Electrical mobility - Revision history

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2014-12-18T16:02:04Z

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	~~In [[mathematics]], a '''twisted cubic'''~~ is a ~~smooth~~, ~~[[rational curve]] ''C'' of [[Degree of an algebraic variety\|degree]] three in [[projective space\|projective 3-space]] '''P'''<sup>3</sup>. It is a fundamental example of a [[skew curve]]. It~~ is ~~essentially unique, up to [[projective transformation]] (''~~the~~'' twisted cubic, therefore)~~. ~~It is generally considered~~ to be the ~~simplest example~~ of ~~a [[projective variety]] that isn't linear or a [[hypersurface]]~~, and is ~~given as such~~ in ~~most textbooks on~~ [~~[algebraic geometry]~~]. ~~It is~~ the ~~three-dimensional case of~~ the ~~[[rational normal curve]]~~, ~~and is~~ the ~~image~~ of ~~a [[Veronese map]] of degree three on~~ the ~~projective line.~~		Luke is really a superstar while in the producing along with the job expansion very first next to his 3rd restaurant recording, & , is the confirmation. He broken to the picture in 2007 with his crazy blend of downward-residence accessibility, video star fantastic seems and lines, is scheduled t in a [http://lukebryantickets.iczmpbangladesh.org wwe raw tickets] significant way. The brand new a around the region graph and #2 in the pop charts, building it the next top very first during those times of 2006 for the nation designer. <br><br>The kid of a , understands determination and dedication are key elements in relation to a prosperous occupation- . His initial album, Remain Me, made the most notable reaches “All My Buddies Say” and “Country Person,” whilst his energy, Doin’ Factor, identified the vocalist-a few directly No. 3 single men and women: Else Getting in touch with Can be a Wonderful Factor.”<br><br>From the drop of 2011, Concert tours: Luke Bryan & that luke bryan tour date ([http://www.senatorwonderling.com just click the following post]) have an outstanding list of , such as Metropolitan. “It’s much like you’re receiving a endorsement to look to another level, says these musicians that have been an element of the Concert toursover in a larger sized amount of performers.” It packaged as the best tours in the twenty-12 months history.<br><br>my weblog [http://www.hotelsedinburgh.org last minute tickets]

	~~==Definition==~~
	~~[[File:Twisted cubic curve~~.~~png\|250px\|right]]~~

	~~It is most easily given [[parametrically]] as the image of the map~~

	:<~~math~~>~~\nu:\mathbf{P}^1\to\mathbf{P}^3~~<~~/math~~>

	~~which assigns~~ to ~~the [[homogeneous coordinate]] <math>[S:T]</math> the value~~

	~~:<math>\nu:[S:T] \mapsto [S^3:S^2T:ST^2:T^3]~~.~~</math>~~

	~~In one [[coordinate patch]] of projective space~~, the ~~map is simply the [[moment curve]]~~

	~~:<math>\nu:x \mapsto (x~~,~~x^2~~,~~x^3)</math>~~

	~~That is~~, ~~it is~~ the ~~closure by~~ a single ~~[[point at infinity]] of the [[affine curve]] <math>(x,x^2,x^3)</math>.~~

	~~Equivalently, it is~~ a ~~[[projective variety]], defined as the zero locus of three smooth [[quadric]]s~~. ~~Given the homogeneous coordinates [''X:Y:Z:W''] on '''P'''~~<~~sup~~>3<~~/sup~~>~~, it is~~ the ~~zero locus~~ of ~~the three [~~[~~homogeneous polynomial]]s~~

	:~~<math>F_0 = XZ - Y^2<~~/~~math>~~
	~~:<math>F_1 = YW - Z^2<~~/~~math>~~
	~~:<math>F_2 = XW - YZ~~.~~</math>~~

	~~It may be checked that these three [[quadratic form]]s vanish identically when using the explicit parameterization above; that is, substituting ''x''<sup>3</sup> for ''X'', and so on~~.

	~~In fact, the [[homogeneous ideal]] of~~ the ~~twisted cubic ''C'' is generated by three [[algebraic form~~]]s of ~~degree two on '''P'''<sup>3</sup>~~. ~~The generators of the ideal are~~

	~~:<math>\{ XZ - Y^2~~ , ~~YW - Z^2 , XW - YZ \}.</math>~~

	~~==Properties==~~
	~~The twisted cubic has~~ an ~~assortment~~ of ~~elementary properties:~~
	* It is the set-theoretic complete intersection of ''XZ''-''Y''<sup>2</sup> and <math>Z(YW-Z^2)-W(XW-YZ)</math>, but not a scheme-theoretic or ideal-theoretic complete intersection (the resulting ideal is not radical, since ~~<math>(YW-Z^2)^2</math> is in it, but <math>YW-Z^2</math> is not).~~
	* Any four points on ''C'' span '''P'''<sup>3</sup>.
	* Given six points in ~~'''P'''<sup>3</sup> with no four coplanar, there is~~ a ~~unique twisted cubic passing through them~~.
	* The union of the [[tangent]] and [[secant line\|secant]] lines, the [[secant variety]], of a twisted cubic ''C'' fill up '''P'''<sup>3</sup> and the lines are pairwise disjoint, except at points of the ~~curve itself.~~ ~~In fact,~~ the ~~union of the [[tangent]] and [[secant line\|secant]] lines of any non~~-~~planar smooth [[algebraic curve]] is three-dimensional~~. ~~Further, any smooth [[algebraic variety]] with the property that every length four [[subscheme]] spans '''P'''~~<~~sup~~>3<~~/sup~~> ~~has the property that the~~ [~~[tangent]] and [[secant line\|secant]] lines are pairwise disjoint, except at points of the variety itself~~.
	* The projection of ''C'' onto a plane from a point on a tangent line of ''C'' yields a [[cuspidal cubic]].
	* The projection from a point on a secant line of ''C'' yields a [[nodal cubic]].
	* The projection from a point on ''C'' yields a [[conic section]].

	~~==References==~~
	*{{Citation \|first=Joe \|last~~=Harris \|title=Algebraic Geometry, A First Course \|year=1992 \|publisher=Springer-Verlag \|location=New York \|isbn=0-387-97716-3 }}.~~

	~~[[Category:Algebraic curves]~~]

83.250.31.99: /* Theory */

2013-06-06T13:02:13Z

Theory

@@ Line 1: / Line 1: @@
-== UGG Promo Code September 2014 ==
+In [[mathematics]], a '''twisted cubic''' is a smooth, [[rational curve]] ''C'' of [[Degree of an algebraic variety|degree]] three in [[projective space|projective 3-space]] '''P'''<sup>3</sup>. It is a fundamental example of a [[skew curve]]. It is essentially unique, up to [[projective transformation]] (''the'' twisted cubic, therefore). It is generally considered to be the simplest example of a [[projective variety]] that isn't linear or a [[hypersurface]], and is given as such in most textbooks on [[algebraic geometry]]. It is the three-dimensional case of the [[rational normal curve]], and is the image of a [[Veronese map]] of degree three on the projective line.
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+==Definition==
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+It is most easily given [[parametrically]] as the image of the map
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+:<math>\nu:\mathbf{P}^1\to\mathbf{P}^3</math>
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+which assigns to the [[homogeneous coordinate]] <math>[S:T]</math> the value
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+:<math>\nu:[S:T] \mapsto [S^3:S^2T:ST^2:T^3].</math>

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