Mu (letter)

Mu(/ˈm(j)uː/;^[1]^[2]uppercaseΜ,lowercaseμ;Ancient Greekμῦ[mŷː],Greek:μιor μυ—both[mi]) is the twelfthletterof theGreek alphabet,representing thevoiced bilabial nasalIPA:[m].In the system ofGreek numeralsit has a value of 40.^[3]Mu was derived from theEgyptian hieroglyphicsymbol for water, which had been simplified by thePhoeniciansand named after their word for water, to become𐤌^img(mem). Letters that derive from mu include theRoman Mand theCyrillic М,though the lowercase resembles a smallLatin U(u).

Names

Ancient Greek

In Greek, the name of the letter was writtenμῦand pronounced[mŷː].

Modern Greek

InModern Greek,the letter is spelledμιand pronounced[mi].In polytonic orthography, it is written with anacute accent:μί.^[4]^[5]

Use as symbol

The lowercase letter mu (μ) is used as a special symbol in manyacademic fields.Uppercase mu is not used, because it appears identical to LatinM.

Prefix for units of measurement

"μ" is used as aunit prefixdenoting a factor of 10⁻⁶(onemillionth), in this context, the symbol's name is "micro".

Metric prefix
International System of Unitsprefix, also known as "SI prefix"
The micrometre with a symbol of "μm" can also be referred to as the non-SI term "micron".

Mathematics

"μ" is conventionally used to denote certain things; however, any Greek letter or other symbol may be used freely as a variable name.

ameasureinmeasure theory
minimalizationincomputability theoryandRecursion theory
theintegrating factorinordinary differential equations
the degree ofmembershipin afuzzy set
theMöbius functioninnumber theory
the populationmeanorexpected valueinprobabilityandstatistics
theRamanujan–Soldner constant

Physics and engineering

Inclassical physicsandengineering:

thecoefficient of friction(also used in aviation as braking coefficient (seeBraking action))
reduced massin thetwo-body problem
Standard gravitational parameterin celestial mechanics
linear density,or mass per unit length, in strings and other one-dimensional objects
permeabilityin electromagnetism
themagnetic dipole momentof acurrent-carryingcoil
dynamic viscosityin fluid mechanics
theamplificationfactor orvoltage gainof atriode vacuum tube^[6]
theelectrical mobilityof a charged particle
therotor advance ratio,the ratio of aircraftairspeedto rotor-tip speed inrotorcraft^[7]^[8]
thepore water pressurein saturated soil

Inparticle physics:

the elementary particles called themuonand antimuon
theproton-to-electron mass ratio

Inthermodynamics:

thechemical potentialof a system or component of a system

Computer science

Inevolutionary algorithms:

μ, population size from which in each generation λ offspring will generate (the terms μ and λ originate fromevolution strategynotation)

Intype theory:

Used to introduce arecursive data type.For example, ${\text{list}}(\tau )=\mu {}\alpha {}.1+\tau {}\alpha$ is the type of lists with elements of type $\tau$ (atype variable): asumofunit,representingnil,with a pair of a $\tau$ and another ${\text{list}}(\tau )$ (represented by $\alpha$ ). In this notation, $\mu$ is a binding form, where the variable ( $\alpha$ ) introduced by $\mu$ is bound within the following term ( $1+\tau {}\alpha$ ) to the term itself. Via substitution and arithmetic, the type expands to $1+\tau +\tau ^{2}+\tau ^{3}+\cdots$ ,an infinite sum of ever-increasingproductsof $\tau$ (that is, a $\tau {}{\text{ list}}$ is any $k$ -tuple of values of type $\tau$ for any $k\geq 0$ ). Another way to express the same type is ${\text{list}}(\tau )=1+\tau {}{\text{list}}(\tau )$ .

Chemistry

Inchemistry:

the prefix given inIUPACnomenclature for abridging ligand

Biology

Inbiology:

themutation ratein population genetics
A class ofImmunoglobulin heavy chainthat definesIgMtypeAntibodies

Pharmacology

Inpharmacology:

an importantopiate receptor

Orbital mechanics

Inorbital mechanics:

Standard gravitational parameterof acelestial body,the product of thegravitational constantGand themassM
planetary discriminant, represents an experimental measure of the actual degree ofcleanlinessof the orbital zone, acriterionfordefiningaplanet.The value of μ is calculated by dividing the mass of the candidate body by the total mass of the other objects that share its orbital zone.

Music

Mu chord
Electronic musicianMike Paradinasruns the labelPlanet Muwhich utilizes the letter as its logo, and releases music under the pseudonym μ-Ziq, pronounced "music"
Used as the name of the school idol group μ's, pronounced "muse", consisting of nine singing idols in the animeLove Live! School Idol Project
Officialfandom nameof Kpop groupf(x),appearing as eitherMeUor 'μ'
Hip-hop artist Muonboy has taken inspiration from the particle for his stage name and his first EP named Mu uses the letter as its title.

Cameras

TheOlympus Corporationmanufactures a series of digital cameras called Olympus μ[mju:]^[9](known asOlympus Stylusin North America).

Linguistics

Inphonology:

mora

Insyntax:

μP (mu phrase) can be used as the name for a functional projection.^[10]

InCelticlinguistics:

/μ/ can represent anOld Irishnasalized labialfricativeof uncertain articulation, the ancestor of the sound represented byModern Irishmh.

Character encodings

^[11]

Character information
Preview	Μ		μ		µ		Ⲙ		ⲙ
Unicode name	GREEK CAPITAL LETTER MU		GREEK SMALL LETTER MU		MICRO SIGN		COPTIC CAPITAL LETTER MI		COPTIC SMALL LETTER MI
Encodings	decimal	hex	dec	hex	dec	hex	dec	hex	dec	hex
Unicode	924	U+039C	956	U+03BC	181	U+00B5	11416	U+2C98	11417	U+2C99
UTF-8	206 156	CE 9C	206 188	CE BC	194 181	C2 B5	226 178 152	E2 B2 98	226 178 153	E2 B2 99
Numeric character reference	Μ	Μ	μ	μ	µ	µ	Ⲙ	Ⲙ	ⲙ	ⲙ
Named character reference	Μ		μ		µ
ISO/IEC 8859-1					181	B5
ISO/IEC 8859-7	204	CC	236	EC
Code page 437,850			230	E6	230	E6
Code page 737	139	8B	163	A3
Code page 851,869	183	B7	230	E6
Code page 1253	204	CC	236	EC
Roman-8,Roman-9			243	F3	243	F3
TeX			\mu		\micro

Character information
Preview	𝚳		𝛍		𝛭		𝜇		𝜧		𝝁
Unicode name	MATHEMATICAL BOLD CAPITAL MU		MATHEMATICAL BOLD SMALL MU		MATHEMATICAL ITALIC CAPITAL MU		MATHEMATICAL ITALIC SMALL MU		MATHEMATICAL BOLD ITALIC CAPITAL MU		MATHEMATICAL BOLD ITALIC SMALL MU
Encodings	decimal	hex	dec	hex	dec	hex	dec	hex	dec	hex	dec	hex
Unicode	120499	U+1D6B3	120525	U+1D6CD	120557	U+1D6ED	120583	U+1D707	120615	U+1D727	120641	U+1D741
UTF-8	240 157 154 179	F0 9D 9A B3	240 157 155 141	F0 9D 9B 8D	240 157 155 173	F0 9D 9B AD	240 157 156 135	F0 9D 9C 87	240 157 156 167	F0 9D 9C A7	240 157 157 129	F0 9D 9D 81
UTF-16	55349 57011	D835 DEB3	55349 57037	D835 DECD	55349 57069	D835 DEED	55349 57095	D835 DF07	55349 57127	D835 DF27	55349 57153	D835 DF41
Numeric character reference	𝚳	𝚳	𝛍	𝛍	𝛭	𝛭	𝜇	𝜇	𝜧	𝜧	𝝁	𝝁

Character information
Preview	𝝡		𝝻		𝞛		𝞵
Unicode name	MATHEMATICAL SANS-SERIF BOLD CAPITAL MU		MATHEMATICAL SANS-SERIF BOLD SMALL MU		MATHEMATICAL SANS-SERIF BOLD ITALIC CAPITAL MU		MATHEMATICAL SANS-SERIF BOLD ITALIC SMALL MU
Encodings	decimal	hex	dec	hex	dec	hex	dec	hex
Unicode	120673	U+1D761	120699	U+1D77B	120731	U+1D79B	120757	U+1D7B5
UTF-8	240 157 157 161	F0 9D 9D A1	240 157 157 187	F0 9D 9D BB	240 157 158 155	F0 9D 9E 9B	240 157 158 181	F0 9D 9E B5
UTF-16	55349 57185	D835 DF61	55349 57211	D835 DF7B	55349 57243	D835 DF9B	55349 57269	D835 DFB5
Numeric character reference	𝝡	𝝡	𝝻	𝝻	𝞛	𝞛	𝞵	𝞵

Image list for readers with font problems

^

References

^"mu".The Chambers Dictionary(9th ed.). Chambers. 2003.ISBN 0-550-10105-5.
^"mu".Oxford English Dictionary(Online ed.).Oxford University Press.(Subscription orparticipating institution membershiprequired.)
^Hadley, James (1884).A Greek Grammar for Schools and Colleges.New York: American Book. p. 79.
^Neoelliniki Grammatiki (Tis Dimotikis).
^Grammatiki tis Dimotikis Glossas.
^Ballou, Glen(1987).Handbook for Sound Engineers: The New Audio Cyclopedia(1 ed.). Howard W. Sams Co. p. 250.ISBN 0-672-21983-2.Amplification factor or voltage gainis the amount the signal at the control grid is increased in amplitude after passing through the tube, which is also referred to as the Greek letter μ (mu) or voltage gain (V_g) of the tube.
^"Nomenclature"NASA
^"Definition".
^"Olympus History: μ[mju:] (Stylus) Series".
^Johnson, Kyle (1991). "Object Positions".Natural Language and Linguistic Theory.9(4): 577–636.doi:10.1007/BF00134751.S2CID 189901613.
^Unicode Code Charts:Greek and Coptic (Range: 0370-03FF)

[1] "mu".The Chambers Dictionary(9th ed.). Chambers. 2003.ISBN 0-550-10105-5.

[2] "mu".Oxford English Dictionary(Online ed.).Oxford University Press.(Subscription orparticipating institution membershiprequired.)

[3] Hadley, James (1884).A Greek Grammar for Schools and Colleges.New York: American Book. p. 79.

[4] Neoelliniki Grammatiki (Tis Dimotikis).

[5] Grammatiki tis Dimotikis Glossas.

[6] Ballou, Glen(1987).Handbook for Sound Engineers: The New Audio Cyclopedia(1 ed.). Howard W. Sams Co. p. 250.ISBN 0-672-21983-2.Amplification factor or voltage gainis the amount the signal at the control grid is increased in amplitude after passing through the tube, which is also referred to as the Greek letter μ (mu) or voltage gain (V_g) of the tube.

[7] "Nomenclature"NASA

[8] "Definition".

[9] "Olympus History: μ[mju:] (Stylus) Series".

[10] Johnson, Kyle (1991). "Object Positions".Natural Language and Linguistic Theory.9(4): 577–636.doi:10.1007/BF00134751.S2CID 189901613.

[11] Unicode Code Charts:Greek and Coptic (Range: 0370-03FF)

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