Lambda

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Λλ Lambda
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'''Lambda''' (uppercase '''Λ''', lowercase '''λ'''; Λάμβδα or Λάμδα, lamda or lamtha) is the 11th letter of the [[Greek alphabet]]. In the system of [[Greek numerals]] lambda has a value of 30. Lambda is related to the [[Phoenician alphabet|Phoenician letter]] [[Lamed]] [[File:Phoenician lamedh.svg|20px|Lamedh]]. Letters in other [[alphabet]]s that stemmed from lambda include the [[Roman alphabet|Roman]] [[L]] and the [[Cyrillic]] letter [[El (Cyrillic)|El]] (Л, л). The ancient [[grammarians]] and dramatists give evidence to the pronunciation as laːbdaː (λάβδα) in Classical Greek times.<sup>[]</sup> In [[Modern Greek]] the name of the letter, Λάμδα, is pronounced lamða; the spoken letter itself has the sound of [l] as with [[Latinate]] "L".
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In [[epichoric alphabets|early Greek alphabets]], the shape and orientation of lambda varied.<sup>[]</sup> Most variants consisted of two straight strokes, one longer than the other, connected at their ends.  The angle might be in the upper left, lower left ("Western" alphabets), or top ("Eastern" alphabets). Other variants had a vertical line with a horizontal or sloped stroke running to the right. With the general adoption of the [[History of the Greek alphabet#Standardization — the Ionic alphabet|Ionic alphabet]], Greek settled on an angle at the top; the Romans, borrowing from Western alphabets, put the angle at the lower left.
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==Symbol==
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===Upper-case letter Λ===
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* Lambda can mean the [[empty set]] in [[mathematics]], though other symbols are more commonly used, such as <math>\varnothing</math>.
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* The [[lambda particle]] is a type of [[subatomic particle]] in [[Physics#High energy/particle physics|subatomic particle physics]].
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* Lambda is the set of logical axioms in the [[axiomatic method]] of logical deduction in [[first-order logic]].
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* Lambda was used as a shield pattern by the [[Sparta]]n Army. This stood for [[Lakedaimon]], the name of the region of Sparta.
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* Lambda is the [[von Mangoldt function]] in mathematical [[number theory]].
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* In [[statistics]], [[Samuel Stanley Wilks|Wilks's lambda]] is used in multivariate analysis of variance ([[MANOVA]] analysis) to compare group means on a combination of dependent variables.
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* In the [[Spectral decomposition#Normal matrices|spectral decomposition of matrices]], lambda indicates the [[diagonal matrix]] of the [[eigenvalues]] of the [[matrix (mathematics)]].
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* In [[computer science]], lambda is the time window over which a process is observed for determining the working memory set for a [[digital computer]]'s  [[virtual memory]] management.
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* In [[astrophysics]], lambda represents the likelihood that a small body will encounter a [[planet]] or a [[dwarf planet]] leading to a deflection of a significant magnitude. An object with a large value of lambda is expected to have [[clearing the neighbourhood|cleared its neighborhood]], satisfying the current [[definition of planet|definition of a planet]].
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* In [[crystal optics]], lambda is used to represent the period of a lattice.
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* In [[NATO]] military operations, a chevron (a capital lambda symbol) is painted on the vehicles of this military alliance for identification. (The [[Spartan army]] used a capital lambda on [[Spartan army#Clothing, arms and armor|its shields]].)
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* In [[electrochemistry]], lambda denotes the "equivalent [[Electrical conductance|conductance]]" of an [[electrolyte]] solution.
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* In [[cosmology]], lambda is the symbol for the [[cosmological constant]].
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* In optics, lambda denotes the grating pitch of a [[Bragg reflector]].
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===Lower-case letter λ===
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[[Image:Greek lc lamda thin.svg|right|thumb|100px|Lower-case lambda]]
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* Lambda indicates the [[wavelength]] of any [[wave]], especially in [[physics]], [[electronics engineering]], and [[mathematics]].
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* Lambda indicates the [[exponential decay|radioactivity decay constant]] in [[nuclear physics]] and [[radioactivity]]. This constant is very simply related (by a multiplicative constant) to the [[half-life]] of any radioactive material.
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* In probability theory, lambda represents the density of occurrences within a time interval, as modeled by the [[Poisson distribution]].
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* In [[mathematical logic]] and [[computer science]], lambda is used to introduce an [[anonymous function]] expressed with the concepts of [[lambda calculus]].
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* Lambda is a non-[[International System of Units|SI]] [[metric system|metric]] [[units of measurement|unit of measure]] of [[volume]] (symbol '''λ''') equal to one [[micro-|micro]][[liter]] (1 μL) or one cubic [[millimeter]] (1&nbsp;mm<sup>3</sup>). This always rare use is currently deprecated.
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* Lambda indicates an [[eigenvalue]] in the mathematics of [[linear algebra]].
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* In the physics of [[electric field]]s, lambda sometimes indicates the linear [[charge density]] of a uniform line of [[electric charge]] (measured in [[coulomb]]s per meter).
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* Lambda denotes a [[Lagrange multiplier]] in [[multivariable calculus|multi-dimensional calculus]].
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* In [[solid-state electronics]], lambda indicates the [[channel length modulation]] parameter of a [[MOSFET]].
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* There is a [[lambda phage]] virus in biology.
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* In [[ecology]], lambda denotes the long-term intrinsic growth rate of a population. This value is often calculated as the dominant eigenvalue of the age/size class [[matrix (mathematics)]].
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* In [[formal language theory]] and in computer science, lambda denotes the [[empty string]].
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* In [[telecommunications]], lambda indicates the wavelength in a [[wavelength-division multiplexing]] [[optical communications]] system. This is actually a form of the long-established concept of [[frequency-division multiplexing]].
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* Lambda denotes the [[Lebesgue measure]] in [[set theory|mathematical set theory]].
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* The [[Goodman and Kruskal's lambda]] in [[statistics]] indicates the [[proportional reduction in error]] when one variable's values are used to predict the values of another variable.
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* Lambda denotes the [[oxygen sensor]] in a vehicle that measures the [[stoichiometric]] [[air-fuel ratio|air-to-fuel ratio]] in the exhaust [[gases]] of an [[internal-combustion engine]].
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* The [[Lambda (rocket)]] is a version of a large [[booster rocket]] in [[rocket|Japanese outer-space technology]].
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* Lambda denotes the [[failure rate]] of devices and systems in [[reliability theory]], and it is measured in failure events per hour. Numerically, this lambda is also the reciprocal of the [[Mean time between failure]]s.
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* In criminology, lambda denotes an individual's frequency of offenses
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* In cartography and navigation, lambda denotes the [[longitude]] of a location.
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* Lambda is the symbol of the musician [[Richard D. James]] or [[Aphex Twin]].
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* Lambda denotes [[Christopher Langton]]'s parameter for the classification of  [[Stephen Wolfram]]'s classes of [[cellular automaton|cellular automata]].
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* In [[electrochemistry]], lambda also denotes the [[ion]]ic conductance of a given ion (The composition of the ion is generally shown as a subscript to the lambda character).
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* In [[neurobiology]], lambda denotes the [[length constant]] (or exponential rate of decay) of the [[electric potential]] across the [[cell membrane]] along a length of a nerve cell's [[axon]].
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* In the science and technology of [[heat transfer]], lambda denotes the [[heat of vaporization]] per mole of material (a.k.a. its "latent heat").<sup>[]</sup>
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* In the technology and science of celestial navigation, lambda denotes the longitude as opposed to the Roman letter '''"L"''' which denotes the [[latitude]].
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* King [[Louis XIII of France]] used the letter lambda as his personal symbol rather than [[monogram]].
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* In [[Volvo]] [[automobile]]s, lambda denotes an engine, fuel, or ignition system failure.
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* Lambda is used as a recurring symbol for the human resistance in the [[Valve Software|Valve]] computer game series ''[[Half-Life (series)|Half-Life]]''.
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* Lambda is used to [[Lambda (LGBT symbol)|connote homosexuality]] and as an international symbol of gay rights<sup>[]</sup>
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==Lambda, the word==
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* In programming languages such as [[Lisp (programming language)#Lambda expressions|Lisp]] and [[Python (programming language)|Python]], '''lambda''' is an operator used to denote anonymous functions or [[closure (computer science)|closures]], following the usage of [[lambda calculus]]. An example of this use of lambda in the Python language is this section of [[computer code]] that sorts a list [[alphabet]]ically by the last character of each entry:
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<source lang="python">>>> list = ['woman', 'man', 'horse', 'boat', 'plane', 'dog']
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>>> sorted(list, key=lambda word: word[-1])
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['horse', 'plane', 'dog', 'woman', 'man', 'boat']</source>
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* In the [[C Sharp (programming language)|C# programming language]] a lambda expression is an anonymous function that can contain expressions and statements.<sup>[]</sup>
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* The language [[Unlambda]] is a functional programming language based upon [[combinatory logic]], a simplification of the lambda calculus that does not involve the lambda at all, hence the un- prefix.
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* An automotive [[oxygen sensor]] (O<sub>2</sub> sensor) is also known as a lambda probe, sensor, sond, or sonde.
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* '''Lambda''' is used in art and photography to refer to a digital [[Type C print]], or to the equipment that is used to produce it.
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* Lambda was used by Pythagoras to denote the "Lambda number sequence" { 1, 2, 3, 4, 8, 9, 27, ... }
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==Lambda as a name==
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*The popular [[science fiction]] universe of ''[[Star Wars]]'' uses a transport vehicle known as the [[Lambda-class shuttle]] that when viewed forward has the shape of the lowercase lambda.<sup>[]</sup>
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*Lambda is occasionally used in graphic design to represent a stylised 'A'. Examples include the Disney movie ''[[Atlantis: The Lost Empire]]'', the logo of the band ''[[Angels & Airwaves]]'', the logo of the band ''[[Dream Theater]]'', the logo of electronics company [[Samsung]] and the logo of the engineering consultancy [[Atkins (company)|Atkins]].  Conversely, the name of the band ''[[Λucifer]]'' (pronounced ''lucifer'') is sometimes spelt ''Aucifer''.
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[[Image:Capital Lambda.svg|thumb|150px|A capital '''Lambda''']]
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*''Stargate SG-1'' uses a modified upper-case lambda, with a small circle above the apex, to indicate Earth. This symbol has since become associated with the entire franchise.<sup>[]</sup><sup>[]</sup>
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== See also ==
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* [[Greek letters used in mathematics, science, and engineering]]
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* [[El (Cyrillic)|Л, л - El (Cyrillic)]]
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* [[Fraser alphabet#Consonants]]
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==References==
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[[Category:Greek letters]]
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[[Category:Units of volume]]

Revision as of 09:10, 14 March 2011

Lambda (uppercase Λ, lowercase λ; Λάμβδα or Λάμδα, lamda or lamtha) is the 11th letter of the Greek alphabet. In the system of Greek numerals lambda has a value of 30. Lambda is related to the Phoenician letter Lamed 20px|Lamedh. Letters in other alphabets that stemmed from lambda include the Roman L and the Cyrillic letter El (Л, л). The ancient grammarians and dramatists give evidence to the pronunciation as laːbdaː (λάβδα) in Classical Greek times.[] In Modern Greek the name of the letter, Λάμδα, is pronounced lamða; the spoken letter itself has the sound of [l] as with Latinate "L".

In early Greek alphabets, the shape and orientation of lambda varied.[] Most variants consisted of two straight strokes, one longer than the other, connected at their ends. The angle might be in the upper left, lower left ("Western" alphabets), or top ("Eastern" alphabets). Other variants had a vertical line with a horizontal or sloped stroke running to the right. With the general adoption of the Ionic alphabet, Greek settled on an angle at the top; the Romans, borrowing from Western alphabets, put the angle at the lower left.

Contents

Symbol

Upper-case letter Λ

Lower-case letter λ

Image:Greek lc lamda thin.svg
Lower-case lambda

Lambda, the word

  • In programming languages such as Lisp and Python, lambda is an operator used to denote anonymous functions or closures, following the usage of lambda calculus. An example of this use of lambda in the Python language is this section of computer code that sorts a list alphabetically by the last character of each entry:

<source lang="python">>>> list = ['woman', 'man', 'horse', 'boat', 'plane', 'dog'] >>> sorted(list, key=lambda word: word[-1]) ['horse', 'plane', 'dog', 'woman', 'man', 'boat']</source>

  • In the C# programming language a lambda expression is an anonymous function that can contain expressions and statements.[]
  • The language Unlambda is a functional programming language based upon combinatory logic, a simplification of the lambda calculus that does not involve the lambda at all, hence the un- prefix.
  • An automotive oxygen sensor (O2 sensor) is also known as a lambda probe, sensor, sond, or sonde.
  • Lambda is used in art and photography to refer to a digital Type C print, or to the equipment that is used to produce it.
  • Lambda was used by Pythagoras to denote the "Lambda number sequence" { 1, 2, 3, 4, 8, 9, 27, ... }

Lambda as a name

Image:Capital Lambda.svg
A capital Lambda
  • Stargate SG-1 uses a modified upper-case lambda, with a small circle above the apex, to indicate Earth. This symbol has since become associated with the entire franchise.[][]

See also

References

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