Phase factor - Revision history

en>Fgnievinski: phase factor is not any phasor, it's a unit phasor

2014-10-13T03:36:12Z

phase factor is not any phasor, it's a unit phasor

← Older revision		Revision as of 05:36, 13 October 2014
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	~~In [[mathematics]], the~~ '~~''Parry–Sullivan invariant''' (or '''Parry–Sullivan number''')~~ is ~~a numerical quantity of interest in the study of [[incidence matrix\|incidence matrices]] in [[graph theory]],~~ and ~~of certain one-dimensional [[dynamical systems]]~~. ~~It provides a partial classification of non-trivial irreducible incidence matrices~~.		Oscar is how he's known as and he totally enjoys this title. South Dakota is exactly where me and my spouse live. Managing individuals is his occupation. To collect cash is 1 of the issues I adore most.<br><br>My web site :: [http://www.alhuloul.com/?p=235037 alhuloul.com]

	It is ~~named after~~ the English mathematician [[Bill Parry (mathematician)\|Bill Parry]] and the American mathematician [[Dennis Sullivan]], who introduced the invariant in a joint paper published in the journal [[Topology (journal)\|''Topology'']] in 1975.

	~~==Definition==~~

	~~Let ''A'' be an ''n'' × ''n'' incidence matrix. Then the '''Parry–Sullivan number''' of ''A'' is defined to be~~

	:<~~math~~>~~\mathrm{PS} (A) = \det (I - A), \,~~ <~~/math~~>

	~~where ''I'' denotes the ''n'' × ''n'' identity matrix.~~

	~~==Properties==~~

	~~It can be shown that, for nontrivial irreducible incidence matrices, flow equivalence is completely determined by the Parry–Sullivan number and the~~ [~~[Bowen–Franks group]].~~

	~~==References==~~

	* {{cite journal \| author=Parry, W.~~, & Sullivan, D~~. ~~\| title~~=~~A topological invariant of flows on 1-dimensional spaces \| journal=Topology \| volume=14 \| year=1975 \| pages=297–299 \| doi=10~~.~~1016/0040-9383(75)90012-9 \| issue=4}}~~

	~~{{DEFAULTSORT:Parry-Sullivan invariant}}~~
	~~[[Category:Dynamical systems]]~~
	~~[[Category:Matrices]]~~
	~~[[Category:Algebraic graph theory]]~~
	~~[[Category:Graph invariants]~~]

en>Headbomb: ce

2013-08-05T18:49:49Z

← Older revision		Revision as of 20:49, 5 August 2013
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	~~The title~~ of the ~~author is Numbers~~. ~~To do aerobics~~ is a ~~thing that I~~'~~m completely addicted to~~. ~~He used to~~ be ~~unemployed but now he is a meter reader~~. ~~California~~ is ~~our beginning location.~~<br><br>~~Visit my web-site - home std test kit (~~[~~http://203~~.~~250~~.78.~~160~~/~~zbxe/?document_srl~~=~~817810&mid=gallery click through the up coming website page~~])		In [[mathematics]], the '''Parry–Sullivan invariant''' (or '''Parry–Sullivan number''') is a numerical quantity of interest in the study of [[incidence matrix\|incidence matrices]] in [[graph theory]], and of certain one-dimensional [[dynamical systems]]. It provides a partial classification of non-trivial irreducible incidence matrices.

			It is named after the English mathematician [[Bill Parry (mathematician)\|Bill Parry]] and the American mathematician [[Dennis Sullivan]], who introduced the invariant in a joint paper published in the journal [[Topology (journal)\|''Topology'']] in 1975.

			==Definition==

			Let ''A'' be an ''n'' × ''n'' incidence matrix. Then the '''Parry–Sullivan number''' of ''A'' is defined to be

			:<math>\mathrm{PS} (A) = \det (I - A), \, </math>

			where ''I'' denotes the ''n'' × ''n'' identity matrix.

			==Properties==

			It can be shown that, for nontrivial irreducible incidence matrices, flow equivalence is completely determined by the Parry–Sullivan number and the [[Bowen–Franks group]].

			==References==

			* {{cite journal \| author=Parry, W., & Sullivan, D. \| title=A topological invariant of flows on 1-dimensional spaces \| journal=Topology \| volume=14 \| year=1975 \| pages=297–299 \| doi=10.1016/0040-9383(75)90012-9 \| issue=4}}

			{{DEFAULTSORT:Parry-Sullivan invariant}}
			[[Category:Dynamical systems]]
			[[Category:Matrices]]
			[[Category:Algebraic graph theory]]
			[[Category:Graph invariants]]

en>Annoyamouse: disambiguation fix

2012-02-23T02:56:52Z

disambiguation fix

New page

The title of the author is Numbers. To do aerobics is a thing that I'm completely addicted to. He used to be unemployed but now he is a meter reader. California is our beginning location.<br><br>Visit my web-site - home std test kit ([http://203.250.78.160/zbxe/?document_srl=817810&mid=gallery click through the up coming website page])