en>Yobot: WP:CHECKWIKI error fixes using AWB (10750)

2015-01-12T07:58:24Z

WP:CHECKWIKI error fixes using AWB (10750)

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en>NicatronTg: Reverted edits by 98.117.12.149 (talk): factual errors (HG)

2014-03-03T01:01:42Z

Reverted edits by 98.117.12.149 (talk): factual errors (HG)

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en>Daniel Mietchen: /* Behaviour and ecology */

2014-02-01T20:16:18Z

Behaviour and ecology

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{{Other uses}}
{{Use dmy dates|date=July 2012}}
{{SpecialChars}}
{{Wiktionary|Ω|ω}}
{{Greek Alphabet|letter=omega}}
'''Omega''' ([[capital letter|capital]]: '''Ω''', [[lower case|lowercase]]: '''ω'''; [[Ancient Greek|Greek]] Ωμέγα) is the 24th and last letter of the [[Greek alphabet]]. In the [[Greek numerals|Greek numeric system]], it has a value of 800. The word literally means "great O" (''ō mega'', mega meaning 'great'), as opposed to [[omicron]], which means "little O" (''o mikron'', micron meaning "little").<ref>[http://www.quinapalus.com/gr0.1.html The Greek Alphabet]</ref> This name is [[Medieval Greek|Byzantine]]; in [[Ancient Greek|Classical Greek]], the letter was called ''ō'' ({{lang|grc|ὦ}}), whereas the omicron was called ''ou'' ({{lang|grc|οὖ}}).<ref>Herbert Weir Smyth. ''A Greek Grammar for Colleges''. §1</ref> The form of the uppercase letter derives from that of an omicron (Ο) broken up at the side ([[File:Greek Omega 09.svg|x16px]]), with the edges subsequently turned outward ([[File:Greek Omega 05.svg|x16px]], [[File:Greek Omega 03.svg|x16px]], [[File:Greek Omega 07.svg|x16px]]).<ref>Anne Jeffery (1961), ''The local scripts of archaic Greece'', p.37–38.</ref> The modern lowercase shape goes back to the [[uncial]] form [[File:Greek uncial Omega.svg|x14px]], a form that developed during the 3rd century BC in ancient handwriting on papyrus, from a flattened-out form of the letter ([[File:Greek Omega 08.svg|x16px]]) that had its edges curved even further upward.<ref>Edward M. Thompson (1912), ''Introduction to Greek and Latin paleography'', Oxford: Clarendon. p.144</ref>

In phonetic terms, the Ancient Greek Ω is a [[vowel length|long]] [[open-mid back rounded vowel|open-mid ''o'']] {{IPA|[ɔː]}}, comparable to the vowel of British English ''raw''. In [[Modern Greek]], Ω represents the same sound as [[omicron]]. The letter omega is [[transcription (linguistics)|transcribed]] ''ō'' or simply ''o''.

Omega (the last letter of the Greek alphabet) is often used to denote the last, the end, or the ultimate limit of a [[set theory|set]], in contrast to [[Alpha (letter)|alpha]], the first letter of the Greek alphabet.

Omega was also adopted into the [[early Cyrillic alphabet]]. See [[omega (Cyrillic)|Cyrillic omega]] ({{Unicode|Ѡ}}, {{Unicode|ѡ}}). A [[Raetic alphabet|Raetic]] variant is conjectured to be at the origin or parallel evolution of the [[Elder Futhark]] [[ᛟ]].

Omega was also adopted into the Latin alphabet, as a letter of the 1982 revision to the [[African reference alphabet]]. It has had little use. See [[Latin omega]].

Omega is also used in Christianity, as a part of the [[Alpha and Omega]] metaphor.

== The symbol Ω (uppercase letter) ==
{{Refimprove section|date=August 2009}}
The [[upper case|uppercase]] letter Ω is used as a symbol:
* In [[physics]]:
** For [[ohm]] – [[SI]] unit of electrical resistance; formerly also used upside down ({{Unicode|℧}}) to represent [[mho]], the old name for the inverse of an ohm (now [[siemens (unit)|siemens]] with symbol S) used for electrical conductance. [[Unicode]] has a separate code point for the [[Ohm (unit)|ohm]] sign (U+2126, Ω), but it is included only for backward compatibility, and the Greek uppercase omega character (U+03A9, Ω) is preferred.<ref>Excerpts from ''[http://www.unicode.org/versions/Unicode4.0.0/ch07.pdf#search=%22character%20U%2B2126%20maps%20OR%20map%20OR%20mapping%22 The Unicode Standard, Version 4.0]''. Retrieved 11 October 2006.</ref>
** In [[statistical mechanics]], Ω refers to the multiplicity (number of microstates) in a system.
** The [[solid angle]] or the rate of precession in a gyroscope.
** In [[particle physics]] to represent the [[Omega baryon]]s.
** In [[astronomy]] ([[physical cosmology|cosmology]]), Ω refers to the density of the universe, also called the [[density parameter]].
** In astronomy ([[orbital mechanics]]), Ω refers to the [[longitude of the ascending node]] of an orbit
*In [[mathematics]] and [[computer science]]:
** In [[complex analysis]], the [[Omega constant]], a solution of [[Lambert's W function]]
** A variable for a 2-dimensional region in calculus, usually corresponding to the domain of a double integral.
** In [[topos theory]], the (codomain of the) [[subobject classifier]] of an elementary topos.
** In [[combinatory logic]], the looping combinator, ''(λ x. x x) (λ x. x x)''
** In [[group theory]], the [[omega and agemo subgroup]]s of a ''p''-group, Ω(''G'') and ℧(''G'')
** In [[statistics]], it is used as the symbol for the [[sample space]], or total set of possible outcomes.
** In [[number theory]], Ω(''n'') is the number of [[prime divisor]]s of ''n''.
** in notation related to [[Big O notation]] to describe the [[asymptotic behavior]] of [[function (mathematics)|function]]s.
** [[Chaitin's constant]].
*As part of logo or trademark:
** The logo of [[Omega Watches]] SA.
** Part of the [[Supreme Court of the United Kingdom|Badge of the Supreme Court]] of the United Kingdom.
** Part of the mission patch for STS-135, as it was the last mission of the Space Shuttle program.
** The logo of the [[God of War (series)|God of War]] video game series based around Greek mythology.
** The logo of the [[Heroes of Olympus]] series, based on Greek mythology.
** the logo of the [[Ultramarines]] in [[Warhammer 40,000]]
*Other
** The symbol of the resistance movement against the Vietnam-era draft
** Year or date of death
** Used to refer to the lowest-ranked wolf in a pack
** [[Eschatology]] the symbol for the end of everything
**In molecular biology, the symbol is used as shorthand to signify a genetic construct introduced by a [[Crossover_(genetic_algorithm)#Two-point_crossover|two-point crossover]]

== The symbol ω (lower case letter) ==

The [[lower case|minuscule]] letter ω is used as a symbol:
*Biochemistry and chemistry:
** Denotes the carbon atom furthest from the [[carboxyl group]] of a [[fatty acid]].
** In [[biochemistry]], for one of the [[RNA]] [[Polymerase]] subunits.
** In biochemistry, for the dihedral angle associated with the peptide group, involving the backbone atoms Cα-C'-N-Cα
** In [[genomics]], as a measure of [[evolution]] at the protein level (also denoted as dN/dS or [[Ka/Ks ratio|Ka/Ks ratio]]).
*Physics
**[[angular velocity]] or [[angular frequency]]
**[[Computational fluid dynamics]]: the specific turbulence dissipation rate
** In [[meteorology]], the change of pressure with respect to time of a [[Fluid parcel|parcel]] of air.
** In [[circuit analysis]] and [[signal processing]] to represent [[natural frequency]], related to [[frequency]] ''f'' by ω = 2π''f''
** In [[astronomy]], as a ranking of a star's brightness within a constellation
** In astronomy ([[orbital mechanics]]), as designation of the [[argument of periapsis]] of an orbit
** In [[particle physics]] to represent the [[Meson|omega meson]]
*Computer science:
** In notation related to [[Big O notation]], the [[asymptotical dominance|asymptotically dominant]] nature of [[function (mathematics)|function]]s
** In [[relational database]] theory to represent [[Null (SQL)|NULL]], a missing or inapplicable value.
*Mathematics:
** The first [[transfinite number|transfinite]] [[ordinal number]], often identified with the set of natural numbers including 0 (sometimes written <math>\omega_0</math>)
** In [[set theory]], the [[first uncountable ordinal|first uncountable ordinal number]] (more commonly written as ω1)
** The complex [[roots of unity|cube roots of 1]]
** The [[Wright Omega Function|Wright Omega function]]
** A generic [[differential form]]
** In [[number theory]], ω(''n'') is the number of distinct [[prime divisor]]s of ''n''.
** In [[number theory]], an [[arithmetic function]]
** In [[combinatory logic]], the self-application combinator, ''(λ x. x x)''
** In mathematical/options finance, the elasticity of financial options
** In analytical investment management, the [[tracking error]] of an investment manager
*Other:
** Used in place of [[ん]] in Japanese typing shorthand.
** In [[linguistics]], the [[phonological word]]
** In [[textual criticism]], the [[archetype]] of a manuscript tradition
** In [[sociology]], used to refer to the lowest ranking member of a group

==Character Encodings==

* Greek Omega / Coptic Oou

{{charmap
|03A9|name1=Greek Capital Letter Omega
|03C9|name2=Greek Small Letter Omega
|2CB0|name3=Coptic Capital Letter Oou
|2CB1|name4=Coptic Small Letter Oou
|map2=DOS Greek|map2char1=97|map2char2=E0
|map3=DOS Greek-2|map3char1=D5|map3char2=FA
|map4=Windows 1253|map4char1=D9|map4char2=F9
|namedref1=[[TeX]]|ref1char1=\Omega|ref1char2=\omega
}}
<ref>Unicode Code Charts: [http://www.unicode.org/charts/PDF/U0370.pdf Greek and Coptic (Range: 0370-03FF)]</ref>

* Cyrillic Omega

{{charmap
|0460|name1=Cyrillic Capital Letter Omega
|0461|name2=Cyrillic Small Letter Omega
|A67B|name3=Combining Cyrillic Letter Omega
}}

{{charmap
|047A|name1=Cyrillic Capital Letter Round Omega
|047B|name2=Cyrillic Small Letter Round Omega
|A64C|name3=Cyrillic Capital Letter Broad Omega
|A64D|name4=Cyrillic Small Letter Broad Omega
}}

* Latin / [[International Phonetic Alphabet|IPA]] Omega

{{charmap
|0277|name1=Latin Small Letter Closed Omega
}}

* Technical Omega symbols

{{charmap
|2375|name1=APL Functional Symbol Omega
|2379|name2=APL Functional Symbol Omega Underbar
|2126|name3=Ohm Sign
|2127|name4=Inverted Ohm Sign
}}

* Mathematical Omega

{{charmap
|1D6C0|name1=Mathematical Bold Capital Omega
|1D6DA|name2=Mathematical Bold Small Omega
|1D6FA|name3=Mathematical Italic Capital Omega
|1D714|name4=Mathematical Italic Small Omega
|1D734|name5=Mathematical Bold Italic Capital Omega
|1D74E|name6=Mathematical Bold Italic Small Omega
}}

{{charmap
|1D76E|name1=Mathematical Sans-Serif Bold Capital Omega
|1D788|name2=Mathematical Sans-Serif Bold Small Omega
|1D7A8|name3=Mathematical Sans-Serif Bold Italic Capital Omega
|1D7C2|name4=Mathematical Sans-Serif Bold Italic Small Omega
|1D7D4|name5=Mathematical Sans-Serif Bold Italic P.OOO Omega
}}

These characters are used only as mathematical symbols. Stylized Greek text should be encoded using the normal Greek letters, with markup and formatting to indicate text style.

== Notes ==

<references />

[[Category:Greek letters]]
[[Category:Vowel letters]]

Ostrich - Revision history

en>Yobot: WP:CHECKWIKI error fixes using AWB (10750)

en>NicatronTg: Reverted edits by 98.117.12.149 (talk): factual errors (HG)

en>Daniel Mietchen: /* Behaviour and ecology */