Motor constants - Revision history

en>Alexandre.willame: added torque constant reference

2014-12-04T15:18:41Z

added torque constant reference

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	~~{{context\|date=August 2012}}~~		There is nothing to tell about me I think.<br>Great to be a part of wmflabs.org.<br>I just hope Im useful at all<br><br>my weblog; [http://www.wat.tv/video/watch-arrow-season-full-episodes-7194f_7142z_.html watch arrow season 3 online for free]

	In mathematics, the '''bracket ring''' is the [[subring]] of the ring of [[polynomial]]s ''k''[''x''<sub>11</sub>,...,''x''<sub>''dn''</sub>] generated by the ''d'' by ''d'' [[Minor (linear algebra)\|minors]] of a generic ''d'' by ''n'' [[matrix (mathematics)\|matrix]] (''x''<sub>''ij''</sub>).

	The bracket ring may be regarded as the ring of polynomials on the image of a [[Grassmannian]] under the [[Plücker embedding]].<ref>{{citation \| last1=Björner \| first1=Anders \| last2=Las Vergnas \| author2-link=Michel Las Vergnas \| first2=Michel \| last3=Sturmfels \| first3=Bernd \| author3-link=Bernd Sturmfels \| last4=White \| first4=Neil \| last5=Ziegler \| first5=Günter \| title=Oriented matroids \| edition=2nd \| series=Encyclopedia of Mathematics and Its Applications \| volume=46 \| publisher=[[Cambridge University Press]] \| year=1999 \| isbn=0-521-77750-X \| zbl=0944.52006 \| page=79 }}</ref>

	For given ''d'' ≤ ''n'' we define as formal variables the ''brackets'' [λ<sub>1</sub> λ<sub>2</sub> ... λ<sub>''d''</sub>] with the λ taken from {1,...,''n''}, subject to [λ<sub>1</sub> λ<sub>2</sub> ... λ<sub>''d''</sub>] = − [λ<sub>2</sub> λ<sub>1</sub> ... λ<sub>''d''</sub>] and similarly for other transpositions. The set Λ(''n'',''d'') of size <math>\binom{n}{d}</math> generates a polynomial ring ''K''[Λ(''n'',''d'')] over a field ''K''. There is ~~a homomorphism Φ(''n'',''d'') from ''K''[Λ(''n'',''d'')]~~ to ~~the polynomial ring ''K''[''x''<sub>''i'',''j''</sub>] in ''nd'' indeterminates given by mapping~~
	~~[λ<sub>1</sub> λ<sub>2</sub>~~ .~~.. λ~~<~~sub~~>~~''d''</sub>]~~ to the determinant of the ''d'' by ''d'' matrix consisting of the columns of the ''x''<sub>''i'',''j''</sub> indexed by the λ. The ''bracket ring'' ''B''(''n'',''d'') is the image of Φ. The kernel ''I''(''n'',''d'') of Φ encodes the relations or ''syzygies'' that exist between the minors of a ~~generic ''n'' by ''d'' matrix. The projective variety defined by the ideal ''I'' is the (''n''−''d'')''d'' dimensional Grassmann variety whose points correspond to ''d''-dimensional subspaces~~ of ~~an ''n''-dimensional space~~.~~<ref>Sturmfels (2008) pp~~.~~78–79~~<~~/ref~~>

	~~To compute with brackets it is necessary to determine when an expression lies in the ideal ''~~I~~''(''n'',''d''). This is achieved by a ''straightening law'' due to Young (1928).~~<~~ref~~>~~Sturmfels (2008) p.80~~<~~/ref~~>

	~~==See also==~~
	* [~~[Bracket algebra]]~~

	~~==References==~~
	~~{{reflist}}~~
	*{{Citation \| last1=Dieudonné \| first1=Jean A. \| last2=Carrell \| first2=James B. ~~\| title=Invariant theory, old and new \| doi=10~~.~~1016~~/~~0001-8708(70)90015-0 \| mr=0255525 \| year=1970 \| journal=Advances in Mathematics \| issn=0001-8708 \| volume=4 \| pages=1–80 \| zbl=0196.05802 }}~~
	*{{Citation \| last1=Dieudonné \| first1=Jean A. \| last2=Carrell \| first2=James B. \| title=Invariant theory, old and new \| publisher=[[Academic Press]] \| location=Boston, MA \| isbn=978-0-12-215540-6 \| doi=10.1016/~~0001~~-~~8708(70)90015~~-~~0 \| mr=0279102 \| year=1971 \| zbl=0258.14011 }}~~
	*{{Citation \| last1=Sturmfels \| first1=Bernd \| author1-~~link=Bernd Sturmfels \| title=Algorithms in Invariant Theory \| series=Texts and Monographs in Symbolic Computation \| others= \| edition=2nd \| publisher=[[Springer~~-~~Verlag]] \| year=2008 \| isbn=3211774165 \| zbl=1154.13003 }}~~
	*{{Citation \| last1=Sturmfels \| first1=Bernd \| author1-link=Bernd Sturmfels \| last2=White \| first2=Neil \| title=Stanley decompositions of the bracket ring \| mr=1096453 \| year=1990 \| journal=Mathematica Scandinavica \| issn=0025-5521 \| volume=67 \| issue=2 \| pages=183–189 \| url=http://www.~~math.ufl.edu/~white/stanley1.ps \| zbl=0727.13005 }}~~

	~~[[Category:Invariant theory]]~~
	~~[[Category:Algebraic geometry]~~]


	~~{{algebra-stub}}~~

93.187.84.100: /* Motor constant */

2014-01-04T19:52:14Z

Motor constant

← Older revision		Revision as of 21:52, 4 January 2014
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	~~Hi there! :) My name~~ is ~~Kelvin~~, I'm a ~~student studying Agriculture~~ and ~~Life Sciences~~ from ~~Bergisch Gladbach Schildgen~~, ~~Germany~~.<br><br><br>~~http:~~//~~brokerltd~~.~~com~~ - ~~webmaster~~<br><br>~~Here~~ is ~~my page ::~~ [http://~~brokerltd~~.~~com sell traffic~~]		{{context\|date=August 2012}}

			In mathematics, the '''bracket ring''' is the [[subring]] of the ring of [[polynomial]]s ''k''[''x''<sub>11</sub>,...,''x''<sub>''dn''</sub>] generated by the ''d'' by ''d'' [[Minor (linear algebra)\|minors]] of a generic ''d'' by ''n'' [[matrix (mathematics)\|matrix]] (''x''<sub>''ij''</sub>).

			The bracket ring may be regarded as the ring of polynomials on the image of a [[Grassmannian]] under the [[Plücker embedding]].<ref>{{citation \| last1=Björner \| first1=Anders \| last2=Las Vergnas \| author2-link=Michel Las Vergnas \| first2=Michel \| last3=Sturmfels \| first3=Bernd \| author3-link=Bernd Sturmfels \| last4=White \| first4=Neil \| last5=Ziegler \| first5=Günter \| title=Oriented matroids \| edition=2nd \| series=Encyclopedia of Mathematics and Its Applications \| volume=46 \| publisher=[[Cambridge University Press]] \| year=1999 \| isbn=0-521-77750-X \| zbl=0944.52006 \| page=79 }}</ref>

			For given ''d'' ≤ ''n'' we define as formal variables the ''brackets'' [λ<sub>1</sub> λ<sub>2</sub> ... λ<sub>''d''</sub>] with the λ taken from {1,...,''n''}, subject to [λ<sub>1</sub> λ<sub>2</sub> ... λ<sub>''d''</sub>] = − [λ<sub>2</sub> λ<sub>1</sub> ... λ<sub>''d''</sub>] and similarly for other transpositions. The set Λ(''n'',''d'') of size <math>\binom{n}{d}</math> generates a polynomial ring ''K''[Λ(''n'',''d'')] over a field ''K''. There is a homomorphism Φ(''n'',''d'') from ''K''[Λ(''n'',''d'')] to the polynomial ring ''K''[''x''<sub>''i'',''j''</sub>] in ''nd'' indeterminates given by mapping
			[λ<sub>1</sub> λ<sub>2</sub> ... λ<sub>''d''</sub>] to the determinant of the ''d'' by ''d'' matrix consisting of the columns of the ''x''<sub>''i'',''j''</sub> indexed by the λ. The ''bracket ring'' ''B''(''n'',''d'') is the image of Φ. The kernel ''I''(''n'',''d'') of Φ encodes the relations or ''syzygies'' that exist between the minors of a generic ''n'' by ''d'' matrix. The projective variety defined by the ideal ''I'' is the (''n''−''d'')''d'' dimensional Grassmann variety whose points correspond to ''d''-dimensional subspaces of an ''n''-dimensional space.<ref>Sturmfels (2008) pp.78–79</ref>

			To compute with brackets it is necessary to determine when an expression lies in the ideal ''I''(''n'',''d''). This is achieved by a ''straightening law'' due to Young (1928).<ref>Sturmfels (2008) p.80</ref>

			==See also==
			* [[Bracket algebra]]

			==References==
			{{reflist}}
			*{{Citation \| last1=Dieudonné \| first1=Jean A. \| last2=Carrell \| first2=James B. \| title=Invariant theory, old and new \| doi=10.1016/0001-8708(70)90015-0 \| mr=0255525 \| year=1970 \| journal=Advances in Mathematics \| issn=0001-8708 \| volume=4 \| pages=1–80 \| zbl=0196.05802 }}
			*{{Citation \| last1=Dieudonné \| first1=Jean A. \| last2=Carrell \| first2=James B. \| title=Invariant theory, old and new \| publisher=[[Academic Press]] \| location=Boston, MA \| isbn=978-0-12-215540-6 \| doi=10.1016/0001-8708(70)90015-0 \| mr=0279102 \| year=1971 \| zbl=0258.14011 }}
			*{{Citation \| last1=Sturmfels \| first1=Bernd \| author1-link=Bernd Sturmfels \| title=Algorithms in Invariant Theory \| series=Texts and Monographs in Symbolic Computation \| others= \| edition=2nd \| publisher=[[Springer-Verlag]] \| year=2008 \| isbn=3211774165 \| zbl=1154.13003 }}
			*{{Citation \| last1=Sturmfels \| first1=Bernd \| author1-link=Bernd Sturmfels \| last2=White \| first2=Neil \| title=Stanley decompositions of the bracket ring \| mr=1096453 \| year=1990 \| journal=Mathematica Scandinavica \| issn=0025-5521 \| volume=67 \| issue=2 \| pages=183–189 \| url=http://www.math.ufl.edu/~white/stanley1.ps \| zbl=0727.13005 }}

			[[Category:Invariant theory]]
			[[Category:Algebraic geometry]]


			{{algebra-stub}}

173.162.211.17: /* Motor velocity constant, back EMF constant */ Fix typo

2012-04-30T13:40:14Z

Motor velocity constant, back EMF constant: Fix typo

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