Mu (letter)

In Ancient Greek, the name of the letter was written μῦ and pronounced [mŷː].

In Modern Greek, the letter is spelled μι and pronounced [mi]. In polytonic orthography, it is written with an acute accent: μί.[4][5]

• the SI prefix micro-, which represents one millionth, or 10⁻⁶. Lowercase letter "u" is often substituted for "μ" when the Greek character is not typographically available; for example the unit "microfarad", correctly "μF", is often rendered as "uF" or "ufarad" in technical documents.[6]
• the micron "μ", an old unit now named the micrometre and denoted "µm"

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

• a measure in measure theory
• minimalization in computability theory and Recursion theory
• the integrating factor in ordinary differential equations
• the degree of membership in a fuzzy set
• the Möbius function in number theory
• the population mean or expected value in probability and statistics
• the Ramanujan–Soldner constant

In classical physics and engineering:

• the coefficient of friction (also used in aviation as braking coefficient)
• reduced mass in the two-body problem
• Standard gravitational parameter in celestial mechanics
• linear density, or mass per unit length, in strings and other one-dimensional objects
• permeability in electromagnetism
• the magnetic dipole moment of a current-carrying coil
• dynamic viscosity in fluid mechanics
• the amplification factor or voltage gain of a triode vacuum tube[7]
• the electrical mobility of a charged particle
• the rotor advance ratio, the ratio of aircraft airspeed to rotor tip speed in rotorcraft[8][9]

In particle physics:

• the elementary particles called the muon and antimuon
• the proton-to-electron mass ratio

In thermodynamics:

• the chemical potential of a system or component of a system

In evolutionary algorithms:

• μ, population size from which in each generation λ offspring will generate (the terms μ and λ originate from evolution strategy notation)

In type theory:

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

In chemistry:

• the prefix given in IUPAC nomenclature for a bridging ligand

In biology:

• the mutation rate in population genetics

In pharmacology:

• an important opiate receptor

In orbital mechanics:

• Standard gravitational parameter of a celestial body, the product of the gravitational constant G and the mass M
• planetary discriminant, represents an experimental measure of the actual degree of cleanliness of the orbital zone, a criterion for defining a planet. 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.

• Mu major chord
• Electronic musician Mike Paradinas runs the label Planet Mu which 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 anime Love Live! School Idol Project
• Official fandom name of Kpop group f(x), appearing as either MeU or 'µ'

The Olympus Corporation manufactures a series of digital cameras called Olympus µ [mju:][10] (known as Olympus Stylus in North America)

In phonology:

• mora

In syntax:

• μP (mu phrase) can be used as the name for a functional projection.[11]

In Celtic linguistics:

• /µ/ can represent an Old Irish nasalized labial fricative of uncertain articulation, the ancestor of the sound represented by Modern Irish mh.