Mu (letter)

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Mu (uppercase ?, lowercase ?; Ancient Greek ?? [m?:], Greek: ?? or ?? [mi] or [miu]) is the 12th letter of the Greek alphabet. In the system of Greek numerals it has a value of 40. Mu was derived from the Egyptian hieroglyphic symbol for water (?), which had been simplified by the Phoenicians and named after their word for water, to become ?^img (mem). Letters that arose from mu include the Roman M and the Cyrillic ?.

Video Mu (letter)

Names

Ancient Greek

In Ancient Greek, the name of the letter was written ?? and pronounced [m?:].

Modern Greek

In Modern Greek, the letter is spelled ?? and pronounced [mi]. In monotonic orthography, the ancient version is written with an acute accent instead of a circumflex: ??.

Maps Mu (letter)

Use as symbol

The lowercase letter mu (?) is used as a special symbol in many academic fields. The uppercase mu is not used, because it is normally identical to Latin M.

Measurement

• the SI prefix micro-, which represents one millionth, or 10^-6
• the micron, an old unit that corresponds to the micrometre (which is now denoted "µm")

Mathematics

This is not exhaustive, since any Greek letter 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 learning rate in artificial neural networks
• the Möbius function in number theory
• the population mean or expected value in probability and statistics
• the Ramanujan-Soldner constant

Physics and engineering

In classical physics and engineering:

• the coefficient of friction (also used in aviation as braking coefficient)
• reduced mass in the two-body problem
• 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
• the electrical mobility of a charged particle
• a.k.a. rotor advance ratio; the ratio of aircraft airspeed to rotor tip speed in rotorcraft

In particle physics:

• the elementary particles called the muon and antimuon

In thermodynamics:

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

Computer science

In evolutionary algorithms:

• ?, population size from which in each generation ? offspring will generate (the terms ? and ? 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 ${\displaystyle {\text{list}}(\tau )=1+\tau {}{\text{list}}(\tau )}$.

Chemistry

In chemistry:

• the prefix given in IUPAC nomenclature for a bridging ligand

Biology

In biology:

• the mutation rate in population genetics

Pharmacology

In pharmacology:

• an important opiate receptor

Orbital mechanics

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.

Music

• 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 in the name of the school idol group ?'s, pronounced "muse", consisting of nine singing teen girls in the anime Love Live! School Idol Project
• Official fandom name of Kpop group f(x), appearing as either MeU or 'µ'

Cameras

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

Linguistics

In phonology, it often stands for mora. In syntax, ?P (mu phrase) can be used as the name for a functional projection.

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Character encodings

• Greek Mu / Coptic Mu

• Mathematical Mu

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.

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Image list for readers with font problems

1. ^

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See also

• Greek letters used in mathematics, science, and engineering
• ?, ? - El (Cyrillic)
• Fraser alphabet#Consonants

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References

Source of the article : Wikipedia