.
4: ... for the no symbol (also called the "Prohibition" symbol) is <code>U+20E0;</code> (&nbsp;&nbsp;&#x20E0;). ...
8: The "no" [[symbol]] is used on traffic signs, so that drivers can i...
14: ...traffic signs, no diagonal line is used, i.e. the symbol is round with a red border and a (usually black) ...

Symbol (4145 bytes)
1: A '''symbol''' or (in many senses) '''token''' is a represent...
3: ==Nature of symbols==
4: ...istianity]], and the [[scepter]] is a traditional symbol of [[monarch|royal]] power.
6: ...clan]]s, and the color [[red]] is often used as a symbol for [[socialism|socialist]] movements, especially...
8: ...nt [[money|monetary]] units, [[chemistry|chemical symbols]] represent elements, and so forth.

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