Musical tuning - Revision history

24.131.80.54: improve

2014-12-27T02:30:56Z

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← Older revision		Revision as of 04:30, 27 December 2014
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en>Saxophilist: /* Tuning practice */

2014-02-06T18:14:26Z

Tuning practice

← Older revision		Revision as of 20:14, 6 February 2014
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	~~In [[Boolean logic]], the '''majority function''' (also called the '''median operator''') is a [[function (mathematics)\|function]] from ''n'' inputs to one output~~. The ~~value of the operation~~ is ~~false~~ when ~~''n''/2 or more arguments are false, and true otherwise.~~		Greetings. The writer's name is Phebe and she home std test kit feels comfortable when individuals use the full name. My working day occupation is a [http://stdcrabsstd.com/ librarian]. One of the things she loves most is to do aerobics and now she is trying to earn cash with it. Her spouse and her live in Puerto Rico but she will have to move one day or an over the counter std test additional.<br><br>Visit my web site :: [http://mediabooked.com/index.php?do=/blog/35109/useful-guidance-for-battling-your-candidiasis/ mediabooked.com]
	~~Alternatively, representing true values as 1 and false values as 0, we may~~ use the ~~formula~~

	:~~<math>\operatorname{Majority} \left ( p_1,\dots,p_n \right ) = \left \lfloor \frac{1}{2} + \frac{\left(\sum_{i=1}^n p_i\right) - 1~~/~~2}{n} \right \rfloor. <~~/~~math>~~

	~~The "−1/2" in the formula serves to break ties in favor of zeros when ''n'' is even~~. ~~If the term "−1~~/~~2" is omitted, the formula can be used for a function that breaks ties in favor of ones.~~

	~~== Boolean circuits ==~~
	~~A ''majority gate'' is a [[logical gate]] used in [[circuit complexity]] and other applications of [[Boolean circuits]~~]. ~~A majority gate returns true if and only if more than 50%~~ of ~~its inputs are true.~~

	~~For instance, in a [[Adder (electronics)\|full adder]],~~ the ~~carry output~~ is ~~found by applying a majority function~~ to ~~the three inputs, although frequently this part of the adder~~ is ~~broken down into several simpler logical gates~~.

	~~A major result~~ in ~~[[circuit complexity]] asserts that the majority function cannot be computed by [[AC0\|AC0 circuits]] of subexponential size.~~

	~~== Monotone formulae for majority ==~~

	~~For ''n'' = 1 the median operator is just the unary identity operation ''x''.~~ ~~For ''n'' = 3~~ the ~~ternary median operator can be expressed using conjunction and disjunction as ''xy'' + ''yz'' + ''zx''~~. ~~Remarkably this expression denotes the same operation independently of whether the symbol + is interpreted as [[disjunction\|inclusive or]] or [[exclusive or]].~~

	~~For an arbitrary ''n'' there exists a monotone formula for majority of size O(''n''~~<~~sup~~>~~5.3~~<~~/sup~~>~~) {{harv\|Valiant\|1984}}. This is proved using~~ [[probabilistic method]]. Thus, this formula is non-constructive. However, one can obtain an explicit formula for majority of polynomial size using a [[sorting network]] of [[Miklós Ajtai\|Ajtai]], [[János Komlós (mathematician)\|Komlós]], and [[Endre Szemerédi\|Szemerédi]].

	~~== Properties ==~~

	~~Among the properties of the ternary median operator < x,y,z > are~~:
	~~# < x,y,y > = y~~
	~~# < x,y,z > = < z,x,y >~~
	~~# < x,y,z > = < x,z,y >~~
	~~# < < x,w,y >, w,z > = < x,w, < y,w,z > >~~

	~~An abstract system satisfying these as axioms is a [[median algebra]]~~.

	~~==References==~~
	*{{Cite journal
	~~\| first = L~~. ~~\| last~~ = ~~Valiant \| authorlink = Leslie Valiant~~
	~~\| title = Short monotone formulae for the majority function~~
	~~\| journal = Journal of Algorithms~~
	~~\| volume = 5~~
	~~\| issue = 3 \| year = 1984 \| pages = 363–366~~
	~~\| doi = 10.1016~~/~~0196~~-~~6774(84)90016~~-6
	~~\| ref = harv~~
	~~\| postscript = <!~~--~~None~~-~~->}}.~~
	* {{cite book \| last=Knuth \| first=Donald E. \| authorlink=Donald Knuth \| title=Introduction to combinatorial algorithms and Boolean functions \| series=[[The Art of Computer Programming]] \| volume=4a \| year=2008 \| isbn=0-321-53496-4 \| pages=64–74 \| publisher=Addison-Wesley \| location=Upper Saddle River, NJ }}

	~~==See also==~~
	~~{{Commonscat-inline\|Majority functions}}~~
	* [[Boolean algebra (structure)]]
	* [[Boolean algebras canonically defined]]
	* [[Majority problem (cellular automaton)]]

	~~[[Category:Logic gates]]~~
	~~[[Category:Circuit complexity]]~~
	~~[[Category:Boolean algebra]~~]

en>Hyacinth: /* Further reading */ {{Music theory}}

2014-01-07T16:23:39Z

Further reading: {{Music theory}}

← Older revision		Revision as of 18:23, 7 January 2014
Line 1:		Line 1:
	~~Trading in Web search giant Google was ceased following~~ the ~~company mistakenly produced~~ a ~~disappointing earnings report about four hours before schedule on Thursday~~ (~~October 18, 2012~~). ~~Google swiftly charged~~ the ~~blunder on its economic printer~~, ~~R.R. Donnelley & Sons Co~~. and ~~then released~~ the ~~state statement about three hours after the triggerfinger one.~~<br><br>~~Make sure~~ to ~~have lots~~ of ~~items onhand to provide away, also, if you~~'~~re setting up a booth at a tradeshow~~. ~~You will would like to get your [http:~~/~~/www.advertisingservicesguide.com/ Ad Agency] solution out to as many people as possible so that your name will~~ be ~~observed with~~ a ~~vast audience~~. ~~Share your products~~ in ~~mailings~~ and ~~fliers,~~ and ~~with any deals you mail out~~. ~~It's often good to send out~~ a ~~reminder of~~ the ~~organization, despite having an item, to keep your name out there.<br><br><br><br>Positioned In~~ a ~~filthy fraction next~~ to the ~~Old City's Blue Mosque~~, ~~Ka Firushi Chicken market~~ is ~~really accustomed to bird-owners~~. ~~In smaller open-fronted shops, budgerigars, bulbuls, canaries and other songbirds are sold~~ by ~~shopkeepers~~.~~<br><br>Sporting lots of make-up~~ and ~~dressed in~~ the ~~most beautiful clothes and jewelry, thousands~~ of ~~teen-age Gypsy females in Roma were associated with their parents to arrive at~~ an ~~open-air woman marketplace so that you can appear for Mr. Right who is prepared to spend~~ a ~~large amount of cash~~ for ~~his future partner. Since The purchase~~ of ~~items, a new woman~~'~~s value around several thousand pounds.~~<br><br>~~The Witches' Market~~ is ~~one of many oddest markets in South Usa~~. ~~The marketplace~~ is ~~within the previous quarter of La Paz~~. ~~It's truly become~~ an ~~attraction~~ for ~~interested travelers~~, ~~selling everything from llama fetuses~~, ~~dry frogs to countless amulets~~ and ~~products~~.~~<br><br>The Witches' Market is one~~ of the ~~oddest markets in South Usa~~. ~~The marketplace is in~~ the ~~previous quarter~~ of ~~La Paz. It has undoubtedly become an attraction for interested visitors, selling everything from llama fetuses, dried frogs to countless amulets and creams~~.<br>~~<br>Nobody has to examine a promotional site prepared for that item~~. ~~Nobody is forced or compelled~~ to ~~review the whole information. All~~-~~one must do is click and click properly. That will suffice for your matter. Cash could be made~~, ~~provided the plan is established with logic, strategy and some thinking.~~		In [[Boolean logic]], the '''majority function''' (also called the '''median operator''') is a [[function (mathematics)\|function]] from ''n'' inputs to one output. The value of the operation is false when ''n''/2 or more arguments are false, and true otherwise.
			Alternatively, representing true values as 1 and false values as 0, we may use the formula

			:<math>\operatorname{Majority} \left ( p_1,\dots,p_n \right ) = \left \lfloor \frac{1}{2} + \frac{\left(\sum_{i=1}^n p_i\right) - 1/2}{n} \right \rfloor. </math>

			The "−1/2" in the formula serves to break ties in favor of zeros when ''n'' is even. If the term "−1/2" is omitted, the formula can be used for a function that breaks ties in favor of ones.

			== Boolean circuits ==
			A ''majority gate'' is a [[logical gate]] used in [[circuit complexity]] and other applications of [[Boolean circuits]]. A majority gate returns true if and only if more than 50% of its inputs are true.

			For instance, in a [[Adder (electronics)\|full adder]], the carry output is found by applying a majority function to the three inputs, although frequently this part of the adder is broken down into several simpler logical gates.

			A major result in [[circuit complexity]] asserts that the majority function cannot be computed by [[AC0\|AC0 circuits]] of subexponential size.

			== Monotone formulae for majority ==

			For ''n'' = 1 the median operator is just the unary identity operation ''x''. For ''n'' = 3 the ternary median operator can be expressed using conjunction and disjunction as ''xy'' + ''yz'' + ''zx''. Remarkably this expression denotes the same operation independently of whether the symbol + is interpreted as [[disjunction\|inclusive or]] or [[exclusive or]].

			For an arbitrary ''n'' there exists a monotone formula for majority of size O(''n''<sup>5.3</sup>) {{harv\|Valiant\|1984}}. This is proved using [[probabilistic method]]. Thus, this formula is non-constructive. However, one can obtain an explicit formula for majority of polynomial size using a [[sorting network]] of [[Miklós Ajtai\|Ajtai]], [[János Komlós (mathematician)\|Komlós]], and [[Endre Szemerédi\|Szemerédi]].

			== Properties ==

			Among the properties of the ternary median operator < x,y,z > are:
			# < x,y,y > = y
			# < x,y,z > = < z,x,y >
			# < x,y,z > = < x,z,y >
			# < < x,w,y >, w,z > = < x,w, < y,w,z > >

			An abstract system satisfying these as axioms is a [[median algebra]].

			==References==
			*{{Cite journal
			\| first = L. \| last = Valiant \| authorlink = Leslie Valiant
			\| title = Short monotone formulae for the majority function
			\| journal = Journal of Algorithms
			\| volume = 5
			\| issue = 3 \| year = 1984 \| pages = 363–366
			\| doi = 10.1016/0196-6774(84)90016-6
			\| ref = harv
			\| postscript = <!--None-->}}.
			* {{cite book \| last=Knuth \| first=Donald E. \| authorlink=Donald Knuth \| title=Introduction to combinatorial algorithms and Boolean functions \| series=[[The Art of Computer Programming]] \| volume=4a \| year=2008 \| isbn=0-321-53496-4 \| pages=64–74 \| publisher=Addison-Wesley \| location=Upper Saddle River, NJ }}

			==See also==
			{{Commonscat-inline\|Majority functions}}
			* [[Boolean algebra (structure)]]
			* [[Boolean algebras canonically defined]]
			* [[Majority problem (cellular automaton)]]

			[[Category:Logic gates]]
			[[Category:Circuit complexity]]
			[[Category:Boolean algebra]]

en>Robertinventor: /* Systems for the twelve-note chromatic scale */

2012-08-29T00:52:16Z

Systems for the twelve-note chromatic scale

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