Potential vorticity - Revision history

en>Daveintex13: /* PV conservation */ Added link to referenced paper.

2014-12-12T21:11:51Z

PV conservation: Added link to referenced paper.

← Older revision		Revision as of 23:11, 12 December 2014
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	~~Define <math>M_{k}^{2}<~~/~~math> as the [[2~~-~~dimensional]~~] [~~[metric space]] of [[constant curvature]] <math>k<~~/~~math>~~. ~~So, for example, <math>M_{0}^{2}<~~/~~math> is the [[Euclidean plane]], <math>M_{1}^{2}<~~/~~math> is the surface of the [[unit sphere]], and <math>M_{-1}^{2}<~~/~~math> is~~ the ~~[[Hyperbolic geometry\|hyperbolic plane]~~].		Greetings. The [http://www.webmd.com/sexual-conditions/std-tests author's title] is Phebe and she feels comfortable when individuals use [http://netwk.hannam.ac.kr/xe/data_2/38191 over the counter std test] complete title. Since she was 18 she's been working as a receptionist but her home std test kit marketing never std home test comes. [http://chatmast.com/index.php?do=/BookerSipessk/info/ at home std testing] To collect coins is what his family members and him enjoy. For many years he's been residing in North Dakota and his family loves it.<br><br>Feel free to surf to my homepage :: [http://Www.Animecontent.com/blog/348813 http://Www.Animecontent.com/blog/348813]

	~~Let <math>X</math> be~~ a ~~[[metric space]]~~. ~~Let <math>T</math> be a~~ [~~[triangle]] in <math>X<~~/~~math>, with vertices <math>p<~~/~~math>, <math>q</math> and <math>r<~~/~~math>~~. ~~A '''comparison triangle''' <math>T*<~~/~~math> in <math>M_{k}^{2}<~~/~~math> for <math>T<~~/~~math>~~ is ~~a triangle~~ in ~~<math>M_{k}^{2}</math> with vertices <math>p'</math>, <math>q'</math>~~ and <~~math>r'</math~~> ~~such that~~ <~~math~~>~~d(p,q) = d(p',q')</math>, <math>d(p,r) = d(p',r')<~~/~~math> and <math>d(r,q) = d(r',q')<~~/~~math>~~.

	~~Such a triangle is unique up to [[isometry]]~~.

	~~The [[interior angle]] of <math>T*</math> at <math>p'<~~/~~math> is called the '''comparison angle''' between <math>q<~~/~~math> and <math>r<~~/~~math> at <math>p<~~/~~math>~~. ~~This is well-defined provided <math>q</math> and <math>r<~~/~~math> are both distinct from <math>p<~~/~~math>.~~

	~~==References==~~
	* M Bridson & [[A Haefliger]] - ''Metric Spaces Of Non-Positive [[Curvature]]'', ISBN 3-540-64324-9

	~~[[Category:Metric geometry]~~]

en>Yobot: WP:CHECKWIKI error fixes, removed stub tag using AWB (9773)

2013-12-04T23:05:45Z

WP:CHECKWIKI error fixes, removed stub tag using AWB (9773)

← Older revision		Revision as of 01:05, 5 December 2013
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	~~Hi there~~. [~~http:~~//~~black7~~.~~mireene~~.~~com~~/~~aqw~~/~~5741 email psychic readings] Allow me start by introducing the author~~, ~~her title is Sophia Boon but she by no means truly liked that online psychics ([http:~~//~~Help~~.~~Ksu.Edu.sa~~/~~node~~/~~65129 http:~~//~~Help.Ksu.Edu.sa~~/~~node~~/~~65129]~~) ~~title~~. ~~North Carolina~~ is ~~the place he loves most but now he is contemplating other options~~. ~~One~~ of the ~~issues she enjoys most is canoeing~~ and ~~she's been doing it for fairly a while~~. He is ~~an information officer.~~<br><br>~~Here is my site ... [http:~~//~~www~~.~~familysurvivalgroup.com/easy~~-~~methods~~-~~planting~~-~~looking~~-~~backyard/ online psychic reading~~]		Define <math>M_{k}^{2}</math> as the [[2-dimensional]] [[metric space]] of [[constant curvature]] <math>k</math>. So, for example, <math>M_{0}^{2}</math> is the [[Euclidean plane]], <math>M_{1}^{2}</math> is the surface of the [[unit sphere]], and <math>M_{-1}^{2}</math> is the [[Hyperbolic geometry\|hyperbolic plane]].

			Let <math>X</math> be a [[metric space]]. Let <math>T</math> be a [[triangle]] in <math>X</math>, with vertices <math>p</math>, <math>q</math> and <math>r</math>. A '''comparison triangle''' <math>T*</math> in <math>M_{k}^{2}</math> for <math>T</math> is a triangle in <math>M_{k}^{2}</math> with vertices <math>p'</math>, <math>q'</math> and <math>r'</math> such that <math>d(p,q) = d(p',q')</math>, <math>d(p,r) = d(p',r')</math> and <math>d(r,q) = d(r',q')</math>.

			Such a triangle is unique up to [[isometry]].

			The [[interior angle]] of <math>T*</math> at <math>p'</math> is called the '''comparison angle''' between <math>q</math> and <math>r</math> at <math>p</math>. This is well-defined provided <math>q</math> and <math>r</math> are both distinct from <math>p</math>.

			==References==
			* M Bridson & [[A Haefliger]] - ''Metric Spaces Of Non-Positive [[Curvature]]'', ISBN 3-540-64324-9

			[[Category:Metric geometry]]

en>Xqbot: r2.7.2) (robot Modifying: de:Potentielle Vortizität

2011-07-16T22:37:09Z

r2.7.2) (robot Modifying: de:Potentielle Vortizität

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