Littelmann path model - Revision history

en>Rjwilmsi: /* References */Journal cites, Added 1 doi to a journal cite using AWB (10365)

2014-08-15T14:38:29Z

References: Journal cites, Added 1 doi to a journal cite using AWB (10365)

← Older revision		Revision as of 16:38, 15 August 2014
Line 1:		Line 1:
	~~Sir '''(Alfred) George Greenhill''', [[Fellow of the Royal Society\|F.R.S.]] (29 November 1847, [[London]] — 10 February 1927, [[London]]), was a [[Great Britain\|British]] [[mathematician]].~~		Alyson is what my spouse enjoys to call me but I don't like when individuals use my full title. To play lacross is one of the things she enjoys most. Kentucky is where I've usually been residing. Office supervising is my profession.<br><br>Also visit my homepage - [http://findyourflirt.net/index.php?m=member_profile&p=profile&id=117823 authentic psychic readings]

	~~George Greenhill was educated at [[Christ's Hospital\|Christ's Hospital School]] and from there he went up~~ to ~~[[St John~~'~~s College, Cambridge]] in 1866~~.~~<ref>{{acad\|id=GRNL866GA\|name=Greenhill, George Alfred}}</ref> In 1876, Greenhill was appointed professor~~ of ~~mathematics at~~ the ~~[[Royal Military Academy, Woolwich\|Royal Military Academy (RMA) at Woolwich]], London, UK~~.~~<ref>School of Mathematics and Statistics, University of St Andrews, Scotland. ''Alfred George Greenhill'~~' ~~(October 2003). http://www-history.mcs.st-andrews.ac.uk/~history/Biographies/Greenhill.html</ref> He held this chair until his retirement in 1908~~. ~~His 1892 textbook on applications of [[elliptic functions]]~~ is ~~of acknowledged excellence.~~

	In 1879, Greenhill developed a [[rule of thumb]] for calculating the optimal [[Rifling#Twist rate\|twist]] rate for lead-core bullets. This shortcut uses the bullet's length, needing no allowances for weight or nose shape.<~~ref~~>Mosdell, Matthew. ''The Greenhill Formula''. http://www.mamut.net/MarkBrooks/newsdet35.htm (Accessed 2009 AUG 19)</ref> Greenhill applied this theory to account for the steadiness of flight conferred upon an elongated projectile by [[rifling]]. The eponymous ''Greenhill Formula'', still used today, is:

	~~<math>Twist = \frac{C D^2}{L} \times \sqrt{\frac{SG}{10.9}}~~<~~/math~~>

	~~where:~~
	*C = 150 (use 180 for muzzle velocities higher than 2,800 f/s)
	*D = bullet's diameter in inches
	*L = bullet's length in inches
	*SG = bullet's [[specific gravity]] (10.9 for lead-~~core bullets, which cancels out the second half of the equation)~~

	The original value of C was 150, which yields a twist rate in inches per turn, when given the diameter D and the length L of the bullet in inches. This works to velocities of about 840 m/s (2800 ft/s); above those velocities, a C of 180 should be used. For instance, with a velocity of 600 m/s (2000 ft/s), a diameter of {{convert\|0.5\|in\|mm}} and a length of {{convert\|1.5\|in\|mm}}, the Greenhill formula would give a value of 25, which means 1 turn in {{convert\|25\|in\|mm}}.

	~~== Textbooks ==~~
	* A. G. Greenhill ''Differential and integral calculus, with applications'' ( London, MacMillan, 1886) [http://~~www~~.~~archive.org~~/~~details/differentialinte00greeuoft archive~~.~~org]~~
	* A. G. Greenhill, ''The applications of elliptic functions'' (MacMillan & Co, New York, 1892). [http://quod.lib.umich.edu/cgi/t/text/text-idx?c=~~umhistmath;idno~~=~~ACQ7072 University of Michigan Historical Mathematical Collection.]~~
	* A. G. Greenhill, ''A treatise on hydrostatics'' (MacMillan, London, 1894) [http://www.archive.org/details/treatiseonhydros00greeuoft archive.org]
	* A. G. Greenhill ''The dynamics of mechanical flight'' (Constable, London, 1912) [http://www.archive.org/details/dynamicsofmechan00greerich archive.org]

	~~==External links==~~
	~~{{Wikisource author}}~~
	* Alfred George Greenhill. [http://www-history.mcs.st-and.ac.uk/Biographies/Greenhill.html The MacTutor History of Mathematics archive]
	* Alfred George Greenhill. [http://www.icmihistory.unito.it/portrait/greenhill.php The First Century of the ICMI (1909 - 2008) ]
	* School of Mathematics and Statistics, University of St Andrews, Scotland. ''Alfred George Greenhill'' (October 2003). http://www-history.mcs.st-andrews.ac.uk/~history/Biographies/Greenhill.html

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

	~~{{Authority control\|VIAF=49986812}}~~

	~~{{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->~~
	~~\| NAME = Greenhill, Alfred George~~
	~~\| ALTERNATIVE NAMES =~~
	~~\| SHORT DESCRIPTION = British mathematician~~
	~~\| DATE OF BIRTH = 1847~~
	~~\| PLACE OF BIRTH =~~
	~~\| DATE OF DEATH = 1927~~
	~~\| PLACE OF DEATH~~ =
	}}
	~~{{DEFAULTSORT:Greenhill, Alfred George}}~~
	~~[[Category:1847 births]]~~
	~~[[Category:1927 deaths]]~~
	~~[[Category:People from London]]~~
	~~[[Category:People educated at Christ's Hospital]]~~
	~~[[Category:Alumni of St John's College, Cambridge]]~~
	~~[[Category:British mathematicians]]~~
	~~[[Category:Royal Medal winners]]~~
	~~[[Category:Second Wranglers]]~~
	~~[[Category:Fellows of the Royal Aeronautical Society]]~~
	~~[[Category:Fellows of the Royal Society]]~~
	~~[[Category:Knights Bachelor]]~~
	~~[[Category:Members of the French Academy of Sciences]]~~
	~~[[Category:De Morgan Medallists]]~~
	~~[[Category:Ballistics experts]]~~
	~~[[Category:ICM 1904 Plenary and Invited Speakers]~~]

209.6.233.136: /* Properties */ Changed the inequality so that the exponent of "e" is positive.

2013-11-24T02:08:02Z

Properties: Changed the inequality so that the exponent of "e" is positive.

← Older revision		Revision as of 04:08, 24 November 2013
Line 1:		Line 1:
	~~I would like~~ to ~~introduce myself to you~~, ~~I am Andrew~~ and ~~my wife doesn~~'~~t like it at all~~. ~~Invoicing~~ is ~~what I do~~. ~~She is really fond~~ of ~~caving but she doesn~~'~~t have the time lately~~. ~~Her family members life in Ohio but her husband wants them~~ to ~~transfer~~.<br><br>~~My web site~~; [http://~~gcjcteam~~.org/~~index~~.php~~?mid~~=~~etc_video&document_srl~~=~~696611&sort_index~~=~~regdate&order_type~~=~~desc accurate psychic readings~~]		Sir '''(Alfred) George Greenhill''', [[Fellow of the Royal Society\|F.R.S.]] (29 November 1847, [[London]] — 10 February 1927, [[London]]), was a [[Great Britain\|British]] [[mathematician]].

			George Greenhill was educated at [[Christ's Hospital\|Christ's Hospital School]] and from there he went up to [[St John's College, Cambridge]] in 1866.<ref>{{acad\|id=GRNL866GA\|name=Greenhill, George Alfred}}</ref> In 1876, Greenhill was appointed professor of mathematics at the [[Royal Military Academy, Woolwich\|Royal Military Academy (RMA) at Woolwich]], London, UK.<ref>School of Mathematics and Statistics, University of St Andrews, Scotland. ''Alfred George Greenhill'' (October 2003). http://www-history.mcs.st-andrews.ac.uk/~history/Biographies/Greenhill.html</ref> He held this chair until his retirement in 1908. His 1892 textbook on applications of [[elliptic functions]] is of acknowledged excellence.

			In 1879, Greenhill developed a [[rule of thumb]] for calculating the optimal [[Rifling#Twist rate\|twist]] rate for lead-core bullets. This shortcut uses the bullet's length, needing no allowances for weight or nose shape.<ref>Mosdell, Matthew. ''The Greenhill Formula''. http://www.mamut.net/MarkBrooks/newsdet35.htm (Accessed 2009 AUG 19)</ref> Greenhill applied this theory to account for the steadiness of flight conferred upon an elongated projectile by [[rifling]]. The eponymous ''Greenhill Formula'', still used today, is:

			<math>Twist = \frac{C D^2}{L} \times \sqrt{\frac{SG}{10.9}}</math>

			where:
			*C = 150 (use 180 for muzzle velocities higher than 2,800 f/s)
			*D = bullet's diameter in inches
			*L = bullet's length in inches
			*SG = bullet's [[specific gravity]] (10.9 for lead-core bullets, which cancels out the second half of the equation)

			The original value of C was 150, which yields a twist rate in inches per turn, when given the diameter D and the length L of the bullet in inches. This works to velocities of about 840 m/s (2800 ft/s); above those velocities, a C of 180 should be used. For instance, with a velocity of 600 m/s (2000 ft/s), a diameter of {{convert\|0.5\|in\|mm}} and a length of {{convert\|1.5\|in\|mm}}, the Greenhill formula would give a value of 25, which means 1 turn in {{convert\|25\|in\|mm}}.

			== Textbooks ==
			* A. G. Greenhill ''Differential and integral calculus, with applications'' ( London, MacMillan, 1886) [http://www.archive.org/details/differentialinte00greeuoft archive.org]
			* A. G. Greenhill, ''The applications of elliptic functions'' (MacMillan & Co, New York, 1892). [http://quod.lib.umich.edu/cgi/t/text/text-idx?c=umhistmath;idno=ACQ7072 University of Michigan Historical Mathematical Collection.]
			* A. G. Greenhill, ''A treatise on hydrostatics'' (MacMillan, London, 1894) [http://www.archive.org/details/treatiseonhydros00greeuoft archive.org]
			* A. G. Greenhill ''The dynamics of mechanical flight'' (Constable, London, 1912) [http://www.archive.org/details/dynamicsofmechan00greerich archive.org]

			==External links==
			{{Wikisource author}}
			* Alfred George Greenhill. [http://www-history.mcs.st-and.ac.uk/Biographies/Greenhill.html The MacTutor History of Mathematics archive]
			* Alfred George Greenhill. [http://www.icmihistory.unito.it/portrait/greenhill.php The First Century of the ICMI (1909 - 2008) ]
			* School of Mathematics and Statistics, University of St Andrews, Scotland. ''Alfred George Greenhill'' (October 2003). http://www-history.mcs.st-andrews.ac.uk/~history/Biographies/Greenhill.html

			==References==
			{{reflist}}

			{{Authority control\|VIAF=49986812}}

			{{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
			\| NAME = Greenhill, Alfred George
			\| ALTERNATIVE NAMES =
			\| SHORT DESCRIPTION = British mathematician
			\| DATE OF BIRTH = 1847
			\| PLACE OF BIRTH =
			\| DATE OF DEATH = 1927
			\| PLACE OF DEATH =
			}}
			{{DEFAULTSORT:Greenhill, Alfred George}}
			[[Category:1847 births]]
			[[Category:1927 deaths]]
			[[Category:People from London]]
			[[Category:People educated at Christ's Hospital]]
			[[Category:Alumni of St John's College, Cambridge]]
			[[Category:British mathematicians]]
			[[Category:Royal Medal winners]]
			[[Category:Second Wranglers]]
			[[Category:Fellows of the Royal Aeronautical Society]]
			[[Category:Fellows of the Royal Society]]
			[[Category:Knights Bachelor]]
			[[Category:Members of the French Academy of Sciences]]
			[[Category:De Morgan Medallists]]
			[[Category:Ballistics experts]]
			[[Category:ICM 1904 Plenary and Invited Speakers]]

en>Bibcode Bot: Adding 0 arxiv eprint(s), 2 bibcode(s) and 0 doi(s). Did it miss something? Report bugs, errors, and suggestions at User talk:Bibcode Bot

2012-08-31T00:58:08Z

Adding 0 arxiv eprint(s), 2 bibcode(s) and 0 doi(s). Did it miss something? Report bugs, errors, and suggestions at User talk:Bibcode Bot

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I would like to introduce myself to you, I am Andrew and my wife doesn't like it at all. Invoicing is what I do. She is really fond of caving but she doesn't have the time lately. Her family members life in Ohio but her husband wants them to transfer.<br><br>My web site; [http://gcjcteam.org/index.php?mid=etc_video&document_srl=696611&sort_index=regdate&order_type=desc accurate psychic readings]