Tonelli–Shanks algorithm - Revision history

en>Yobot: Removed invisible unicode characters + other fixes, removed: using AWB (10691)

2015-01-06T13:30:17Z

Removed invisible unicode characters + other fixes, removed: using AWB (10691)

← Older revision		Revision as of 15:30, 6 January 2015
Line 1:		Line 1:
	~~In [[statistics]],~~ the '''Fano factor''',<ref>{{Cite doi\|10.1103/PhysRev.72.26}}</ref> like the [[coefficient of variation]], is a measure of the [[statistical dispersion\|dispersion]] of a [[probability distribution]] of a [[Fano noise]]. It is ~~named after [[Ugo Fano]], an Italian American physicist~~.		Greetings! I am Marvella and I feel comfy when people use the complete title. North Dakota is our birth place. For years he's been operating as a receptionist. Doing ceramics is what her family and her enjoy.<br><br>Feel free to surf to my web-site - home std test, [http://www.uknewsx.com/what-you-want-to-do-when-confronted-with-candida-albicans/ Read More In this article],

	~~The Fano factor is defined~~ as

	~~:<math>F=\frac{\sigma_W^2}{\mu_W},</math>~~

	~~where <math>\sigma_W^2</math> is the variance and <math>\mu_W</math> is the mean of~~ a ~~[[random process]] in some time window <math>W</math>~~. ~~The Fano factor can be viewed as a kind of noise-to-signal ratio; it~~ is ~~a measure of the reliability with which the [[random variable]] could be estimated from a time window that on average contains several [[random event]]s~~.

	~~For a [[Poisson process]], the variance in the count equals the mean count, so~~ <~~math~~> ~~F=1~~ <~~/math~~> ~~(normalization).~~

	~~If the time window is chosen~~ to ~~be infinity, the Fano factor is similar~~ to ~~the [[variance~~-to-~~mean ratio]] (VMR) which in [[statistics]] is also known as the [[Index of dispersion]].~~

	~~In [[Particle detector\| particle detectors]]~~, the Fano Factor results from the energy loss in a collision not being purely statistical. The process giving rise to each individual charge carrier is not independent as the number of ways an atom may be ionized is limited by the discrete electron shells. The net result is a better energy resolution than predicted by purely statistical considerations. For example, if <math>w\,</math> is the average energy for a particle to produce a charge carrier in a detector, then the [[Full width at half maximum\|FWHM]] resolution for measuring the particle energy <math>E</math> is:<ref name=Leo>{{Cite book \|title=Techniques for Nuclear and Particle Physics Experiments: An How-to Approach \|first=W.R. \|last=Leo \|year=1987 \|isbn=3-540-17386-2 \|publisher=Springer-Verlag \|pages=109–125}}</ref>
	:~~<math> R = 2.35 \sqrt{\frac{F w}{E}}, <~~/~~math>~~
	~~where the factor of 2.35 relates the standard deviation to the FWHM.~~

	~~The Fano factor is material specific. Some theoretical values are:<ref>{{Cite doi\|10.1103~~/~~PhysRevB~~.22.~~5565}}<~~/~~ref>~~
	~~:{\|~~
	\|-
	~~\| Si: \|\| 0.115~~
	\|-
	~~\| Ge: \|\| 0.13~~
	\|-
	~~\|GaAs: \|\| 0.10~~
	\|-
	~~\|Diamond: \|\| 0.08~~
	\|}

	~~Measuring the Fano factor is difficult because many factors contribute~~ to ~~the resolution, but some experimental values are:~~
	~~:{\|~~
	\|-
	~~\| Ar (gas): \|\| 0.20 ± 0.01/0.02<ref>{{Cite doi\|10.1016/0168~~-~~9002(84)90139~~-~~6}}</ref>~~
	\|-
	~~\| Xe (gas): \|\| 0.13 to 0.29<ref>{{Cite doi\|10.1109/TNS.2008.2003075}}</ref>~~
	\|-
	\| [[Cadmium zinc telluride \|CZT]]: \|\| 0.089±0.005<ref>{{cite web\|last=Redus\|first=R. H.\|title=Fano Factor Determination For CZT\|work=MRS Proceedings\|coauthors=Pantazis, J. A.; Huber, A. C.; Jordanov, V. T.; Butler, J. F.; Apotovsky, B.\|doi=10.1557/PROC-~~487-101\|date=NaN undefined NaN}}<~~/~~ref>~~
	\|}

	~~==See also==~~
	* [[Fano noise]]
	* [[Index of dispersion]] – equivalent to the Fano factor for an infinite time window
	* [[Ugo Fano]]
	~~==References==~~
	~~{{reflist}}~~

	~~[[Category:Statistical deviation and dispersion]]~~
	~~[[Category:Statistical ratios]~~]

72.37.171.164: Added a link to Dickson's History of the theory of numbers

2013-08-16T17:04:04Z

Added a link to Dickson's History of the theory of numbers

← Older revision		Revision as of 19:04, 16 August 2013
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	~~Hello and welcome~~. ~~My title~~ is ~~Figures Wunder~~. ~~My day occupation~~ is a ~~meter reader~~. ~~One~~ of the ~~extremely best things~~ in the ~~world for me~~ is to ~~do aerobics and now I'm attempting~~ to ~~earn money with it~~. For ~~many years he's been residing~~ in ~~North Dakota~~ and ~~his family enjoys it~~.<br><br>~~my page; [http~~://~~www~~.~~alhuloul~~.~~com~~/~~?p=235037 http~~://~~www~~.~~alhuloul~~.~~com~~/?p=~~235037~~]		In [[statistics]], the '''Fano factor''',<ref>{{Cite doi\|10.1103/PhysRev.72.26}}</ref> like the [[coefficient of variation]], is a measure of the [[statistical dispersion\|dispersion]] of a [[probability distribution]] of a [[Fano noise]]. It is named after [[Ugo Fano]], an Italian American physicist.

			The Fano factor is defined as

			:<math>F=\frac{\sigma_W^2}{\mu_W},</math>

			where <math>\sigma_W^2</math> is the variance and <math>\mu_W</math> is the mean of a [[random process]] in some time window <math>W</math>. The Fano factor can be viewed as a kind of noise-to-signal ratio; it is a measure of the reliability with which the [[random variable]] could be estimated from a time window that on average contains several [[random event]]s.

			For a [[Poisson process]], the variance in the count equals the mean count, so <math> F=1 </math> (normalization).

			If the time window is chosen to be infinity, the Fano factor is similar to the [[variance-to-mean ratio]] (VMR) which in [[statistics]] is also known as the [[Index of dispersion]].

			In [[Particle detector\| particle detectors]], the Fano Factor results from the energy loss in a collision not being purely statistical. The process giving rise to each individual charge carrier is not independent as the number of ways an atom may be ionized is limited by the discrete electron shells. The net result is a better energy resolution than predicted by purely statistical considerations. For example, if <math>w\,</math> is the average energy for a particle to produce a charge carrier in a detector, then the [[Full width at half maximum\|FWHM]] resolution for measuring the particle energy <math>E</math> is:<ref name=Leo>{{Cite book \|title=Techniques for Nuclear and Particle Physics Experiments: An How-to Approach \|first=W.R. \|last=Leo \|year=1987 \|isbn=3-540-17386-2 \|publisher=Springer-Verlag \|pages=109–125}}</ref>
			:<math> R = 2.35 \sqrt{\frac{F w}{E}}, </math>
			where the factor of 2.35 relates the standard deviation to the FWHM.

			The Fano factor is material specific. Some theoretical values are:<ref>{{Cite doi\|10.1103/PhysRevB.22.5565}}</ref>
			:{\|
			\|-
			\| Si: \|\| 0.115
			\|-
			\| Ge: \|\| 0.13
			\|-
			\|GaAs: \|\| 0.10
			\|-
			\|Diamond: \|\| 0.08
			\|}

			Measuring the Fano factor is difficult because many factors contribute to the resolution, but some experimental values are:
			:{\|
			\|-
			\| Ar (gas): \|\| 0.20 ± 0.01/0.02<ref>{{Cite doi\|10.1016/0168-9002(84)90139-6}}</ref>
			\|-
			\| Xe (gas): \|\| 0.13 to 0.29<ref>{{Cite doi\|10.1109/TNS.2008.2003075}}</ref>
			\|-
			\| [[Cadmium zinc telluride \|CZT]]: \|\| 0.089±0.005<ref>{{cite web\|last=Redus\|first=R. H.\|title=Fano Factor Determination For CZT\|work=MRS Proceedings\|coauthors=Pantazis, J. A.; Huber, A. C.; Jordanov, V. T.; Butler, J. F.; Apotovsky, B.\|doi=10.1557/PROC-487-101\|date=NaN undefined NaN}}</ref>
			\|}

			==See also==
			* [[Fano noise]]
			* [[Index of dispersion]] – equivalent to the Fano factor for an infinite time window
			* [[Ugo Fano]]
			==References==
			{{reflist}}

			[[Category:Statistical deviation and dispersion]]
			[[Category:Statistical ratios]]

188.163.238.74: /* Speed of the algorithm */

2012-02-14T16:03:03Z

Speed of the algorithm

New page

Hello and welcome. My title is Figures Wunder. My day occupation is a meter reader. One of the extremely best things in the world for me is to do aerobics and now I'm attempting to earn money with it. For many years he's been residing in North Dakota and his family enjoys it.<br><br>my page; [http://www.alhuloul.com/?p=235037 http://www.alhuloul.com/?p=235037]

Tonelli–Shanks algorithm - Revision history

en>Yobot: Removed invisible unicode characters + other fixes, removed: ­ using AWB (10691)

72.37.171.164: Added a link to Dickson's History of the theory of numbers

188.163.238.74: /* Speed of the algorithm */

en>Yobot: Removed invisible unicode characters + other fixes, removed: using AWB (10691)