Geophysical fluid dynamics - Revision history

en>Yobot: /* Buoyancy and stratification */WP:CHECKWIKI error fixes using AWB (10093)

2014-05-05T11:53:36Z

Buoyancy and stratification: WP:CHECKWIKI error fixes using AWB (10093)

← Older revision		Revision as of 13:53, 5 May 2014
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	In [~~[general topology]~~], the '~~''lexicographic ordering~~ on the ~~unit square''' is a~~ [~~[Topological space\|topology]~~] on the ~~[[unit square]] ''S''~~, i.e. on the ~~set~~ of ~~points (''x''~~,'~~'y'')~~ in the [~~[Plane (geometry)\|plane]~~] ~~such that {{nowrap\|1=0 ≤ ''x'' ≤ 1}} and {{nowrap\|1=0 ≤ ''y'' ≤ 1~~.}}<~~ref name="CEIT"~~>~~{{Citation\|first=L~~. A.~~\|last=Steen\|first2=J~~. A.~~\|last2=Seebach\|title=[[Counterexamples in Topology]]\|publisher=Dover\|year=1995\|page=73\|ISBN=0~~-~~486~~-~~68735~~-~~X}}<~~/~~ref> It is an example of an [[order topology]~~] in ~~which there are~~ [~~[uncountably]] many [[pairwise disjoint\|pairwise~~-~~disjoint]] [[homeomorphic]] copies of the [[real line]]~~.		One other female witness came forward and informed police that Dwiggins approached her as she was driving in her golf cart. He requested her for a journey and then told her that he had just stabbed someone throughout a combat. 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	=~~= Construction ==~~
	~~As the name suggests, we use the [[lexicographical order]~~]~~ing~~ on the ~~square~~ to ~~define a topology~~. ~~Given two points~~ in the ~~square~~, ~~say (~~'~~'x'',''y'')~~ and ~~(''u''~~,~~''v'')~~, ~~we say that {{nowrap\|1=(''x'',''y'') <math>\scriptstyle\prec</math> (''u'',''v'')}} if~~ and ~~only if either {{nowrap\|1=''x'' < ''u''}} or '''both''' {{nowrap\|1=''x'' = ''u''}} '''and''' {{nowrap\|1=''y'' < ''v''}}~~.
	~~Given~~ the ~~lexicographical ordering on~~ the ~~square, we use~~ the ~~order topology to define the topology on ''S''~~.<~~ref name="CEIT"/~~> ~~For each point (''u'',''v'') we get an open set, denoted ''U~~<~~sub~~>u,~~v</sub>''~~, ~~given by all~~ the ~~points in ''S''~~ that ~~precede (''u'~~',~~''v'') with respect to~~ the ~~lexicographical ordering:~~
	~~:<math> U_{u~~,~~v} = \{ (x,y) \~~in S : ~~(x,y) \prec (u,v) \} \~~ . </~~math>~~
	~~The open sets~~ in the ~~lexicographic ordering on the unit square~~ are ~~the whole set ''S'', the empty set ∅~~, and ~~those sets generated by the~~ ''U<~~sub~~>~~u,v~~<~~/sub~~>~~'', i~~.e. ~~the sets formed~~ by ~~all possible unions~~ of ~~finite intersections~~.~~<ref>{{Citation\|first=L~~. A.~~\|last=Steen\|first2=J~~. ~~A.\|last2=Seebach\|title=Counterexamples in Topology\|publisher=Dover\|year=1995\|page=4\|ISBN=0~~-~~486~~-~~68735~~-~~X}}</ref>~~

	~~== See also ==~~
	* [[Long line (topology)\|Long line]]

	~~== References ==~~
	~~{{reflist}}~~

	~~[[Category:General topology]]~~
	~~[[Category:Topological spaces]]~~

en>Yobot: WP:CHECKWIKI error fixes using AWB (9075)

2013-04-08T14:39:38Z

WP:CHECKWIKI error fixes using AWB (9075)

← Older revision		Revision as of 16:39, 8 April 2013
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carbon steel]. My investigation steer me towards the Smith~~'~~s Ceramic Edge Pro. Is this the right selection? Also~~, ~~any suggestions for in the [http://cogito.no-ip.info/cogito/tutowiki/index.php/Best_EDC_Knife_2014 field application]? – Mr. Giles It doesn~~'~~t genuinely matter what steel this thing~~'~~s created from, of course, as extended as it has a very good edge and stays sharp when you use it. This too doesn~~'~~t matter to folks like me who buy a issue like this purely as a toy, but this is meant to be a hunting and/or camping and/or survival sort of knife. So it should really take~~ an ~~edge~~, ~~keep that edge reasonably effectively, and tolerate abuse.~~<br><br>~~Some knives also come with various interchangeable blades~~, ~~enabling~~ the user to swap one blade for a different when unique blade kinds are required for distinct tasks. This folded knife from Kershaw is also produced of high-grade S30V stainless steel with an ambidextrous opening method so you can manage it even with just 1 hand. The Kershaw 1670S30V Blur Knife with S30V Steel Blade also has a stone-washed finish, ~~adding to its ‘unique look~~'~~. Throwing Knives – Throwing knives are small and straightforward~~ to throw. They have a metal manage and are sharp enough to turn into impacted when they strike solid material. These knives are frequently smaller sized and shaped for throwing at targets. Cody Lundin & Doug Ritter Encouraged Experienced Survival Gear SCHF1SM Intense Survival Knife<br><br>The ~~blade~~'~~s sabre grind is very deep~~, ~~which qualifies~~ the ~~knife as a flat grind. Extra yet~~, the ~~knife~~'~~s clipped~~, ~~sharp point (with a false edge) tends to make the Trail Buddy a perfect knife for piercing hides~~. ~~General,~~ the ~~SOG Aura-Hunting knife checked out meeting~~ all of ~~my expectations~~. ~~I would propose this brand to all my buddies and relatives~~. ~~Hopefully I will get to try out the gut hook ought to I be fortunate adequate to take a deer this fall~~. ~~I know one point for certain I undoubtedly will not anticipate it~~. ~~But I will try my ideal~~. ~~Dusty Reid, Hunt's End Deer Ranch, BLADE Magazine – Wisconsin Complete~~-~~size folder Benchmade Griptillian 551. OutdoorGearLab Editors' Hands~~-~~on Review Victorinox SwissChamp Swiss Army Knife Greatest Manual Sharpener System Image and Price tag Picking The Ideal Knife~~		In [[general topology]], the '''lexicographic ordering on the unit square''' is a [[Topological space\|topology]] on the [[unit square]] ''S'', i.e. on the set of points (''x'',''y'') in the [[Plane (geometry)\|plane]] such that {{nowrap\|1=0 ≤ ''x'' ≤ 1}} and {{nowrap\|1=0 ≤ ''y'' ≤ 1.}}<ref name="CEIT">{{Citation\|first=L. A.\|last=Steen\|first2=J. A.\|last2=Seebach\|title=[[Counterexamples in Topology]]\|publisher=Dover\|year=1995\|page=73\|ISBN=0-486-68735-X}}</ref> It is an example of an [[order topology]] in which there are [[uncountably]] many [[pairwise disjoint\|pairwise-disjoint]] [[homeomorphic]] copies of the [[real line]].

			== Construction ==
			As the name suggests, we use the [[lexicographical order]]ing on the square to define a topology. Given two points in the square, say (''x'',''y'') and (''u'',''v''), we say that {{nowrap\|1=(''x'',''y'') <math>\scriptstyle\prec</math> (''u'',''v'')}} if and only if either {{nowrap\|1=''x'' < ''u''}} or '''both''' {{nowrap\|1=''x'' = ''u''}} '''and''' {{nowrap\|1=''y'' < ''v''}}.
			Given the lexicographical ordering on the square, we use the order topology to define the topology on ''S''.<ref name="CEIT"/> For each point (''u'',''v'') we get an open set, denoted ''U<sub>u,v</sub>'', given by all the points in ''S'' that precede (''u'',''v'') with respect to the lexicographical ordering:
			:<math> U_{u,v} = \{ (x,y) \in S : (x,y) \prec (u,v) \} \ . </math>
			The open sets in the lexicographic ordering on the unit square are the whole set ''S'', the empty set ∅, and those sets generated by the ''U<sub>u,v</sub>'', i.e. the sets formed by all possible unions of finite intersections.<ref>{{Citation\|first=L. A.\|last=Steen\|first2=J. A.\|last2=Seebach\|title=Counterexamples in Topology\|publisher=Dover\|year=1995\|page=4\|ISBN=0-486-68735-X}}</ref>

			== See also ==
			* [[Long line (topology)\|Long line]]

			== References ==
			{{reflist}}

			[[Category:General topology]]
			[[Category:Topological spaces]]

en>Duncanpark: Added References

2012-07-20T06:04:37Z

Added References

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carbon steel]. My investigation steer me towards the Smith's Ceramic Edge Pro. Is this the right selection? Also, any suggestions for in the [http://cogito.no-ip.info/cogito/tutowiki/index.php/Best_EDC_Knife_2014 field application]? – Mr. Giles It doesn't genuinely matter what steel this thing's created from, of course, as extended as it has a very good edge and stays sharp when you use it. This too doesn't matter to folks like me who buy a issue like this purely as a toy, but this is meant to be a hunting and/or camping and/or survival sort of knife. So it should really take an edge, keep that edge reasonably effectively, and tolerate abuse. Some knives also come with various interchangeable blades, enabling the user to swap one blade for a different when unique blade kinds are required for distinct tasks. This folded knife from Kershaw is also produced of high-grade S30V stainless steel with an ambidextrous opening method so you can manage it even with just 1 hand. The Kershaw 1670S30V Blur Knife with S30V Steel Blade also has a stone-washed finish, adding to its ‘unique look'. Throwing Knives – Throwing knives are small and straightforward to throw. They have a metal manage and are sharp enough to turn into impacted when they strike solid material. These knives are frequently smaller sized and shaped for throwing at targets. Cody Lundin & Doug Ritter Encouraged Experienced Survival Gear SCHF1SM Intense Survival Knife The blade's sabre grind is very deep, which qualifies the knife as a flat grind. Extra yet, the knife's clipped, sharp point (with a false edge) tends to make the Trail Buddy a perfect knife for piercing hides. General, the SOG Aura-Hunting knife checked out meeting all of my expectations. I would propose this brand to all my buddies and relatives. Hopefully I will get to try out the gut hook ought to I be fortunate adequate to take a deer this fall. I know one point for certain I undoubtedly will not anticipate it. 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