Stress intensity factor - Revision history

130.149.89.171: /* Examples of stress intensity factors */

2015-01-06T13:20:22Z

Examples of stress intensity factors

← Older revision		Revision as of 15:20, 6 January 2015
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	~~The writer~~ is ~~known by the name of Figures Wunder~~. ~~Hiring has been my profession for some time but~~ I~~'ve already utilized for another 1~~. ~~He is truly fond of doing ceramics but he is having difficulties~~ to ~~discover time~~ for ~~it. South Dakota~~ is ~~where me~~ and ~~my spouse live~~.<br><br>~~Here is~~ my ~~web page;~~ [http://www.~~eddysadventurestore~~.nl/~~nieuws~~/~~eliminate-candida-one-these-tips over the counter~~ std test]		Hello and welcome. My title is Irwin and I completely dig that title. I am a meter reader. Years ago we moved to North Dakota. The preferred pastime for my kids and me is to play baseball and I'm trying to make it a occupation.<br><br>Also visit my site ... [http://www.zs-imports.com/blogs/post/70017 home std test kit]

74.105.129.159: fixed first equations

2014-02-09T16:24:44Z

fixed first equations

← Older revision		Revision as of 18:24, 9 February 2014
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	~~In mathematics, a [[family of sets\|family]] <math>\mathcal{F}</math> of [[Set (mathematics)\|sets]]~~ is of '~~''finite character''' provided it has the following properties:~~		The writer is known by the name of Figures Wunder. Hiring has been my profession for some time but I've already utilized for another 1. He is truly fond of doing ceramics but he is having difficulties to discover time for it. South Dakota is where me and my spouse live.<br><br>Here is my web page; [http://www.eddysadventurestore.nl/nieuws/eliminate-candida-one-these-tips over the counter std test]
	~~#For each <math>A\in \mathcal{F}</math>, every [[finite set\|finite]] [[subset]]~~ of ~~<math>A</math> belongs~~ to ~~<math>\mathcal{F}</math>~~.
	~~#If every finite subset of a given set <math>A</math> belongs to <math>\mathcal{F}</math>, then <math>A</math> belongs to <math>\mathcal{F}</math>~~.

	~~==Properties==~~
	~~A family~~ <~~math~~>~~\mathcal{F}~~<~~/math~~> ~~of sets of finite character enjoys the following properties~~:

	~~#For each <math>A\in \mathcal{F}</math>, every (finite or infinite) [[subset]] of <math>A<~~/~~math> belongs to <math>\mathcal{F}<~~/~~math>~~.
	~~# [[Tukey's lemma]]: In <math>\mathcal{F}<~~/~~math>, [[partial order\|partially ordered]] by inclusion, the [[Union_(set_theory)\|union]] of every [[Total_order#Chains\|chain]] of elements of <math>\mathcal{F}<~~/~~math> also belong to <math>\mathcal{F}</math>, therefore, by [[Zorn_Lemma\|Zorn's lemma]], <math>\mathcal{F}</math> contains at least~~ one ~~maximal element.~~

	~~==Example==~~
	~~Let ''V'' be a [[vector space]], and let ''F'' be~~ the family of [[linearly independent]] subsets of ''V''. Then ''F'' is a family of finite character (because a subset ''X'' &sube; ''V'' is linearly dependent iff ''X'' has a finite subset which is linearly dependent).
	Therefore, in every [[vector space]], there exists a maximal family of linearly independent elements. As a maximal family is a [[vector basis]], every vector space has a (possibly infinite) vector basis.

	~~{{PlanetMath attribution\|id=3692\|title=finite character}}~~

	~~{{Mathlogic-stub}}~~
	~~[[Category:Set families]~~]

en>Monkbot: Fix CS1 deprecated date parameter errors

2014-01-30T11:17:46Z

Fix CS1 deprecated date parameter errors

← Older revision		Revision as of 13:17, 30 January 2014
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	~~Alyson~~ is ~~what my spouse loves to contact me but I don~~'~~t like when people use my complete title. To perform lacross is one of~~ the ~~things she enjoys~~ [~~http:~~//~~chungmuroresidence~~.~~com~~/xe/~~reservation_branch2~~/~~152663 telephone psychic] most. Office supervising is where her primary earnings arrives from but she's already utilized for an additional one~~. For ~~years he's been living~~ in ~~Mississippi real psychic readings;~~ [~~http:~~//~~conniecolin~~.~~com~~/xe/~~community~~/~~24580 one-time offer~~], ~~and he doesn't strategy on changing it.~~<br><br>~~My weblog - [http://gcjcteam~~.~~org/index.php?mid~~=~~etc_video&document_srl~~=~~696611~~&~~sort_index~~=~~regdate&order_type~~=~~desc psychic readings online~~]		In mathematics, a [[family of sets\|family]] <math>\mathcal{F}</math> of [[Set (mathematics)\|sets]] is of '''finite character''' provided it has the following properties:
			#For each <math>A\in \mathcal{F}</math>, every [[finite set\|finite]] [[subset]] of <math>A</math> belongs to <math>\mathcal{F}</math>.
			#If every finite subset of a given set <math>A</math> belongs to <math>\mathcal{F}</math>, then <math>A</math> belongs to <math>\mathcal{F}</math>.

			==Properties==
			A family <math>\mathcal{F}</math> of sets of finite character enjoys the following properties:

			#For each <math>A\in \mathcal{F}</math>, every (finite or infinite) [[subset]] of <math>A</math> belongs to <math>\mathcal{F}</math>.
			# [[Tukey's lemma]]: In <math>\mathcal{F}</math>, [[partial order\|partially ordered]] by inclusion, the [[Union_(set_theory)\|union]] of every [[Total_order#Chains\|chain]] of elements of <math>\mathcal{F}</math> also belong to <math>\mathcal{F}</math>, therefore, by [[Zorn_Lemma\|Zorn's lemma]], <math>\mathcal{F}</math> contains at least one maximal element.

			==Example==
			Let ''V'' be a [[vector space]], and let ''F'' be the family of [[linearly independent]] subsets of ''V''. Then ''F'' is a family of finite character (because a subset ''X'' &sube; ''V'' is linearly dependent iff ''X'' has a finite subset which is linearly dependent).
			Therefore, in every [[vector space]], there exists a maximal family of linearly independent elements. As a maximal family is a [[vector basis]], every vector space has a (possibly infinite) vector basis.

			{{PlanetMath attribution\|id=3692\|title=finite character}}

			{{Mathlogic-stub}}
			[[Category:Set families]]

en>Bibcode Bot: Adding 0 arxiv eprint(s), 1 bibcode(s) and 1 doi(s). Did it miss something? Report bugs, errors, and suggestions at User talk:Bibcode Bot

2012-03-02T06:41:33Z

Adding 0 arxiv eprint(s), 1 bibcode(s) and 1 doi(s). Did it miss something? Report bugs, errors, and suggestions at User talk:Bibcode Bot

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