Spin representation - Revision history

73.9.109.131: /* Complex spin representations */

2014-12-22T21:50:37Z

Complex spin representations

← Older revision		Revision as of 23:50, 22 December 2014
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	~~The name of the writer~~ is ~~Nestor. Her friends say it's not great for~~ her ~~but what she enjoys performing is flower arranging~~ and she is ~~trying to make~~ it ~~a occupation~~. ~~She~~ is ~~currently a cashier~~ but ~~quickly~~ she'~~ll be on~~ her ~~own~~. ~~My house is~~ now ~~in Kansas~~.<br><br>~~Also visit~~ my ~~website -~~ [http://~~www~~.~~True-life~~.~~org~~/~~Activity~~-~~Feed/My-Profile/UserId/2850~~ http://www.~~True-life~~.org/~~Activity-Feed~~/~~My-Profile~~/~~UserId~~/~~2850~~]		Claude is her title and [http://pcresourcesllc.com/UserProfile/tabid/61/userId/94025/Default.aspx car warranty] she totally digs that title. [http://www.death-amigoz.de/index.php?mod=users&action=view&id=3149 extended car warranty] His working day job is a monetary car [http://en.wikipedia.org/wiki/Extended_warranty warranty officer] but he ideas on changing it. The thing she adores most is car warranty to play handball but she can't make it her occupation. I presently live in Arizona but now I'm contemplating other options.<br><br>Here is my web site ... extended car [http://Www.consumerautomotiveresearch.com/typesofwarranties.htm warranty -] [http://www.Saintpeteryouthbasketball.org/ActivityFeed/MyProfile/tabid/60/userId/95760/Default.aspx navigate to this website],

en>Wavelength: inserting 1 hyphen: —> "one-dimensional"—wikt:one-dimensional

2014-02-20T05:02:48Z

inserting 1 hyphen: —> "one-dimensional"—wikt:one-dimensional

← Older revision		Revision as of 07:02, 20 February 2014
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	~~{{underlinked\|date=October 2012}}~~		The name of the writer is Nestor. Her friends say it's not great for her but what she enjoys performing is flower arranging and she is trying to make it a occupation. She is currently a cashier but quickly she'll be on her own. My house is now in Kansas.<br><br>Also visit my website - [http://www.True-life.org/Activity-Feed/My-Profile/UserId/2850 http://www.True-life.org/Activity-Feed/My-Profile/UserId/2850]
	~~{{sections\|date=October 2012}}~~

	~~'''Shape moiré''' is one type of [[moiré pattern]]s demonstrating the phenomenon of moiré magnification.<ref>{{cite paper~~
	~~\| title = Optical inspection of arrays and periodic structures using moire magnification~~
	~~\| author = M.C. Hutley~~
	~~\| coauthors = R.F. Stevens~~
	~~\| publisher = IEE Colloquium, Microengineering in Optics and Optoelectronics~~
	~~\| date = 1999-11-16~~
	~~\| url = http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=IEESEM001999000187000008000001&idtype=cvips&gifs=yes~~
	~~}}</ref><ref>{{cite journal~~
	~~\| title = Properties of moiré magnifiers~~
	~~\| author = Hala Kamal~~
	~~\| coauthors= Reinhard Völkel and Javier Alda~~
	~~\| journal = Optical Engineering~~
	~~\| volume= 37 (11)~~
	~~\| pages= 3007–3014~~
	~~\|date=November 1998~~
	~~\| url = http://4z.com/people/emin-gabrielyan/public/070227-moire-ref/Kamal98a.pdf~~
	~~\| accessdate = 2007-03-26~~
	\|format=PDF}}</ref> 1D shape moiré is the particular simplified case of 2D shape moiré. 1D patterns may appear when superimposing an opaque layer containing tiny horizontal transparent lines on top of a layer containing a complex shape which is periodically repeating along the vertical axis. Shape moiré is sometimes referred as '''band moiré'''. The ~~opaque layer with transparent lines is called the '''revealing layer'''. The layer containing the periodically repeating shapes is called the '''base layer'''. The period~~ of ~~shapes in~~ the ~~base layer~~ is ~~denoted as ''p''<sub>b</sub>~~. ~~The period of transparent lines in the revealing layer is denoted as~~ ''p''<sub>r</sub>. The periods of both layers must be sufficiently close. The superimposition image reveals the shapes of the base layer stretched along the vertical axis. The magnified shapes appear periodically along the vertical axis. The dimensions along the horizontal axis are not ~~changed. If the complex shape of the base layer~~ is a ~~sequence of symbols (e.g~~. a ~~horizontal text) compressed along the vertical axis, then the superimposition of the revealing layer can restore the original proportions of these symbols. The size of optical shapes ''p'~~'~~<sub>m</sub>, magnified along the vertical axis is expressed by the following formula:~~
	~~:<math>p_m=-\frac{p_b \cdot p_r}{p_b-p_r}</math>~~
	~~Negative values of ''p''<sub>m</sub> signify mirrored appearance (the magnified shapes will~~ be ~~inverted along the vertical axis) of the stretched shapes.~~

	~~When the revealing layer is moved along the vertical axis, the magnified shapes move along the vertical axis at a faster speed~~. ~~The speedup factor~~ is ~~expressed by the following formula:~~
	~~:<math>\frac{v_m}{v_r}=-\frac{p_b}{p_b-p_r}</math>~~
	~~Negative values of ''v''<sub>m</sub> / ''v''<sub>r</sub> signify the movement of optical shapes~~ in ~~reverse direction~~.

	~~When ''p''<sub>r~~<~~/sub>~~ > ~~''p''~~<~~sub~~>~~b</sub>, the magnified shapes appear normally, but they move in reverse direction compared to the movement of the revealing layer. See the figure below:~~

	[~~[Image~~:~~070320-a6-shape-moire-pr-gt-pb.gif]]~~

	~~When ''p''<sub>r<~~/~~sub> < ''p''<sub>b<~~/~~sub>, the magnified shapes appear inverted along the vertical axis, but they move in the same direction as the revealing layer~~. ~~See the figure below:~~

	~~[[Image:070320-shape~~-~~moire-a6-pr-lt-pb~~.~~gif]]~~

	~~[[Line moiré]] can be considered as a particular case of shape moiré when the shape embedded in the base layer is simply a straight or curved line.~~

	~~==External links==~~
	*Shape moiré intro page: [http://~~4z.com/people/emin~~-~~gabrielyan~~/~~public~~/~~070320-shape-moire/ USA], [~~http://~~switzernet~~.~~com/people~~/~~emin~~-~~gabrielyan~~/~~070320-shape~~-~~moire~~/ ~~Switzerland]~~

	~~== References ==~~

	~~<references~~/>

	~~{{DEFAULTSORT:Shape moire}}~~
	~~[[Category:Optics]]~~
	~~[[Category:Geometry]]~~
	~~[[Category:Interference]]~~
	~~[[Category:Patterns]]~~
	~~[[Category:Printing]~~]

en>RJFJR: link in citation template

2013-11-03T22:24:57Z

link in citation template

← Older revision		Revision as of 00:24, 4 November 2013
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	~~Nice to satisfy you, my name~~ is [~~http://Www~~.~~allstate~~.~~com/tools-and-resources/car-insurance/whats-in-a-new-car-warranty~~.~~aspx Araceli Oquendo] but I don't like when people use my complete~~ ~~extended car warranty name~~. ~~He currently life~~ in ~~Idaho~~ and ~~his mothers and fathers reside close [~~http://~~www~~.~~empredators~~.de/~~index.php~~?~~mod~~=~~users~~&~~action~~=~~view~~&id=~~10734 auto warranty] by. The factor I adore most bottle tops gathering~~ and ~~extended [~~http://~~help~~.~~ksu~~.~~edu~~.sa/~~node~~/~~63594 auto warranty] now I have time to take on new issues~~. The ~~occupation he~~'~~s been occupying for car warranty many years~~ is ~~a [http~~://~~www~~.~~allstate~~.~~com/tools~~-~~and~~-~~resources~~/~~car~~-~~insurance/whats~~-in-a-~~new~~-~~car~~-~~warranty~~.~~aspx messenger~~].<br><br>~~Review my page~~ ... [http://~~Phoenixbiofuel~~.com/~~ActivityFeed~~/~~MyProfile~~/~~tabid~~/60/~~userId~~/~~184800~~/~~Default~~.~~aspx auto warranty~~]		{{underlinked\|date=October 2012}}
			{{sections\|date=October 2012}}

			'''Shape moiré''' is one type of [[moiré pattern]]s demonstrating the phenomenon of moiré magnification.<ref>{{cite paper
			\| title = Optical inspection of arrays and periodic structures using moire magnification
			\| author = M.C. Hutley
			\| coauthors = R.F. Stevens
			\| publisher = IEE Colloquium, Microengineering in Optics and Optoelectronics
			\| date = 1999-11-16
			\| url = http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=IEESEM001999000187000008000001&idtype=cvips&gifs=yes
			}}</ref><ref>{{cite journal
			\| title = Properties of moiré magnifiers
			\| author = Hala Kamal
			\| coauthors= Reinhard Völkel and Javier Alda
			\| journal = Optical Engineering
			\| volume= 37 (11)
			\| pages= 3007–3014
			\|date=November 1998
			\| url = http://4z.com/people/emin-gabrielyan/public/070227-moire-ref/Kamal98a.pdf
			\| accessdate = 2007-03-26
			\|format=PDF}}</ref> 1D shape moiré is the particular simplified case of 2D shape moiré. 1D patterns may appear when superimposing an opaque layer containing tiny horizontal transparent lines on top of a layer containing a complex shape which is periodically repeating along the vertical axis. Shape moiré is sometimes referred as '''band moiré'''. The opaque layer with transparent lines is called the '''revealing layer'''. The layer containing the periodically repeating shapes is called the '''base layer'''. The period of shapes in the base layer is denoted as ''p''<sub>b</sub>. The period of transparent lines in the revealing layer is denoted as ''p''<sub>r</sub>. The periods of both layers must be sufficiently close. The superimposition image reveals the shapes of the base layer stretched along the vertical axis. The magnified shapes appear periodically along the vertical axis. The dimensions along the horizontal axis are not changed. If the complex shape of the base layer is a sequence of symbols (e.g. a horizontal text) compressed along the vertical axis, then the superimposition of the revealing layer can restore the original proportions of these symbols. The size of optical shapes ''p''<sub>m</sub>, magnified along the vertical axis is expressed by the following formula:
			:<math>p_m=-\frac{p_b \cdot p_r}{p_b-p_r}</math>
			Negative values of ''p''<sub>m</sub> signify mirrored appearance (the magnified shapes will be inverted along the vertical axis) of the stretched shapes.

			When the revealing layer is moved along the vertical axis, the magnified shapes move along the vertical axis at a faster speed. The speedup factor is expressed by the following formula:
			:<math>\frac{v_m}{v_r}=-\frac{p_b}{p_b-p_r}</math>
			Negative values of ''v''<sub>m</sub> / ''v''<sub>r</sub> signify the movement of optical shapes in reverse direction.

			When ''p''<sub>r</sub> > ''p''<sub>b</sub>, the magnified shapes appear normally, but they move in reverse direction compared to the movement of the revealing layer. See the figure below:

			[[Image:070320-a6-shape-moire-pr-gt-pb.gif]]

			When ''p''<sub>r</sub> < ''p''<sub>b</sub>, the magnified shapes appear inverted along the vertical axis, but they move in the same direction as the revealing layer. See the figure below:

			[[Image:070320-shape-moire-a6-pr-lt-pb.gif]]

			[[Line moiré]] can be considered as a particular case of shape moiré when the shape embedded in the base layer is simply a straight or curved line.

			==External links==
			*Shape moiré intro page: [http://4z.com/people/emin-gabrielyan/public/070320-shape-moire/ USA], [http://switzernet.com/people/emin-gabrielyan/070320-shape-moire/ Switzerland]

			== References ==

			<references/>

			{{DEFAULTSORT:Shape moire}}
			[[Category:Optics]]
			[[Category:Geometry]]
			[[Category:Interference]]
			[[Category:Patterns]]
			[[Category:Printing]]

en>Helpful Pixie Bot: ISBNs (Build KE)

2012-05-11T17:06:29Z

ISBNs (Build KE)

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