History of trigonometry - Revision history

88.142.112.83 at 14:02, 7 January 2015

2015-01-07T14:02:11Z

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	~~Irwin Butts~~ is what my ~~wife loves~~ to ~~contact me although I don't truly like becoming known as like that~~. Managing people is ~~what I do~~ and ~~the wage has been truly fulfilling~~. ~~California is exactly where I've always been living~~ and ~~I adore each working day living here~~. ~~Doing ceramics is what love doing~~.<br><br>My ~~webpage~~ [http://~~mirim~~.ir/~~index.php?do=~~/~~profile-699~~/~~info~~/ ~~home std test kit~~]		Claude is her name and she totally digs that title. Her friends say it's [http://gcjcteam.org/index.php?mid=etc_video&document_srl=654672&sort_index=regdate&order_type=desc extended auto warranty] car warranty auto warranty not great for her but what she [http://autos.jdpower.com/content/buying-tip/xa345A7/pros-and-cons-of-buying-an-extended-warranty-for-a-car.htm loves performing] is flower arranging and she is attempting to make it a occupation. Years ago we moved [http://www.jvawest.com/UserProfile/tabid/152/userId/2157/Default.aspx extended car warranty] warranty to Arizona but my spouse wants us to transfer. Managing people is auto warranty how she makes money and she will not change it [http://Autos.Jdpower.com/content/buying-tip/xa345A7/pros-and-cons-of-buying-an-extended-warranty-for-a-car.htm anytime] soon.<br><br>My web page: [http://Pchelpnow.biz/ActivityFeed/MyProfile/tabid/60/userId/48445/Default.aspx extended auto warranty]

2601:5:380:4CA:D0B0:B652:F9AA:28B6: /* European mathematics */

2014-02-28T23:32:15Z

European mathematics

← Older revision		Revision as of 01:32, 1 March 2014
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	~~[[File:Karplus.svg\|thumb\|300px\| Graph of the Karplus relation~~ ''J''<sub>HH</sub>(φ) = 12 cos<sup>2</sup>φ - cosφ+2 obtained for ethane derivatives <ref name="Minch1994">{{cite journal \| doi = 10.1002/cmr.1820060104 \| journal = [[Concepts in Magnetic Resonance]] \| volume = 6 \|pages=41–56 \| year =1994 \| first=M. J.\|last=Minch\| title = Orientational Dependence of Vicinal Proton-Proton NMR Coupling Constants: The Karplus Relationship}}</ref>]]		Irwin Butts is what my wife loves to contact me although I don't truly like becoming known as like that. Managing people is what I do and the wage has been truly fulfilling. California is exactly where I've always been living and I adore each working day living here. Doing ceramics is what love doing.<br><br>My webpage [http://mirim.ir/index.php?do=/profile-699/info/ home std test kit]

	The '''Karplus equation''', named after [[Martin Karplus]], describes the correlation between <sup>3</sup>[[J-coupling]] constants and [[dihedral angle\|dihedral torsion angles]] in [[nuclear magnetic resonance spectroscopy]]:<ref name="Dalton2003">{{cite journal \| journal = [[Chemical & Engineering News]] \| volume = 81 \| issue = 51 \|page=37 \| date =2003-12-22 \| first=Louisa \|last=Dalton \| title = Karplus Equation \| url = http://pubs.acs.~~org/cen/science/8151/8151karplus.html \| doi = 10.1021/cen-v081n036.p037}}</ref>~~
	~~:<math>J(\phi) = A \cos^2 \phi + B \cos\,\phi + C</math>~~

	~~where ''J''~~ is ~~the <sup>3</sup>''J'' coupling constant, <math> \phi </math> is the [[dihedral angle]], and ''A'', ''B'', and ''C'' are empirically derived parameters whose values depend on the atoms~~ and substituents involved.<ref name="Karplus1959">{{cite journal \|last=Karplus \|first=Martin \| title = Contact Electron-Spin Coupling of Nuclear Magnetic Moments \| year = 1959 \| journal = [[J. Chem. Phys.]] \| volume = 30 \| issue = 1 \| pages = 11–15 \| doi = 10.1063/1.1729860\|bibcode = 1959JChPh..30...11K }}</ref> The relationship may be expressed in a variety of equivalent ways e.g. involving cos 2 φ rather than cos<sup>2</sup>φ —these lead to different numerical values of ''A'', ''B'', and ''C'' but do not change the ~~nature of the relationship~~.

	~~The relationship~~ is ~~used for <sup>3</sup>~~'~~'J''<sub>H,H</sub> coupling constants~~. ~~The superscript "3" indicates that a <sup>1</sup>H atom~~ is ~~coupled to another <sup>1</sup>H atom three bonds away, via H-C-C-H bonds. (Such hydrogens bonded to neighbouring carbon atoms are termed [[Vicinal (chemistry)\|vicinal]])~~.<~~ref name="Karplus1963"~~>{{cite journal \|last=Karplus \|first=Martin \|title = Vicinal Proton Coupling in Nuclear Magnetic Resonance \| year = 1963 \| journal = [[J. Am. Chem. Soc.]] \| volume = 85 \| issue = 18 \| pages = 2870–2871 \| doi = 10.1021/ja00901a059}}<~~/ref~~> ~~The magnitude of these couplings are generally smallest when the torsion angle is close to 90° and largest at angles of 0 and 180°.~~

	This relationship between local geometry and coupling constant is of great value throughout [[nuclear magnetic resonance]] spectroscopy and is particularly valuable for determining [[Backbone chain\|backbone]] torsion angles in [[protein NMR]] studies.

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

	~~==External links==~~
	* [http://~~www~~.~~stenutz~~.eu/~~conf~~/~~jhh.html Generalized Karplus calculation of proton-proton coupling constants]~~

	~~[[Category:Nuclear magnetic resonance]~~]

en>Faizan: Reverted 1 edit by 205.154.44.2 identified as test/vandalism using STiki

2014-01-30T18:30:20Z

Reverted 1 edit by 205.154.44.2 identified as test/vandalism using STiki

← Older revision		Revision as of 20:30, 30 January 2014
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	~~Friends call him Royal~~. ~~The occupation I~~'~~ve been occupying for many years is a bookkeeper but I~~'~~ve currently applied~~ for ~~an additional one~~. The ~~favorite pastime for my kids~~ and me is ~~taking part in crochet~~ and ~~now I~~'~~m trying to make cash with it. Kansas is our birth place~~ and ~~my mothers~~ and ~~fathers reside nearby~~.<br><br>~~Also visit my web page: [http:~~//~~www~~.Pr-~~boot~~-~~camp~~.eu/~~index~~.~~php?mod~~=~~users&action~~=~~view&id~~=~~11672~~ http://www.~~Pr-boot-camp~~.eu]		[[File:Karplus.svg\|thumb\|300px\| Graph of the Karplus relation ''J''<sub>HH</sub>(φ) = 12 cos<sup>2</sup>φ - cosφ+2 obtained for ethane derivatives <ref name="Minch1994">{{cite journal \| doi = 10.1002/cmr.1820060104 \| journal = [[Concepts in Magnetic Resonance]] \| volume = 6 \|pages=41–56 \| year =1994 \| first=M. J.\|last=Minch\| title = Orientational Dependence of Vicinal Proton-Proton NMR Coupling Constants: The Karplus Relationship}}</ref>]]

			The '''Karplus equation''', named after [[Martin Karplus]], describes the correlation between <sup>3</sup>[[J-coupling]] constants and [[dihedral angle\|dihedral torsion angles]] in [[nuclear magnetic resonance spectroscopy]]:<ref name="Dalton2003">{{cite journal \| journal = [[Chemical & Engineering News]] \| volume = 81 \| issue = 51 \|page=37 \| date =2003-12-22 \| first=Louisa \|last=Dalton \| title = Karplus Equation \| url = http://pubs.acs.org/cen/science/8151/8151karplus.html \| doi = 10.1021/cen-v081n036.p037}}</ref>
			:<math>J(\phi) = A \cos^2 \phi + B \cos\,\phi + C</math>

			where ''J'' is the <sup>3</sup>''J'' coupling constant, <math> \phi </math> is the [[dihedral angle]], and ''A'', ''B'', and ''C'' are empirically derived parameters whose values depend on the atoms and substituents involved.<ref name="Karplus1959">{{cite journal \|last=Karplus \|first=Martin \| title = Contact Electron-Spin Coupling of Nuclear Magnetic Moments \| year = 1959 \| journal = [[J. Chem. Phys.]] \| volume = 30 \| issue = 1 \| pages = 11–15 \| doi = 10.1063/1.1729860\|bibcode = 1959JChPh..30...11K }}</ref> The relationship may be expressed in a variety of equivalent ways e.g. involving cos 2 φ rather than cos<sup>2</sup>φ —these lead to different numerical values of ''A'', ''B'', and ''C'' but do not change the nature of the relationship.

			The relationship is used for <sup>3</sup>''J''<sub>H,H</sub> coupling constants. The superscript "3" indicates that a <sup>1</sup>H atom is coupled to another <sup>1</sup>H atom three bonds away, via H-C-C-H bonds. (Such hydrogens bonded to neighbouring carbon atoms are termed [[Vicinal (chemistry)\|vicinal]]).<ref name="Karplus1963">{{cite journal \|last=Karplus \|first=Martin \|title = Vicinal Proton Coupling in Nuclear Magnetic Resonance \| year = 1963 \| journal = [[J. Am. Chem. Soc.]] \| volume = 85 \| issue = 18 \| pages = 2870–2871 \| doi = 10.1021/ja00901a059}}</ref> The magnitude of these couplings are generally smallest when the torsion angle is close to 90° and largest at angles of 0 and 180°.

			This relationship between local geometry and coupling constant is of great value throughout [[nuclear magnetic resonance]] spectroscopy and is particularly valuable for determining [[Backbone chain\|backbone]] torsion angles in [[protein NMR]] studies.

			==References==
			{{reflist}}

			==External links==
			* [http://www.stenutz.eu/conf/jhh.html Generalized Karplus calculation of proton-proton coupling constants]

			[[Category:Nuclear magnetic resonance]]

14.98.138.34: /* Etymology */ Deleted a line which gave an alternative but erroneous etymology for the word "trigonometry". It is of purely Greek origin and not Sanskitic.

2012-08-22T15:00:09Z

Etymology: Deleted a line which gave an alternative but erroneous etymology for the word "trigonometry". It is of purely Greek origin and not Sanskitic.

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Friends call him Royal. The occupation I've been occupying for many years is a bookkeeper but I've currently applied for an additional one. The favorite pastime for my kids and me is taking part in crochet and now I'm trying to make cash with it. Kansas is our birth place and my mothers and fathers reside nearby.<br><br>Also visit my web page: [http://www.Pr-boot-camp.eu/index.php?mod=users&action=view&id=11672 http://www.Pr-boot-camp.eu]