Numerical continuation - Revision history

en>Markhurd: Disambiguate Jacobian to Jacobian matrix and determinant using popups

2014-07-02T15:18:25Z

Disambiguate Jacobian to Jacobian matrix and determinant using popups

← Older revision		Revision as of 17:18, 2 July 2014
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	~~{{refimprove\|date=October 2013}}~~		Hi there, I am Andrew Berryhill. Office supervising is what she does for a living. For years he's been living in Mississippi and he doesn't strategy on altering it. What me and my family members love is performing ballet but I've been taking on new things lately.<br><br>my page :: psychic readings online ([http://cpacs.org/index.php?document_srl=90091&mid=board_zTGg26 visit my home page])
	The '''bicarbonate buffering system''' is an important [[buffer solution\|buffer]] system in the [[acid-base homeostasis]] of living things, including humans. As a buffer, it tends to maintain a relatively constant [[blood plasma\|plasma]] [[pH]] and counteract any force that would alter.
	~~In this system, [[carbon dioxide]] (CO<sub>2</sub>) combines with [[water]] to form [[carbonic acid]] (H<sub>2</sub>CO<sub>3</sub>)~~, ~~which in turn rapidly dissociates to form [[hydrogen ions]] and [[bicarbonate]] (HCO<sub>3</sub><sup>- </sup>) as shown in the reactions below~~. ~~The carbon dioxide - carbonic acid equilibrium~~ is ~~[[catalysis\|catalyzed]] by the [[enzyme]] [[carbonic anhydrase]]; the carbonic acid - bicarbonate equilibrium is simple proton dissociation/association and needs no catalyst.~~
	~~:<math>\rm CO_2 + H_2O \rightleftarrows H_2CO_3 \rightleftarrows HCO_3^- + H^+ </math>~~

	~~Any disturbance of the system will be compensated by~~ a ~~shift in the [[chemical equilibrium]] according to [[Le Chatelier's principle]]~~. For example, if one attempted to acidify the blood by dumping in an excess of hydrogen ions ([[acidemia]]), some of those hydrogen ions will associate with bicarbonate, forming carbonic acid, resulting in a smaller net increase of acidity than otherwise. This buffering system becomes an even more powerful regulator of acidity when it is coupled with the body's ~~capacity for [[respiratory compensation]],~~ in ~~which [[breathing]] is altered to modify the amount of CO<sub>2</sub> in circulation~~. In the above example, increased ventilation would increase the loss of CO<sub>2</sub> to the atmosphere, driving the equilibria above to the left. The process could continue until the excess acid is all [[exhalation\|exhaled]].

	~~This process is extremely important in the [[physiology]] of blood-having animals. It manages the many [[acid-base imbalance\|acid and base imbalances]] that can be produced by both normal~~ and ~~[[pathophysiology\|abnormal physiology]]. It also affects the handling of carbon dioxide, the constantly produced waste product of [[cellular respiration]].~~

	~~==Henderson–Hasselbalch equation==~~
	A modified version of the [[Henderson–Hasselbalch equation]] can be used to relate the pH of [[blood]] to constituents of the bicarbonate buffering system:<ref name=Bray1999>[http://books.google.com.my/books?id=qyHu0Iu-XOUC&pg=PA556 page 556], section "Estimating plasma pH" in: {{Cite book \| last1 = Bray \| first1 = John J. \| title = Lecture notes on human physiolog \| year = 1999 \| publisher = Blackwell Science \| location = Malden, Mass. \| isbn = 978-0-86542-775-4 \| pages = }}</ref>

	~~:<math> pH = pK_{a~H_2CO_3}+ \log \left ( \frac{[HCO_3^-]}{[H_2CO_3]} \right )</math>~~

	~~, where:~~
	*pK<sub>a H<sub>2</sub>CO<sub>3</sub></sub> is the negative logarithm (base 10) of the [[acid dissociation constant]] of [[carbonic acid]]. It is ~~equal to 6.1.~~
	*[HCO<sub>3</sub><sup>-</sup>] is the concentration of [[bicarbonate]] in the blood
	*[H<sub>2</sub>CO<sub>3</sub>] is the concentration of carbonic acid in the blood

	~~This is useful in [[arterial blood gas]],~~ but ~~these usually state~~ '~~'pCO~~<~~sub~~>2<~~/sub~~>~~'', that is, the [[partial pressure]] of [[carbon dioxide]], rather than H<sub>2</sub>CO<sub>3</sub>. However, these are related by the equation~~:~~<ref name=Bray1999/>~~

	:~~<math>~~ [~~H_2CO_3] = k_{\rm H~CO_2}\, \times pCO_2 </math>~~
	~~, where~~:
	*[H<sub>2</sub>CO<sub>3</sub>] is the concentration of carbonic acid in the blood
	*''k<sub>H CO<sub>2</~~sub><~~/~~sub>'' is a constant including the [[solubility]] of carbon dioxide in blood~~. ~~''k<sub>H CO<sub>2<~~/~~sub></sub>'' is approximately 0~~.~~03 ([[millimole\|mmol]]/[[Litre\|L]])/[[mmHg]]~~
	*''pCO<sub>2</sub>'' is the [[partial pressure]] of [[carbon dioxide]] in the blood

	~~Taken together, the following equation can be used to relate the pH of blood to the concentration of bicarbonate and the partial pressure of carbon dioxide:<ref name~~=~~Bray1999/>~~

	~~:<math> pH~~ = ~~6.1 + \log \left ( \frac{[HCO_3^-~~]~~}{0.03 \times pCO_2} \right~~ )~~</math>~~
	~~, where:~~
	*pH is the acidity in the blood
	*[HCO<sub>3</sub><sup>-</sup>] is the concentration of bicarbonate in the blood
	*''pCO<sub>2</sub>'' is the partial pressure of carbon dioxide in the blood

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

	~~==External links==~~
	* {{GeorgiaPhysiology\|7/7ch12/7ch12p17}}

	~~{{Renal physiology}}~~

	~~[[Category:Electrolyte disturbances]]~~
	~~[[Category:Buffers]]~~

en>David Eppstein: /* Books */ authorlink Marty Golubitsky

2014-01-20T05:03:45Z

Books: authorlink Marty Golubitsky

← Older revision		Revision as of 07:03, 20 January 2014
Line 1:		Line 1:
	[~~http://www~~.~~Consumerreports~~.~~org~~/~~cro~~/~~magazine~~/~~2014~~/04/~~extended~~-~~warranties~~-~~for-cars-are~~-an-~~expensive~~-~~game/ Royal Votaw~~] ~~is my title but I never truly liked~~ that ~~title~~. [http://~~blog~~.~~caranddriver~~.com/~~buying~~-~~peace~~-of-~~mind~~-~~how-to-buy~~-a-~~used-car-warranty/ extended~~] ~~car~~ [~~http~~://~~www~~.~~nurcac~~.~~org~~/~~UserProfile~~/~~tabid~~/43/~~userId~~/~~18128~~/~~Default~~.~~aspx extended auto warranty~~] ~~The car warranty thing I adore most flower arranging and now I have time to consider on new issues. The occupation I~~'~~ve been occupying for years~~ is a ~~bookkeeper but I~~'~~ve already utilized for another one~~. ~~Delaware has usually been my residing location and~~ [~~http:~~//~~www.elterninitiative-hanfmuehle.de/index.php?mod=users&action=view&id=47185 extended car warranty~~] ~~will by no means transfer.~~<br><br>~~Also visit my webpage~~ [~~http~~:/~~/Owenphelps~~.~~com~~/~~UserProfile~~/~~tabid~~/~~355~~/~~userId~~/~~172983~~/~~Default.aspx extended auto warranty~~]		{{refimprove\|date=October 2013}}
			The '''bicarbonate buffering system''' is an important [[buffer solution\|buffer]] system in the [[acid-base homeostasis]] of living things, including humans. As a buffer, it tends to maintain a relatively constant [[blood plasma\|plasma]] [[pH]] and counteract any force that would alter.
			In this system, [[carbon dioxide]] (CO<sub>2</sub>) combines with [[water]] to form [[carbonic acid]] (H<sub>2</sub>CO<sub>3</sub>), which in turn rapidly dissociates to form [[hydrogen ions]] and [[bicarbonate]] (HCO<sub>3</sub><sup>- </sup>) as shown in the reactions below. The carbon dioxide - carbonic acid equilibrium is [[catalysis\|catalyzed]] by the [[enzyme]] [[carbonic anhydrase]]; the carbonic acid - bicarbonate equilibrium is simple proton dissociation/association and needs no catalyst.
			:<math>\rm CO_2 + H_2O \rightleftarrows H_2CO_3 \rightleftarrows HCO_3^- + H^+ </math>

			Any disturbance of the system will be compensated by a shift in the [[chemical equilibrium]] according to [[Le Chatelier's principle]]. For example, if one attempted to acidify the blood by dumping in an excess of hydrogen ions ([[acidemia]]), some of those hydrogen ions will associate with bicarbonate, forming carbonic acid, resulting in a smaller net increase of acidity than otherwise. This buffering system becomes an even more powerful regulator of acidity when it is coupled with the body's capacity for [[respiratory compensation]], in which [[breathing]] is altered to modify the amount of CO<sub>2</sub> in circulation. In the above example, increased ventilation would increase the loss of CO<sub>2</sub> to the atmosphere, driving the equilibria above to the left. The process could continue until the excess acid is all [[exhalation\|exhaled]].

			This process is extremely important in the [[physiology]] of blood-having animals. It manages the many [[acid-base imbalance\|acid and base imbalances]] that can be produced by both normal and [[pathophysiology\|abnormal physiology]]. It also affects the handling of carbon dioxide, the constantly produced waste product of [[cellular respiration]].

			==Henderson–Hasselbalch equation==
			A modified version of the [[Henderson–Hasselbalch equation]] can be used to relate the pH of [[blood]] to constituents of the bicarbonate buffering system:<ref name=Bray1999>[http://books.google.com.my/books?id=qyHu0Iu-XOUC&pg=PA556 page 556], section "Estimating plasma pH" in: {{Cite book \| last1 = Bray \| first1 = John J. \| title = Lecture notes on human physiolog \| year = 1999 \| publisher = Blackwell Science \| location = Malden, Mass. \| isbn = 978-0-86542-775-4 \| pages = }}</ref>

			:<math> pH = pK_{a~H_2CO_3}+ \log \left ( \frac{[HCO_3^-]}{[H_2CO_3]} \right )</math>

			, where:
			*pK<sub>a H<sub>2</sub>CO<sub>3</sub></sub> is the negative logarithm (base 10) of the [[acid dissociation constant]] of [[carbonic acid]]. It is equal to 6.1.
			*[HCO<sub>3</sub><sup>-</sup>] is the concentration of [[bicarbonate]] in the blood
			*[H<sub>2</sub>CO<sub>3</sub>] is the concentration of carbonic acid in the blood

			This is useful in [[arterial blood gas]], but these usually state ''pCO<sub>2</sub>'', that is, the [[partial pressure]] of [[carbon dioxide]], rather than H<sub>2</sub>CO<sub>3</sub>. However, these are related by the equation:<ref name=Bray1999/>

			:<math> [H_2CO_3] = k_{\rm H~CO_2}\, \times pCO_2 </math>
			, where:
			*[H<sub>2</sub>CO<sub>3</sub>] is the concentration of carbonic acid in the blood
			*''k<sub>H CO<sub>2</sub></sub>'' is a constant including the [[solubility]] of carbon dioxide in blood. ''k<sub>H CO<sub>2</sub></sub>'' is approximately 0.03 ([[millimole\|mmol]]/[[Litre\|L]])/[[mmHg]]
			*''pCO<sub>2</sub>'' is the [[partial pressure]] of [[carbon dioxide]] in the blood

			Taken together, the following equation can be used to relate the pH of blood to the concentration of bicarbonate and the partial pressure of carbon dioxide:<ref name=Bray1999/>

			:<math> pH = 6.1 + \log \left ( \frac{[HCO_3^-]}{0.03 \times pCO_2} \right )</math>
			, where:
			*pH is the acidity in the blood
			*[HCO<sub>3</sub><sup>-</sup>] is the concentration of bicarbonate in the blood
			*''pCO<sub>2</sub>'' is the partial pressure of carbon dioxide in the blood

			==References==
			{{reflist}}

			==External links==
			* {{GeorgiaPhysiology\|7/7ch12/7ch12p17}}

			{{Renal physiology}}

			[[Category:Electrolyte disturbances]]
			[[Category:Buffers]]

en>Carlos.felippa: Corrected the priority for discovery and publication of arclength continuation methods.

2012-04-11T17:11:30Z

Corrected the priority for discovery and publication of arclength continuation methods.

New page

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