Polynomial arithmetic - Revision history

en>FrescoBot: Bot: link syntax

2014-05-18T07:25:21Z

← Older revision		Revision as of 09:25, 18 May 2014
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	In [~~[chemistry]~~]~~, the '''mass fraction''' <math>w_i</math>~~ is the ~~ratio~~ of ~~one substance with mass <math>m_i</math>~~ to the ~~mass of the total mixture <math>m_{tot}~~<~~/math~~>~~, defined as~~<~~ref>{{GoldBookRef \| file = M03722 \| title = mass fraction}}</ref~~>		Surely the second option would be more beneficial for any website. If you liked this information and you would certainly like to receive more facts regarding [http://www.buagaga.com/profile/dippv.html wordpress backup] kindly check out our internet site. The next step is to visit your Word - Press blog dashboard. These templates are professionally designed and are also Adsense ready. s ultimately easy to implement and virtually maintenance free. Also our developers are well convergent with the latest technologies and bitty-gritty of wordpress website design and promises to deliver you the best solution that you can ever have. <br><br>

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	~~The sum~~ of ~~all~~ the ~~mass fractions~~ is ~~equal~~ to 1:

	~~:<math>\sum_{i=1}^{N} m_i = m_{tot} ; \sum_{i=1}^{N} w_i = 1</math>~~

	~~Mass fraction is one way~~ of ~~expressing~~ the ~~composition of~~ a ~~mixture~~ in ~~a dimensionless size ([[mole fraction]] is another).~~

	~~For [[elemental analysis]]~~, ~~mass fraction (or "mass percent composition")~~ can ~~also refer to~~ the ~~ratio~~ of the ~~mass of one element to~~ the ~~total mass of a compound. It can be calculated for any compound using its [[empirical formula]]~~.<~~ref~~>~~[http://khanexercises.appspot.com/video?v=xatVrAh2U0E Formula from Mass Composition]~~<~~/ref~~> ~~or its [[chemical formula]]<ref>[http://chemistry.about.com/od/workedchemistryproblems/~~a~~/mass-percent-worked-problem.htm]</ref>~~

	~~==Terminology==~~
	~~"Percent concentration" does not refer~~ to ~~this quantity. This improper name persists, especially~~ in ~~elementary textbooks~~. ~~In biology~~, ~~the unit "%"~~ is ~~sometimes (incorrectly) used~~ to ~~denote mass concentration, also called "mass/volume percentage~~.~~" A solution with 1 g of solute dissolved in~~ a ~~final volume~~ of ~~100 mL of solution would be labeled as "1 %" or "1 % m/v" (mass/volume)~~. ~~The notation is mathematically flawed because~~ the ~~unit "%"~~ can ~~only~~ be ~~used for dimensionless quantities~~. ~~"Percent~~ solution" or ~~"percentage solution" are thus terms best reserved for "mass percent solutions" (m/m = m% = mass solute/mass total solution after mixing)~~, ~~or "volume percent solutions" (v/v = v% = volume solute per volume of total solution after mixing)~~. ~~The very ambiguous terms "percent solution"~~ and ~~"percentage solutions" with no other qualifiers continue~~ to ~~occasionally be encountered.~~

	~~In [[thermal engineering]] '''[[vapor quality]]''' is used for the mass fraction of vapor in the steam~~.

	~~In alloys~~, ~~especially those of noble metals~~, ~~the term '''[[fineness]]''' is used for the mass fraction of the noble metal~~ in ~~the alloy~~.

	~~==Properties==~~
	~~The mass fraction is independent of temperature~~.

	~~==Related quantities==~~
	~~===Mass concentration===~~
	The ~~mass fraction of a component in a solution~~ is ~~the ratio of the [[mass concentration (chemistry)\|mass concentration]] of that component <math>\rho_i</math> (density of that component~~ in ~~the mixture) to the [[density]]~~ of ~~solution <math>\rho</math>~~.

	:<~~math~~>~~w_i = \frac {\rho_i}{\rho}~~<~~/math~~>

	~~===Molar concentration===~~
	~~The relation to molar concentration is like that from above substituting the relation between mass and molar concentration.~~

	~~:<math~~>~~w_i = \frac {\rho_i}{\rho}=\frac {c_i M_i}{\rho}</math>~~

	~~===Mass percentage===~~

	~~Multiplying mass fraction by 100 gives the mass percentage. It is sometimes called weight percent (wt%)~~ or ~~weight-weight percentage. However~~, ~~since~~
	~~mass~~ and ~~weight are different quantities~~, ~~this is incorrect (see [[mass versus weight]] for details)~~.

	~~===Mole fraction===~~
	~~The [[mole fraction]] <math>x_i</math>~~ can ~~be calculated using the formula~~

	~~:<math>x_i = w_i \cdot \frac {M}{M_i}</math>~~

	~~where <math>M_i</math> is the molar mass of the component <math>i</math>~~ and ~~<math>M</math> is~~ the ~~average [[molar mass]]~~ of the ~~mixture.~~

	~~Replacing~~ the ~~expression~~ of ~~the molar mass produces:~~

	~~: <math>x_i = \frac {\frac{w_i}{M_i}}{\sum_i \frac{w_i}{M_i}}</math>~~

	~~==Spatial variation~~ and ~~gradient==~~

	~~In a [[inhomogeneous\|spatially non-uniform]] mixture~~, the ~~mass fraction [[gradient]] triggers~~ the ~~phenomenon of [[diffusion]]~~.

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

	~~{{Chemical solutions}}~~

	~~<!--Categories-->~~
	~~[[Category:Chemical properties]]~~
	~~[[Category:Dimensionless numbers of chemistry]]~~

en>Fab8275: addition of a paragraph about prime polynomials and related theorems

2014-01-25T17:10:17Z

addition of a paragraph about prime polynomials and related theorems

← Older revision		Revision as of 19:10, 25 January 2014
Line 1:		Line 1:
	My name is ~~Connie~~ (~~37 years old~~) ~~and my hobbies~~ are ~~Crocheting~~ and ~~Bboying~~.<br><br>~~Here~~ is ~~my web page~~ ... [~~http~~://~~www~~.~~buagaga.com~~/~~profile/dippv~~.~~html wordpress backup~~]		In [[chemistry]], the '''mass fraction''' <math>w_i</math> is the ratio of one substance with mass <math>m_i</math> to the mass of the total mixture <math>m_{tot}</math>, defined as<ref>{{GoldBookRef \| file = M03722 \| title = mass fraction}}</ref>

			:<math>w_i = \frac {m_i}{m_{tot}}</math>

			The sum of all the mass fractions is equal to 1:

			:<math>\sum_{i=1}^{N} m_i = m_{tot} ; \sum_{i=1}^{N} w_i = 1</math>

			Mass fraction is one way of expressing the composition of a mixture in a dimensionless size ([[mole fraction]] is another).

			For [[elemental analysis]], mass fraction (or "mass percent composition") can also refer to the ratio of the mass of one element to the total mass of a compound. It can be calculated for any compound using its [[empirical formula]].<ref>[http://khanexercises.appspot.com/video?v=xatVrAh2U0E Formula from Mass Composition]</ref> or its [[chemical formula]]<ref>[http://chemistry.about.com/od/workedchemistryproblems/a/mass-percent-worked-problem.htm]</ref>

			==Terminology==
			"Percent concentration" does not refer to this quantity. This improper name persists, especially in elementary textbooks. In biology, the unit "%" is sometimes (incorrectly) used to denote mass concentration, also called "mass/volume percentage." A solution with 1 g of solute dissolved in a final volume of 100 mL of solution would be labeled as "1 %" or "1 % m/v" (mass/volume). The notation is mathematically flawed because the unit "%" can only be used for dimensionless quantities. "Percent solution" or "percentage solution" are thus terms best reserved for "mass percent solutions" (m/m = m% = mass solute/mass total solution after mixing), or "volume percent solutions" (v/v = v% = volume solute per volume of total solution after mixing). The very ambiguous terms "percent solution" and "percentage solutions" with no other qualifiers continue to occasionally be encountered.

			In [[thermal engineering]] '''[[vapor quality]]''' is used for the mass fraction of vapor in the steam.

			In alloys, especially those of noble metals, the term '''[[fineness]]''' is used for the mass fraction of the noble metal in the alloy.

			==Properties==
			The mass fraction is independent of temperature.

			==Related quantities==
			===Mass concentration===
			The mass fraction of a component in a solution is the ratio of the [[mass concentration (chemistry)\|mass concentration]] of that component <math>\rho_i</math> (density of that component in the mixture) to the [[density]] of solution <math>\rho</math>.

			:<math>w_i = \frac {\rho_i}{\rho}</math>

			===Molar concentration===
			The relation to molar concentration is like that from above substituting the relation between mass and molar concentration.

			:<math>w_i = \frac {\rho_i}{\rho}=\frac {c_i M_i}{\rho}</math>

			===Mass percentage===

			Multiplying mass fraction by 100 gives the mass percentage. It is sometimes called weight percent (wt%) or weight-weight percentage. However, since
			mass and weight are different quantities, this is incorrect (see [[mass versus weight]] for details).

			===Mole fraction===
			The [[mole fraction]] <math>x_i</math> can be calculated using the formula

			:<math>x_i = w_i \cdot \frac {M}{M_i}</math>

			where <math>M_i</math> is the molar mass of the component <math>i</math> and <math>M</math> is the average [[molar mass]] of the mixture.

			Replacing the expression of the molar mass produces:

			: <math>x_i = \frac {\frac{w_i}{M_i}}{\sum_i \frac{w_i}{M_i}}</math>

			==Spatial variation and gradient==

			In a [[inhomogeneous\|spatially non-uniform]] mixture, the mass fraction [[gradient]] triggers the phenomenon of [[diffusion]].

			==References==
			{{reflist}}

			{{Chemical solutions}}

			<!--Categories-->
			[[Category:Chemical properties]]
			[[Category:Dimensionless numbers of chemistry]]

en>Pemboid: Link to Polynomial long division

2012-07-03T07:46:53Z

Link to Polynomial long division

New page

My name is Connie (37 years old) and my hobbies are Crocheting and Bboying.<br><br>Here is my web page ... [http://www.buagaga.com/profile/dippv.html wordpress backup]