Color triangle - Revision history

en>Monkbot: Task 3: Fix CS1 deprecated coauthor parameter errors

2014-05-06T23:30:02Z

Task 3: Fix CS1 deprecated coauthor parameter errors

← Older revision		Revision as of 01:30, 7 May 2014
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	~~'''Gy's sampling theory''' is a [[scientific theory\|theory]] about the sampling of materials, developed by [[Pierre Gy]]~~ from ~~the 1950s to beginning 2000s<ref name="Gy2004"> Gy, P (2004), Chemometrics and Intelligent Laboratory Systems, 74, 61-70~~.~~</ref> in articles and books including:~~		I am Zachary from Kahl. I am learning to play the Dobro. Other hobbies are Leaf collecting and pressing.<br><br>Also visit my site :: [http://www.spellenaanbod.nl/profile/lofryar wordpress dropbox backup]

	*(1960) Sampling nomogram
	*(1979) Sampling of particulate materials; theory and practice
	*(1982) Sampling of particulate materials; theory and practice; 2nd edition
	*(1992) Sampling of [[Heterogeneous]] and Dynamic Material Systems: Theories of Heterogeneity, Sampling and Homogenizing
	*(1998) Sampling for Analytical Purposes

	~~The abbreviation "TOS" is also used~~ to denote Gy's sampling theory.<ref name="Esbensen">K.H. Esbensen. 50 years of Pierre Gy's “Theory of Sampling”—WCSB1: a tribute. Chemometrics and Intelligent Laboratory Systems. Volume 74, Issue 1, 28 November 2004, pages 3–6.</ref>

	Gy's sampling theory uses a [[scientific model\|model]] in which the sample taking is represented by [[statistical independence\|independent]] [[Bernoulli trials]] for every particle in the parent population from which the ~~sample is drawn~~. ~~The two possible outcomes of each Bernoulli trial~~ are~~: (1) the particle is selected~~ and ~~(2) the particle is not selected. The probability of selecting a particle may be different during each Bernoulli trial. The model used by Gy is mathematically equivalent to [[Poisson sampling]]~~.<~~ref name="Geelhoed"~~>{{cite journal \|first=B. \|last=Geelhoed \|first2=H. J. \|last2=Glass \|title=Comparison of theories for the variance caused by the sampling of random mixtures of non-identical particles \|journal=Geostandards and Geoanalytical Research \|volume=28 \|issue=2 \|year=2004 \|pages=263–276 \|doi=10.1111/j.1751-908X.2004.tb00742.x }}<~~/ref~~> ~~Using this model, the following equation for the [[variance]] of the [[sampling error]] in the mass concentration in a sample was derived by Gy~~:

	:~~<math>V = \frac{1}{(\sum_{i=1}^N q_i m_i)^2} \sum_{i=1}^N q_i(1-q_i) m_{i}^{2} \left(a_i - \frac{\sum_{j=1}^N q_j a_j m_j}{\sum_{j=1}^N q_j m_j}\right)^2 .</math>~~

	in which ''V'' is the variance of the sampling error, ''N'' is the number of particles in the population (before the sample was taken), ''q''<sub> ''i''</sub> is the probability of including the ''i''th particle of the population in the sample (i.e. the [[first-order inclusion probability]] of the ''i''th particle), ''m''<sub> ''i''</sub> is the mass of the ''i''th particle of the population and ''a''<sub> ''i''</sub> is the mass concentration of the property of interest in the ''i''th particle of the population.

	~~It is noted that the above equation for the variance of the sampling error is an approximation based on a [[linearization]] of the mass concentration in a sample.~~

	In the theory of Gy, [[correct sampling]] is defined as a sampling scenario in which all particles have the same probability of being included in the sample. This implies that ''q''<sub> ''i''</sub> no longer depends on ''i'', and can therefore be replaced by the symbol ''q''. Gy's equation for the variance of the sampling error becomes:

	~~:<math>V = \frac{1-q}{q M_\text{batch}^2} \sum_{i=1}^N m_{i}^{2} \left(a_i - a_\text{batch} \right)^2 .</math>~~

	where ''a''<sub>batch</sub> is the concentration of the property of interest in the population from which the sample is to be drawn and ''M''<sub>batch</sub> is the mass of the population from which the sample is to be drawn. It has been noted that a similar equation had already been derived in 1935 by Kassel and Guy.<ref name="Kassel">{{cite journal \|last=Kassel \|first=L. S. \|last2=Guy \|first2=T. W. \|title=Determining the correct weight of sample in coal sampling \|journal=Industrial and Engineering Chemistry Analytical Edition \|year=1935 \|volume=7 \|issue=2 \|pages=112–115 \|doi= }}</ref><ref name="Cheng">{{cite journal \|last=Cheng \|first=H. \|last2=Geelhoed \|first2=B. \|last3=Bode \|first3=P. \|year=2011 \|title=A Markov Chain Monte Carlo comparison of variance estimators for the sampling of particulate mixtures \|journal=Applied Stochastic Models in Business and Industry \|volume= \|issue= \|pages= \|doi=10.1002/asmb.878 }}</ref>

	~~==Criticism on Gy's sampling theory==~~
	~~Recent experimental results and novel insights show that parts of Gy's theory need to be updated or revised.<ref name="Critique">~~http://www.~~vixra.org/abs/1203~~.~~0081<~~/ref> The main points of criticism are that Gy's theory fails to show that certain of its parts are in fact compatible with each other, that the theory relies sometimes on the use of [[Wiktionary:fudge factor\|fudge factors]], and that the theory is at various points in its presentation unnecessarily complex.<ref name="Critique"/>

	~~== See also ==~~
	*[[Statistical sampling]]

	~~== References ==~~
	~~{{Reflist}}~~

	~~{{DEFAULTSORT:Gy's Sampling Theory}}~~
	~~[[Category:Sampling (statistics)]~~]

en>Monkbot: Fix CS1 deprecated date parameter errors

2014-02-04T02:26:26Z

Fix CS1 deprecated date parameter errors

← Older revision		Revision as of 04:26, 4 February 2014
Line 1:		Line 1:
			'''Gy's sampling theory''' is a [[scientific theory\|theory]] about the sampling of materials, developed by [[Pierre Gy]] from the 1950s to beginning 2000s<ref name="Gy2004"> Gy, P (2004), Chemometrics and Intelligent Laboratory Systems, 74, 61-70.</ref> in articles and books including:

			*(1960) Sampling nomogram
			*(1979) Sampling of particulate materials; theory and practice
			*(1982) Sampling of particulate materials; theory and practice; 2nd edition
			*(1992) Sampling of [[Heterogeneous]] and Dynamic Material Systems: Theories of Heterogeneity, Sampling and Homogenizing
			*(1998) Sampling for Analytical Purposes

	~~In toԀay~~'s ~~nutritional universe~~, it is ~~recommended to come with an knowledge of just what~~ the ~~bodʏ demands to obtain probably tҺe most diet daily. A lot of this information~~ is ~~readily available for those eaǥer to find it~~. ~~Thе tips within the next number~~ of ~~sentеnces can help you crack throughout~~ the ~~deceitful advertising~~ and ~~marketing and comprehend which dіet are healthy and that haρpen tߋ bе~~ not.<br>~~<br>Buy your [http://Imgur~~.~~com/hot?q~~=~~protein protein] from variоus rеsources~~. ~~Health proteins comeѕ in greɑt shape you will enjoy~~. ~~As an example, try out eating beans, butѕ, soy ƿroducts, seafood,~~ and ~~much morе~~. ~~Numerouѕ can Ьe used as preservatives to ѕeveгal food or even the main dish~~. ~~Mіx up ƴour ɦealth proteins choices to continue to keep any diet program fascinating~~.<br>~~<br>You neеd to take in~~ the ~~suggestеd volume~~ of health proteins every singlе day. Prοtein retains and grows youг own muscles, body orցans, skin and blоod. In addition they help ѡith vitality metabolic ƿrocess and yоur mobile procеsses. Health proteins also provides the ~~body tҺe energy it must ѕhield~~ by ~~itself from disease. You ϲan get top quality proteins in cereаls, dairy products, seafood ɑnd fowl, meat, soy products items, legumes and beans.~~<br><br>~~Avoid ɑny meals who have a substantіal amount~~ of trans fat simply because food items who have trans excess fat are processed. Eɑting meals with trans fats is really a solution to establishing coronary disease. Trans saturated fats are terrible becauѕe they lessen your HDL degrees, the ~~great cholesterol levels~~, ~~and increase ʏoսr LDL levels, wɦicɦ~~ is the ~~bad cholesterol.~~<br><br>~~You have to be sure that your meals are giving you an adequate volume~~ of ~~selenium. Ѕelenium, a nutrient, can help buіld-up muscle гesilience, which means your epidermis age ranges more sloաly. 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Breakfast iѕ crucial since you are literally splitting~~ the ~~fɑst you have gone thгough all night, and your system needs nutrients and high quality foods allow it vitality whenever ƴօu awaken~~.<br><br>~~When you pսrchase wisely~~, ~~nut ρroducts really are a nutгitious additiоn to your diet~~. ~~Almonds ɑre a fantastic choice~~ for ~~taste, fіber, crսnchiness, and nutrients and vitamins.~~<br><br>~~Frosty, processed or fresh vegetables are reduϲed іn energy аnd therefore are~~ a good food items ϲhoice. These are рacked witҺ nutritional supplements that hеlp keep you healthier and pleased. Always consume a couƿle ρortions each day they аre often included with soups and salads!<br><br>~~When expecting a baby, giving up your prefeгred food items isn't requireԀ providing you set restrictions on what you eat. Consist~~ of ~~somе wholеsome vegetables or just a tiny amount~~ of ~~аlmonds to obtain your day-to-day sugary treat resolve. 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Go even furtheг and then add hot pepρers if you appreciate it warm~~.<br>~~<br>Do not imаgine thɑt using a great deal~~ of ~~vitamin supplements can make the food you eat more healthy. As his or heг labеl suggests, supplements~~ need to be utiliƶed to bolster a healthy ɗiet plan. It's Ƅetter tο go on a basic everyday multi-vitamin and concentгate on enhancing your overall diet regime rather than weight through to amazing supplements and assume incredible outcomes.<br><br>The ~~best way to bоost yoսr nutrients and incrеase your nutritional consumption is actually by adding juice into the dіet program. Orange liquid and apple company juice aren~~'~~t the only options, either. Yօu can also beverage carrot fruit juice, tomato fruit juice, beet liquid or wheat or ցrain grɑss juice. Drinks may be blended~~ to ~~improve the taste. Remember~~ that ~~no matter whɑt you put~~ in ~~tҺe juice extractor comes~~ with ~~nutrients~~ and ~~sߋ outstanding for~~ the ~~body~~.<br>~~<br>The idеas previoսѕly mentioned are dedicated to enhancing your diet, which in turn enables you to feel better about your self. Diet must be your everydaү oЬjective for the healthier lifе.~~		The abbreviation "TOS" is also used to denote Gy's sampling theory.<ref name="Esbensen">K.H. Esbensen. 50 years of Pierre Gy's “Theory of Sampling”—WCSB1: a tribute. Chemometrics and Intelligent Laboratory Systems. Volume 74, Issue 1, 28 November 2004, pages 3–6.</ref>

			Gy's sampling theory uses a [[scientific model\|model]] in which the sample taking is represented by [[statistical independence\|independent]] [[Bernoulli trials]] for every particle in the parent population from which the sample is drawn. The two possible outcomes of each Bernoulli trial are: (1) the particle is selected and (2) the particle is not selected. The probability of selecting a particle may be different during each Bernoulli trial. The model used by Gy is mathematically equivalent to [[Poisson sampling]].<ref name="Geelhoed">{{cite journal \|first=B. \|last=Geelhoed \|first2=H. J. \|last2=Glass \|title=Comparison of theories for the variance caused by the sampling of random mixtures of non-identical particles \|journal=Geostandards and Geoanalytical Research \|volume=28 \|issue=2 \|year=2004 \|pages=263–276 \|doi=10.1111/j.1751-908X.2004.tb00742.x }}</ref> Using this model, the following equation for the [[variance]] of the [[sampling error]] in the mass concentration in a sample was derived by Gy:

			:<math>V = \frac{1}{(\sum_{i=1}^N q_i m_i)^2} \sum_{i=1}^N q_i(1-q_i) m_{i}^{2} \left(a_i - \frac{\sum_{j=1}^N q_j a_j m_j}{\sum_{j=1}^N q_j m_j}\right)^2 .</math>

			in which ''V'' is the variance of the sampling error, ''N'' is the number of particles in the population (before the sample was taken), ''q''<sub> ''i''</sub> is the probability of including the ''i''th particle of the population in the sample (i.e. the [[first-order inclusion probability]] of the ''i''th particle), ''m''<sub> ''i''</sub> is the mass of the ''i''th particle of the population and ''a''<sub> ''i''</sub> is the mass concentration of the property of interest in the ''i''th particle of the population.

			It is noted that the above equation for the variance of the sampling error is an approximation based on a [[linearization]] of the mass concentration in a sample.

			In the theory of Gy, [[correct sampling]] is defined as a sampling scenario in which all particles have the same probability of being included in the sample. This implies that ''q''<sub> ''i''</sub> no longer depends on ''i'', and can therefore be replaced by the symbol ''q''. Gy's equation for the variance of the sampling error becomes:

			:<math>V = \frac{1-q}{q M_\text{batch}^2} \sum_{i=1}^N m_{i}^{2} \left(a_i - a_\text{batch} \right)^2 .</math>

			where ''a''<sub>batch</sub> is the concentration of the property of interest in the population from which the sample is to be drawn and ''M''<sub>batch</sub> is the mass of the population from which the sample is to be drawn. It has been noted that a similar equation had already been derived in 1935 by Kassel and Guy.<ref name="Kassel">{{cite journal \|last=Kassel \|first=L. S. \|last2=Guy \|first2=T. W. \|title=Determining the correct weight of sample in coal sampling \|journal=Industrial and Engineering Chemistry Analytical Edition \|year=1935 \|volume=7 \|issue=2 \|pages=112–115 \|doi= }}</ref><ref name="Cheng">{{cite journal \|last=Cheng \|first=H. \|last2=Geelhoed \|first2=B. \|last3=Bode \|first3=P. \|year=2011 \|title=A Markov Chain Monte Carlo comparison of variance estimators for the sampling of particulate mixtures \|journal=Applied Stochastic Models in Business and Industry \|volume= \|issue= \|pages= \|doi=10.1002/asmb.878 }}</ref>

			==Criticism on Gy's sampling theory==
			Recent experimental results and novel insights show that parts of Gy's theory need to be updated or revised.<ref name="Critique">http://www.vixra.org/abs/1203.0081</ref> The main points of criticism are that Gy's theory fails to show that certain of its parts are in fact compatible with each other, that the theory relies sometimes on the use of [[Wiktionary:fudge factor\|fudge factors]], and that the theory is at various points in its presentation unnecessarily complex.<ref name="Critique"/>

			== See also ==
			*[[Statistical sampling]]

			== References ==
			{{Reflist}}

			{{DEFAULTSORT:Gy's Sampling Theory}}
			[[Category:Sampling (statistics)]]

en>ZéroBot: r2.7.1) (Robot: Adding pl:Trójkąt Maxwella

2012-08-26T12:26:27Z

r2.7.1) (Robot: Adding pl:Trójkąt Maxwella

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