Klein geometry - Revision history

en>Quondum: /* Formal definition */ ⋅ → . (making notation for the group action consistent with that in Group action)

2014-06-17T00:14:41Z

Formal definition: ⋅ → . (making notation for the group action consistent with that in Group action)

← Older revision		Revision as of 02:14, 17 June 2014
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	~~The author~~ is known as ~~Irwin~~. ~~To collect badges is what her family members~~ and ~~her enjoy. California is exactly where~~ I~~'ve usually been residing~~ and I ~~adore every working~~ day residing here. ~~For years~~ he~~'s been working as a meter reader and~~ it~~'s some thing he truly enjoy~~.<br><br>~~Review~~ my ~~webpage ... std home test [~~[~~https~~://~~www~~.~~machlitim.org~~.~~il/subdomain/megila~~/~~end~~/~~node~~/~~9243 mouse click the following internet site]~~]		Jayson Berryhill is how I'm known as and my spouse doesn't like it at all. My spouse and I live in Mississippi and I love each day residing right here. The preferred hobby for him and his kids is to perform lacross and he would by no means give it up. He is an information officer.<br><br>Feel free to visit my web-site; clairvoyants ([http://ustanford.com/index.php?do=/profile-38218/info/ websites])

en>Psh1136: I switched the order of subgroups in semi direct product of Euclidean group and Affine group.

2014-02-14T10:07:35Z

I switched the order of subgroups in semi direct product of Euclidean group and Affine group.

← Older revision		Revision as of 12:07, 14 February 2014
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	~~[[Image:Forest fire model.gif\|thumb\|right\|Evolution of forest with p/f=100]]~~		The author is known as Irwin. To collect badges is what her family members and her enjoy. California is exactly where I've usually been residing and I adore every working day residing here. For years he's been working as a meter reader and it's some thing he truly enjoy.<br><br>Review my webpage ... std home test [[https://www.machlitim.org.il/subdomain/megila/end/node/9243 mouse click the following internet site]]

	In applied mathematics, a '''forest-fire model''' is any of a number of [[dynamical system]]s displaying [[self-organized criticality]]. Note, however, that according to Pruessner et al. (2002, 2004) the forest-fire model does not behave critically on very large, i.e. physically relevant scales. Early versions go back to Henley (1989) and Drossel and Schwabl (1992). The ~~model~~ is ~~defined~~ as ~~a [[cellular automaton]] on a grid with ''L''<sup>''d''</sup> cells~~. ''L'' is the sidelength of the grid and ''d'' is its dimension. A cell can be empty, occupied by a tree, or burning. The model of Drossel and Schwabl (1992) is defined by four rules which are executed simultaneously:

	~~# A burning cell turns into an empty cell~~
	~~# A tree will burn if at least one neighbor is burning~~
	~~# A tree ignites with probability ''f'' even if no neighbor~~ is ~~burning~~
	~~# An empty space fills with a tree with probability ''p''~~

	~~The controlling parameter of the model is ''p''/''f'' which gives the average number of trees planted between two lightning strikes (see Schenk et al. (1996)~~ and ~~[[Peter Grassberger \| Grassberger]] (1993))~~. ~~In order to exhibit a [[fractal]] frequency-size distribution of clusters a double separation of time scales~~ is ~~necessary~~

	~~:<math>f \ll p \ll T_\mathrm{smax}\,</math>~~

	where '~~'T''<sub>smax</sub> is the burn time of the largest cluster. The scaling behavior is not simple, however ([[Peter Grassberger \| Grassberger]] 1993,2002~~ and ~~Pruessner et al~~. ~~2002,2004).~~

	A '~~''cluster''' is defined~~ as a ~~coherent set of cells, all of which have the same state. Cells are coherent if they can reach each other via nearest neighbor relations~~. ~~In most cases, the von Neumann neighborhood (four adjacent cells) is considered.~~

	~~The first condition~~ <~~math~~>~~f\ll p~~<~~/math~~> ~~allows large structures to develop, while the second condition <math>p\ll T_\mathrm{smax}</math> keeps trees from popping up alongside a cluster while burning.~~

	~~In landscape ecology, the forest fire model is used to illustrate the role of the fuel mosaic in the wildfire regime~~. ~~The importance of the fuel mosaic on wildfire spread is debated~~. ~~Parsimonious models such as the forest fire model can help to explore the role of the fuel mosaic and its limitations in explaining observed patterns.~~

	~~== References ==~~

	* Bak, P., Chen, K. and Tang, C. (1990), "A forest-fire model and some thoughts on turbulence." ''Phys. Lett. A'' '''147''', 297–300. [~~http~~://www.~~papercore~~.org~~/summaries/a-forest-fire-model-and-some-thoughts-on-turbulenc Papercore Summary]~~
	* Chen, K., Bak, P. and Jensen, M. H. (1990), "A deterministic critical forest-fire model." ''Phys. Lett. A'' '''149''', 207–210.
	* Drossel, B. and Schwabl, F. (1992), "Self-organized critical forest-fire model." ''Phys. Rev. Lett.'' '''69''', 1629–1632.
	* [[Peter Grassberger \| Grassberger, P.]] (2002), "Critical behaviour of the Drossel-Schwabl forest fire model." ''New J. Phys.'' '''4''', 17.
	* Henley, C. L. (1989), "Self-organized percolation: a simpler model." ''Bull. Am. Phys. Soc.'' '''34''', 838.
	* Henley, C. L. (1993), "Statics of a 'self-organized' percolation model." ''Phys. Rev. ~~Lett.'' '''71''', 2741–2744.~~
	* Pruessner, G. and Jensen, H. J. (2002), "Broken scaling in the forest-fire model." ''Phys. Rev. E'' '''65''', 056707.
	* Zinck, R. and Grimm, V. (2009), "Unifying wildfire models from ecology and statistical physics". The American Naturalist, '''174''', E170-E185.
	*[http://xstructure.inr.ac.ru/~~x-bin/theme3.py?level=1&index1=-156507 Forest-fire model on arxiv.org]~~

	~~== External links ==~~
	* [http://~~aryannayra.com~~/~~randomstuff~~/~~forestfire.html An HTML 5 demo of~~ the ~~forest fire model].~~
	* A [http://www.joakimlinde.se/java/forestfire/index.php Forest-fire model java applet].

	~~[[Category:Self-organization~~]]

en>Addbot: Bot: Migrating 1 interwiki links, now provided by Wikidata on d:q2132698

2013-03-14T18:39:09Z

Bot: Migrating 1 interwiki links, now provided by Wikidata on d:q2132698

← Older revision		Revision as of 20:39, 14 March 2013
Line 1:		Line 1:
	~~Marvella~~ is ~~what you can contact her but it'~~s not ~~the most feminine name out there~~. ~~Years ago we moved~~ to ~~North Dakota~~ and ~~I love every working day living here~~. ~~For years he~~'~~s been working as~~ a ~~receptionist~~. ~~One~~ of the ~~things she loves most~~ is to ~~do aerobics~~ and ~~now she~~ is ~~trying to make cash with it~~.<br><br>~~Here~~ is ~~my web page std testing at home~~ ([http://www.zs-~~imports~~.com/~~blogs~~/~~post~~/~~70017 visit the next document~~])		[[Image:Forest fire model.gif\|thumb\|right\|Evolution of forest with p/f=100]]

			In applied mathematics, a '''forest-fire model''' is any of a number of [[dynamical system]]s displaying [[self-organized criticality]]. Note, however, that according to Pruessner et al. (2002, 2004) the forest-fire model does not behave critically on very large, i.e. physically relevant scales. Early versions go back to Henley (1989) and Drossel and Schwabl (1992). The model is defined as a [[cellular automaton]] on a grid with ''L''<sup>''d''</sup> cells. ''L'' is the sidelength of the grid and ''d'' is its dimension. A cell can be empty, occupied by a tree, or burning. The model of Drossel and Schwabl (1992) is defined by four rules which are executed simultaneously:

			# A burning cell turns into an empty cell
			# A tree will burn if at least one neighbor is burning
			# A tree ignites with probability ''f'' even if no neighbor is burning
			# An empty space fills with a tree with probability ''p''

			The controlling parameter of the model is ''p''/''f'' which gives the average number of trees planted between two lightning strikes (see Schenk et al. (1996) and [[Peter Grassberger \| Grassberger]] (1993)). In order to exhibit a [[fractal]] frequency-size distribution of clusters a double separation of time scales is necessary

			:<math>f \ll p \ll T_\mathrm{smax}\,</math>

			where ''T''<sub>smax</sub> is the burn time of the largest cluster. The scaling behavior is not simple, however ([[Peter Grassberger \| Grassberger]] 1993,2002 and Pruessner et al. 2002,2004).

			A '''cluster''' is defined as a coherent set of cells, all of which have the same state. Cells are coherent if they can reach each other via nearest neighbor relations. In most cases, the von Neumann neighborhood (four adjacent cells) is considered.

			The first condition <math>f\ll p</math> allows large structures to develop, while the second condition <math>p\ll T_\mathrm{smax}</math> keeps trees from popping up alongside a cluster while burning.

			In landscape ecology, the forest fire model is used to illustrate the role of the fuel mosaic in the wildfire regime. The importance of the fuel mosaic on wildfire spread is debated. Parsimonious models such as the forest fire model can help to explore the role of the fuel mosaic and its limitations in explaining observed patterns.

			== References ==

			* Bak, P., Chen, K. and Tang, C. (1990), "A forest-fire model and some thoughts on turbulence." ''Phys. Lett. A'' '''147''', 297–300. [http://www.papercore.org/summaries/a-forest-fire-model-and-some-thoughts-on-turbulenc Papercore Summary]
			* Chen, K., Bak, P. and Jensen, M. H. (1990), "A deterministic critical forest-fire model." ''Phys. Lett. A'' '''149''', 207–210.
			* Drossel, B. and Schwabl, F. (1992), "Self-organized critical forest-fire model." ''Phys. Rev. Lett.'' '''69''', 1629–1632.
			* [[Peter Grassberger \| Grassberger, P.]] (2002), "Critical behaviour of the Drossel-Schwabl forest fire model." ''New J. Phys.'' '''4''', 17.
			* Henley, C. L. (1989), "Self-organized percolation: a simpler model." ''Bull. Am. Phys. Soc.'' '''34''', 838.
			* Henley, C. L. (1993), "Statics of a 'self-organized' percolation model." ''Phys. Rev. Lett.'' '''71''', 2741–2744.
			* Pruessner, G. and Jensen, H. J. (2002), "Broken scaling in the forest-fire model." ''Phys. Rev. E'' '''65''', 056707.
			* Zinck, R. and Grimm, V. (2009), "Unifying wildfire models from ecology and statistical physics". The American Naturalist, '''174''', E170-E185.
			*[http://xstructure.inr.ac.ru/x-bin/theme3.py?level=1&index1=-156507 Forest-fire model on arxiv.org]

			== External links ==
			* [http://aryannayra.com/randomstuff/forestfire.html An HTML 5 demo of the forest fire model].
			* A [http://www.joakimlinde.se/java/forestfire/index.php Forest-fire model java applet].

			[[Category:Self-organization]]

en>Foxjwill: /* Examples */ added mathrm to a bunch of places

2012-07-14T05:22:47Z

Examples: added mathrm to a bunch of places

New page

Marvella is what you can contact her but it's not the most feminine name out there. Years ago we moved to North Dakota and I love every working day living here. For years he's been working as a receptionist. One of the things she loves most is to do aerobics and now she is trying to make cash with it.<br><br>Here is my web page std testing at home ([http://www.zs-imports.com/blogs/post/70017 visit the next document])