Quadratically constrained quadratic program - Revision history

134.102.148.146: /* Solvers and scripting (programming) languages */

2014-08-27T09:17:39Z

Solvers and scripting (programming) languages

← Older revision		Revision as of 11:17, 27 August 2014
Line 1:		Line 1:
	~~The '''American Death Triangle''', also known as the "American Triangle",<ref>Long, 110.</ref> "Death Triangle" or "Triangle Anchor"<ref name="The Mountaineers, 114">The Mountaineers, 114.</ref>~~ is ~~a type of [[rock climbing\|rock]]~~ and ~~[[ice climbing]] [[Anchor (climbing)\|anchor]] infamous for both magnifying load forces on fixed anchors and lack of redundancy in attachment to the anchor.~~		Claude is her title and she totally digs that title. She is presently a cashier but quickly she'll be on her own. To perform badminton is something he really enjoys doing. He presently lives in Idaho and his mothers and fathers reside close by.<br><br>Also visit my webpage :: car warranty ([http://holder11.Dothome.Co.kr/xe/center/733909 mouse click on holder11.Dothome.Co.kr])

	~~==Description==~~
	~~A two-point climbing anchor requires three [[carabiner]]s: one at each fixed point and one at the "focal point" where the load is transferred to the climbing rope~~. ~~The aim~~ is ~~to distribute the force equally to each fixed point. A triangle anchor is formed by clipping~~ a ~~length of [[webbing]] or cord through all three carabiners, creating a shape which gives the dangerous anchor its descriptive name.~~

	The force on each fixed point depends on the angle at the focal point. The following table lists the percentage of force transferred to the fixed point for various focal point angles, followed by figures for a standard "V" shaped anchor.<ref name="The Mountaineers, 114"/>

	~~[[File:AmericanDeathTriangle.png\|thumb\|right\|American death triangle showing the associated lines of force (in blue) acting on the anchors]]~~
	~~{\| class="wikitable"~~
	~~\|+ Load per anchor based~~ on ~~a central, perpendicular application of 100 [[lbf]] of force~~
	\|-
	~~! Bottom angle~~
	~~! Load per anchor (V arrangement)~~
	~~! Load per anchor (triangle arrangement)~~
	\|-
	~~\| 0°~~
	~~\| 50 lbf~~
	~~\| 71 lbf (not physically possible)~~
	\|-
	~~\| 5°~~
	~~\| 50 lbf~~
	~~\| 72 lbf~~
	\|-
	~~\| 10°~~
	~~\| 50 lbf~~
	~~\| 74 lbf~~
	\|-
	~~\| 30°~~
	~~\| 52 lbf~~
	~~\| 82 lbf~~
	\|-
	~~\| 60°~~
	~~\| 58 lbf~~
	~~\| 100 lbf~~
	\|-
	~~\| 90°~~
	~~\| 71 lbf~~
	~~\| 131 lbf~~
	\|-
	~~\| 120°~~
	~~\| 100 lbf~~
	~~\| 193 lbf~~
	\|-
	~~\| 150°~~
	~~\| 193 lbf~~
	~~\| 380 lbf~~
	\|}

	~~Table values are derived from [[parallelogram of force\|vector analysis]]:~~

	* For a V arrangement, <math>F_{\mathrm{Anchor}} = \frac {\mathrm{Weight}} {2 \cos(\frac 1 2 {\theta_\mathrm{Bottom}})} \approx \mathrm{Weight}\times 0.5 + O({\theta_\mathrm{Bottom}}^2)</math>

	* For the Triangle, <math>F_{\mathrm{Anchor}} =\frac {\mathrm{Weight}} {2 \cos (45 ^{\circ} + \frac 1 4 {\theta_{\mathrm{Bottom}}} )} \approx\mathrm{Weight}\times 0.~~707 + O(\theta_{\mathrm{Bottom}})</math>~~

	~~The load on the sling~~ is ~~the same in each example~~. ~~For the V arrangement, the anchor force is equal to the tension~~ in ~~the sling, but for the triangle the anchor force is greater than the sling tension.~~

	~~Aside from the magnification of forces, the ''death triangle'' violates several rules for building climbing anchors, including~~

	* Redundancy: if the webbing fails on one leg of the anchor, the entire anchor will fail.
	* Extension: if one of the anchors fails, the webbing will extend its full length and ~~shock load the remaining components of the system~~

	An alternate V-shaped form of the ''death triangle'' involves clipping a single loop of webbing or cord to each anchor then clipping the third carabiner over the loop rather than through it, allowing the latter to slip off the loop if either anchor fails. The correct method puts a half twist in the cord and ~~clips the free carabiner through it. If either anchor fails the free carabiner will remain attached to the cord.~~

	Special circumstances, such as when an experienced climber employs opposing forces to keep passive [[Nut (climbing)\|chocks]], simple cams, or [[spring-loaded camming device\|spring loaded multiple camming devices]] in a crack, may call for a triangle.<~~ref~~>~~Long, 67~~<~~/ref~~> ~~Even then, special provision must be made to provide redundancy and eliminate extension in the [[Protection (climbing)\|protection]] system.~~

	~~==See also==~~
	* [[Climbing]]

	~~==Notes==~~
	~~{{reflist}}~~

	~~==References==~~
	* {{cite book\|last=[[John Long (climber)\|Long]]\|first=[[John Long (climber)\|John]] \|title=How to Rock Climb: ~~Climbing Anchors\|year=1993\|publisher=[[Chockstone Press]], Evergreen, Colorado\|isbn=0-934641-37-4}}~~
	* {{cite book\|last=Mountaineers\|first=The\|title=Mountaineering: ~~Freedom of the Hills\|edition=Fifth Edition\|year=2002\|publisher=[[The Mountaineers~~ (~~Pacific NW)\|The Mountaineers]], [[Seattle]], [[Washington (U.S. state)\|Washington]]\|isbn=0-89886-309-0}}~~

	~~==External links==~~
	* [http://~~www~~.~~spadout~~.~~com/wiki/index~~.~~php~~/~~Anchor Climbing Anchor]~~
	* [http://~~www~~.~~uoregon~~.~~edu/~opp/climbing/topics/anchors~~.~~html Climbing Anchors] includes photo~~

	~~[[Category:Climbing]]~~
	~~[[Category:Mountaineering]~~]

en>Jones1980: /* Solvers and scripting (programming) languages */

2013-12-25T21:25:28Z

Solvers and scripting (programming) languages

← Older revision		Revision as of 23:25, 25 December 2013
Line 1:		Line 1:
	~~Alyson~~ is the ~~title people use~~ to ~~call me and I believe it seems fairly good when you say it~~. ~~To play lacross~~ is the ~~thing I love most~~ of all. ~~I've usually loved residing in Mississippi~~. ~~Office supervising is my profession~~.<br>~~<br>my web blog~~; ~~tarot readings~~ ([~~http~~://~~alles~~-~~herunterladen~~.de/~~excellent~~-~~advice~~-~~for~~-~~picking~~-~~the~~-~~ideal~~-~~hobby~~/ ~~Read the Full Piece of writing~~])		The '''American Death Triangle''', also known as the "American Triangle",<ref>Long, 110.</ref> "Death Triangle" or "Triangle Anchor"<ref name="The Mountaineers, 114">The Mountaineers, 114.</ref> is a type of [[rock climbing\|rock]] and [[ice climbing]] [[Anchor (climbing)\|anchor]] infamous for both magnifying load forces on fixed anchors and lack of redundancy in attachment to the anchor.

			==Description==
			A two-point climbing anchor requires three [[carabiner]]s: one at each fixed point and one at the "focal point" where the load is transferred to the climbing rope. The aim is to distribute the force equally to each fixed point. A triangle anchor is formed by clipping a length of [[webbing]] or cord through all three carabiners, creating a shape which gives the dangerous anchor its descriptive name.

			The force on each fixed point depends on the angle at the focal point. The following table lists the percentage of force transferred to the fixed point for various focal point angles, followed by figures for a standard "V" shaped anchor.<ref name="The Mountaineers, 114"/>

			[[File:AmericanDeathTriangle.png\|thumb\|right\|American death triangle showing the associated lines of force (in blue) acting on the anchors]]
			{\| class="wikitable"
			\|+ Load per anchor based on a central, perpendicular application of 100 [[lbf]] of force
			\|-
			! Bottom angle
			! Load per anchor (V arrangement)
			! Load per anchor (triangle arrangement)
			\|-
			\| 0°
			\| 50 lbf
			\| 71 lbf (not physically possible)
			\|-
			\| 5°
			\| 50 lbf
			\| 72 lbf
			\|-
			\| 10°
			\| 50 lbf
			\| 74 lbf
			\|-
			\| 30°
			\| 52 lbf
			\| 82 lbf
			\|-
			\| 60°
			\| 58 lbf
			\| 100 lbf
			\|-
			\| 90°
			\| 71 lbf
			\| 131 lbf
			\|-
			\| 120°
			\| 100 lbf
			\| 193 lbf
			\|-
			\| 150°
			\| 193 lbf
			\| 380 lbf
			\|}

			Table values are derived from [[parallelogram of force\|vector analysis]]:

			* For a V arrangement, <math>F_{\mathrm{Anchor}} = \frac {\mathrm{Weight}} {2 \cos(\frac 1 2 {\theta_\mathrm{Bottom}})} \approx \mathrm{Weight}\times 0.5 + O({\theta_\mathrm{Bottom}}^2)</math>

			* For the Triangle, <math>F_{\mathrm{Anchor}} =\frac {\mathrm{Weight}} {2 \cos (45 ^{\circ} + \frac 1 4 {\theta_{\mathrm{Bottom}}} )} \approx\mathrm{Weight}\times 0.707 + O(\theta_{\mathrm{Bottom}})</math>

			The load on the sling is the same in each example. For the V arrangement, the anchor force is equal to the tension in the sling, but for the triangle the anchor force is greater than the sling tension.

			Aside from the magnification of forces, the ''death triangle'' violates several rules for building climbing anchors, including

			* Redundancy: if the webbing fails on one leg of the anchor, the entire anchor will fail.
			* Extension: if one of the anchors fails, the webbing will extend its full length and shock load the remaining components of the system

			An alternate V-shaped form of the ''death triangle'' involves clipping a single loop of webbing or cord to each anchor then clipping the third carabiner over the loop rather than through it, allowing the latter to slip off the loop if either anchor fails. The correct method puts a half twist in the cord and clips the free carabiner through it. If either anchor fails the free carabiner will remain attached to the cord.

			Special circumstances, such as when an experienced climber employs opposing forces to keep passive [[Nut (climbing)\|chocks]], simple cams, or [[spring-loaded camming device\|spring loaded multiple camming devices]] in a crack, may call for a triangle.<ref>Long, 67</ref> Even then, special provision must be made to provide redundancy and eliminate extension in the [[Protection (climbing)\|protection]] system.

			==See also==
			* [[Climbing]]

			==Notes==
			{{reflist}}

			==References==
			* {{cite book\|last=[[John Long (climber)\|Long]]\|first=[[John Long (climber)\|John]] \|title=How to Rock Climb: Climbing Anchors\|year=1993\|publisher=[[Chockstone Press]], Evergreen, Colorado\|isbn=0-934641-37-4}}
			* {{cite book\|last=Mountaineers\|first=The\|title=Mountaineering: Freedom of the Hills\|edition=Fifth Edition\|year=2002\|publisher=[[The Mountaineers (Pacific NW)\|The Mountaineers]], [[Seattle]], [[Washington (U.S. state)\|Washington]]\|isbn=0-89886-309-0}}

			==External links==
			* [http://www.spadout.com/wiki/index.php/Anchor Climbing Anchor]
			* [http://www.uoregon.edu/~opp/climbing/topics/anchors.html Climbing Anchors] includes photo

			[[Category:Climbing]]
			[[Category:Mountaineering]]

en>Zfeinst: /* References */

2012-08-30T20:56:01Z

References

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Alyson is the title people use to call me and I believe it seems fairly good when you say it. To play lacross is the thing I love most of all. I've usually loved residing in Mississippi. Office supervising is my profession.<br><br>my web blog; tarot readings ([http://alles-herunterladen.de/excellent-advice-for-picking-the-ideal-hobby/ Read the Full Piece of writing])