Hyperbolic distribution - Revision history

en>UKoch: /* Properties */ added an explanation (sort of), formatting of formula, no links in headings

2014-11-30T18:27:44Z

Properties: added an explanation (sort of), formatting of formula, no links in headings

← Older revision		Revision as of 20:27, 30 November 2014
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	~~In [[mathematics]], the~~ '~~''multicomplex number''' systems C<sub>''n''</sub> are defined inductively as follows: Let C<sub>0</sub> be~~ the ~~[[real number]] system~~. ~~For every {{nowrap\|~~'~~'n'' > 0}} let ''i''<sub>''n''</sub> be a square root of −1, that is, an [[imaginary number]]~~. ~~Then <math>\text{C}_{n+1} = \lbrace z = x + y i_{n+1} : x,y \~~in ~~\text{C}_n \rbrace</math>. In~~ the ~~multicomplex number systems one also requires that <math>i_n i_m = i_m i_n</math> ([[commutativity]])~~. ~~Then C<sub>1</sub>~~ is the [[complex number]] system, C<sub>2</sub> is the [[bicomplex number]] system, C<sub>3</sub> is the ''tricomplex number'' system of [[Corrado Segre]], and C<sub>''n''</sub> is the multicomplex number system of order ''n''.		Myrtle Benny is how I'm called and I really feel comfy when people use the complete title. What I adore performing is to collect badges but I've been using on new issues lately. Years in the past he moved to North Dakota and his family members enjoys it. Managing individuals is his profession.<br><br>Stop by my web page: [http://203.250.78.160/zbxe/?document_srl=817810&mid=gallery at home std test]

	~~Each C~~<~~sub~~>~~''n''~~<~~/sub~~> ~~forms a~~ [~~[Banach algebra]]. [[Griffith Baley Price\|G. Bayley Price]] has written about the function theory of multicomplex systems, providing details for the bicomplex system C<sub>2<~~/~~sub>.~~

	The multicomplex number systems are not to be confused with ''Clifford numbers'' (elements of a [[Clifford algebra]]), since Clifford's square roots of −1 anti-commute (<math>i_n i_m + i_m i_n = 0</~~math> when {{nowrap\|''m'' ≠ ''n''}} for Clifford).~~

	~~With respect to [[subalgebra]] C<sub>''k''</sub>, ''k'' = 0, 1,~~ ...~~, {{nowrap\|''n'' − 1}}, the multicomplex system C<sub>''n''</sub> is of [[dimension]] {{nowrap\|2<sup>''n'' − ''k''<~~/~~sup>}} over C<sub>''k''<~~/~~sub>.~~

	~~==References~~==
	* [[Griffith Baley Price\|G. Baley Price]] (1991) ''An Introduction to Multicomplex Spaces and Functions'', [[Marcel Dekker]].
	* [[Corrado Segre]] (1892) "The real representation of complex elements and hyperalgebraic entities" (Italian), [[Mathematische Annalen]] 40:413–67 (see especially pages 455–67).

	~~[[Category:Hypercomplex numbers]~~]

en>Yobot: /* References */WP:CHECKWIKI error fixes (59) using AWB (9842)

2014-01-08T12:03:37Z

References: WP:CHECKWIKI error fixes (59) using AWB (9842)

← Older revision		Revision as of 14:03, 8 January 2014
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	~~Hi there. My name is Garland even though car warranty it is not~~ the ~~title on my birth certification. Arizona [https~~:/~~/www~~.~~epapyrus.com~~/~~xe/Purchase/5246873 extended car warranty~~] ~~[http~~://~~Automobiles~~.~~Honda.com~~/~~certified-pre-owned~~/~~warranty.aspx warranty~~] is ~~her beginning location~~ and ~~she will never transfer. Interviewing~~ is ~~what she does but soon she~~'~~ll be on her personal~~. ~~The factor I adore most flower arranging and now~~ [~~http://www~~.~~battdouglas~~.~~com~~/~~ActivityFeed/MyProfile/tabid/61/userId/6189/Default~~.~~aspx auto warranty~~] ~~I have time to take on new issues.~~<br><br>~~Also visit my~~ [~~http:~~/~~/www~~.~~Edmunds~~.~~com~~/~~auto-warranty/ extended auto~~] ~~warranty web-site; [http:~~//~~www~~.~~elterninitiative-hanfmuehle~~.~~de/index~~.~~php?mod=users~~&~~action=view~~&~~id=47185 http~~:~~//www.elterninitiative-hanfmuehle.de/~~]		In [[mathematics]], the '''multicomplex number''' systems C<sub>''n''</sub> are defined inductively as follows: Let C<sub>0</sub> be the [[real number]] system. For every {{nowrap\|''n'' > 0}} let ''i''<sub>''n''</sub> be a square root of −1, that is, an [[imaginary number]]. Then <math>\text{C}_{n+1} = \lbrace z = x + y i_{n+1} : x,y \in \text{C}_n \rbrace</math>. In the multicomplex number systems one also requires that <math>i_n i_m = i_m i_n</math> ([[commutativity]]). Then C<sub>1</sub> is the [[complex number]] system, C<sub>2</sub> is the [[bicomplex number]] system, C<sub>3</sub> is the ''tricomplex number'' system of [[Corrado Segre]], and C<sub>''n''</sub> is the multicomplex number system of order ''n''.

			Each C<sub>''n''</sub> forms a [[Banach algebra]]. [[Griffith Baley Price\|G. Bayley Price]] has written about the function theory of multicomplex systems, providing details for the bicomplex system C<sub>2</sub>.

			The multicomplex number systems are not to be confused with ''Clifford numbers'' (elements of a [[Clifford algebra]]), since Clifford's square roots of −1 anti-commute (<math>i_n i_m + i_m i_n = 0</math> when {{nowrap\|''m'' ≠ ''n''}} for Clifford).

			With respect to [[subalgebra]] C<sub>''k''</sub>, ''k'' = 0, 1, ..., {{nowrap\|''n'' − 1}}, the multicomplex system C<sub>''n''</sub> is of [[dimension]] {{nowrap\|2<sup>''n'' − ''k''</sup>}} over C<sub>''k''</sub>.

			==References==
			* [[Griffith Baley Price\|G. Baley Price]] (1991) ''An Introduction to Multicomplex Spaces and Functions'', [[Marcel Dekker]].
			* [[Corrado Segre]] (1892) "The real representation of complex elements and hyperalgebraic entities" (Italian), [[Mathematische Annalen]] 40:413–67 (see especially pages 455–67).

			[[Category:Hypercomplex numbers]]

en>Pol098: wording of first sentence

2012-06-14T10:18:44Z

wording of first sentence

New page

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