Lambda
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Lambda, Λ, λ (uppercase Λ, lowercase λ; Greek: λάμ(β)δα lám(b)da) 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 . Letters in other alphabets that stemmed from lambda include the Latin 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.^{[1]} 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.^{[2]} Most variants consisted of two straight strokes, one longer than the other, connected at their ends. The angle might be in the upperleft, lowerleft ("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 put the angle at the lowerleft.
The HTML 4 character entity references for the Greek capital and small letter lambda are "Λ" and "λ", respectively.^{[3]} The Unicode code points for lambda are U+039B and U+03BB.
Contents
Symbol
Uppercase letter Λ
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 The lambda particle is a type of subatomic particle in subatomic particle physics.
 Lambda is the set of logical axioms in the axiomatic method of logical deduction in firstorder logic.
 Lambda was used as a shield pattern by the Spartan army. This stood for Lacedaemon, (Λακεδαίμων, Lakedaímōn), the name of the polis of the Spartans, as opposed to the city itself.
 Lambda is the von Mangoldt function in mathematical number theory.
 In statistics, Wilks's lambda is used in multivariate analysis of variance (MANOVA analysis) to compare group means on a combination of dependent variables.
 In the spectral decomposition of matrices, lambda indicates the diagonal matrix of the eigenvalues of the matrix.
 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.
 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 cleared its neighborhood, satisfying the current definition of a planet.
 In crystal optics, lambda is used to represent the period of a lattice.
 In NATO military operations, a chevron (a capital lambda symbol) is painted on the vehicles of this military alliance for identification.
 In chemistry there are Δ (delta) and Λ (lambda) isomers, see: coordination complex
 In electrochemistry, lambda denotes the "equivalent conductance" of an electrolyte solution.
 In cosmology, lambda is the symbol for the cosmological constant, a term added to some dynamical equations to account for the acceleration of the universe.
 In optics, lambda denotes the grating pitch of a Bragg reflector.
 In blockhandwritten Russian, this letter represents Л in both uppercase and lowercase.
Lowercase letter λ
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 In evolutionary algorithms, λ indicates the number of offspring that would be generated from μ current population in each generation. The terms μ and λ are originated from Evolution strategy notation.
 Lambda indicates the wavelength of any wave, especially in physics, electronics engineering, and mathematics.^{[4]}
 Lambda indicates the radioactivity decay constant in nuclear physics and radioactivity. This constant is very simply related (by a multiplicative constant) to the halflife of any radioactive material.
 In probability theory, lambda represents the density of occurrences within a time interval, as modeled by the Poisson distribution.
 In mathematical logic and computer science, lambda is used to introduce anonymous functions expressed with the concepts of lambda calculus.
 Lambda is a unit of volume, synonymous with one microliter (1 μL), that is, one cubic millimetre (1 mm^{3}). This use is currently deprecated.
 Lambda indicates an eigenvalue in the mathematics of linear algebra.
 In the physics of electric fields, lambda sometimes indicates the linear charge density of a uniform line of electric charge (measured in coulombs per meter).
 Lambda denotes a Lagrange multiplier in multidimensional calculus.
 In solidstate electronics, lambda indicates the channel length modulation parameter of a MOSFET.
 There is a lambda phage virus in biology.
 In ecology, lambda denotes the longterm intrinsic growth rate of a population. This value is often calculated as the dominant eigenvalue of the age/size class matrix (mathematics).
 In formal language theory and in computer science, lambda denotes the empty string.
 Lambda is a nonstandard symbol in the International Phonetic Alphabet.
 In telecommunications, lambda indicates the wavelength in a wavelengthdivision multiplexing optical communications system. This is actually a form of the longestablished concept of frequencydivision multiplexing.
 Lambda denotes the Lebesgue measure in mathematical set theory.
 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.
 Lambda denotes the oxygen sensor in a vehicle that measures the airtofuel ratio in the exhaust gases of an internalcombustion engine.
 A Lambda 4S solidfuel rocket was used to launch Japan's first orbital satellite in 1970.^{[5]}
 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 failures.
 In criminology, lambda denotes an individual's frequency of offenses.
 In cartography and navigation, lambda denotes the longitude of a location.
 Lambda denotes Christopher Langton's parameter for the classification of Stephen Wolfram's classes of cellular automata.
 In electrochemistry, lambda also denotes the ionic conductance of a given ion (The composition of the ion is generally shown as a subscript to the lambda character).
 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.
 In the science and technology of heat transfer, lambda denotes the heat of vaporization per mole of material (a.k.a. its "latent heat").^{[6]}
 In the technology and science of celestial navigation, lambda denotes the longitude as opposed to the Roman letter "L", which denotes the latitude.
 King Louis XIII of France used the letter lambda as his personal symbol rather than monogram.
 In Volvo automobiles, lambda denotes an engine, fuel, or ignition system failure.
 A block style Lambda is used as a recurring symbol in the Valve Corporation computer game series HalfLife,^{[7]} referring to the Lambda complex of the fictional Black Mesa Research Facility, as well as making appearances in the sequel HalfLife 2.^{[8]}
 The lambda was selected as a symbol by the Gay Activists Alliance of New York in 1970, and declared the international symbol for gay and lesbian rights by the International Gay Rights Congress in Edinburgh, Scotland, in 1974.
 The "lambda sign" is used for diagnosis of dichorionic twins in obstetric ultrasonography
 In bifurcation theory, lambda is used to parameterize a family of differential equations
 Lambda was used by Pythagoras to denote the "Lambda number sequence" 1, 2, 3, 4, 9, 8, 27, ...,(sequence A098293 in the OEIS) formed by the integers of the form 2^{i} and 3^{i}, for nonnegative integer i.^{[9]}
Litra symbol
The Roman libra and Byzantine lítra (λίτρα), which served as both the pound mass unit and liter volume unit, were abbreviated in Greek using lambda with modified forms of the iota subscript (as λͅ). These are variously encoded in Unicode. The Ancient Greek Numbers Unicode block includes 10183 GREEK LITRA SIGN (𐆃) as well as 𐅢, which is described as 10162 GREEK ACROPHONIC HERMIONIAN TEN^{[10]} but was much more common as a form of the litra sign. A variant of the sign can be formed from 0338 COMBINING LONG SOLIDUS OVERLAY and either 039B GREEK CAPITAL LETTER LAMDA (Λ̸) or 03BB GREEK SMALL LETTER LAMDA (λ̸).^{[11]}
Lambda as a name
 Stargate SG1 uses a modified uppercase lambda, with a small circle above the apex, to indicate Earth. This symbol has since become associated with the entire franchise.^{[12]}^{[13]}
 Brothers of the Lambda Theta Phi Latin Fraternity are considered Lambda Men, or simply Lambdas.
 Brothers of the Lambda Phi Epsilon Asian American interest fraternity are commonly referred to as Lambdas.
 The popular science fiction universe of Star Wars uses a transport vehicle known as the Lambdaclass shuttle that when viewed forward has the shape of the lowercase lambda.^{[14]}
 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 logos of the engineering consultancy Atkins and car manufacturer Kia (KIΛ). Conversely, the name of the band Λucifer (pronounced lucifer) is sometimes spelled Aucifer.
 The uppercase lambda is used as the alias of Providence, Rhode Island based musician Xavier Valentine.^{[15]}
 The HalfLife franchise of video games uses an encircled block style lowercase lambda as the franchise logo (HalfLife 2 adds the numeral 2 into the logo as superscript), prominently featured on the chest of Gordon Freeman's (the protagonist) powered armor,^{[16]} known as an HEV suit.
 In the 2D fighting game series BlazBlue, a recurring character named Lambda11 appears in the various games' story modes and as a playable character.
 Several LGBT rights organizations, such as Lambda Legal and the Lambda Literary Award derive their names from the use of a lowercase lambda as a symbol for LGBT rights.
 In the Visual Novel Umineko: When They Cry, there is a character named Lambdadelta.
 In the RPG game Tales of Graces, originally made for the Wii, Lambda is the name of the main story's antagonist (voiced by Keith Silverstein).
 There is a PlayStation Vita game known as Cytus Lambda.
 The musical group Axwell Λ Ingrosso use the lambda as symbol in their name.
 An automotive oxygen sensor (O_{2} 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.
 In the study of gasoline engines, Lambda sometimes refers to the air/fuel mixture going into the engine.^{[17]}^{[citation needed]}
 In the popular Japan based; light novel, animated series, and manga; "Full Metal Panic!","Full Metal Panic? Fumoffu", and "Full Metal Panic! The Second Raid", it utilizes a machine called a "Lambda Driver".^{[citation needed]}
Character encodings
Unicode uses the spelling "lamda" in character names, instead of "lambda", due to "preferences expressed by the Greek National Body".^{[18]}
 Greek Lambda / Coptic Laula
Character  Λ  λ  ᴧ  Ⲗ  ⲗ  

Unicode name  GREEK CAPITAL LETTER LAMDA  GREEK SMALL LETTER LAMDA  GREEK LETTER SMALL CAPITAL LAMDA  COPTIC CAPITAL LETTER LAULA  COPTIC SMALL LETTER LAULA  
Encodings  decimal  hex  decimal  hex  decimal  hex  decimal  hex  decimal  hex 
Unicode  923  U+039B  955  U+03BB  7463  U+1D27  11414  U+2C96  11415  U+2C97 
UTF8  206 155  CE 9B  206 187  CE BB  225 180 167  E1 B4 A7  226 178 150  E2 B2 96  226 178 151  E2 B2 97 
Numeric character reference  Λ  Λ  λ  λ  ᴧ  ᴧ  Ⲗ  Ⲗ  ⲗ  ⲗ 
Named character reference  Λ  λ  
DOS Greek  138  8A  162  A2  
DOS Greek2  182  B6  229  E5  
Windows 1253  203  CB  235  EB  
TeX  \Lambda  \lambda 
 Mathematical Lambda
Character  𝚲  𝛌  𝛬  𝜆  𝜦  𝝀  

Unicode name  MATHEMATICAL BOLD CAPITAL LAMDA 
MATHEMATICAL BOLD SMALL LAMDA 
MATHEMATICAL ITALIC CAPITAL LAMDA 
MATHEMATICAL ITALIC SMALL LAMDA 
MATHEMATICAL BOLD ITALIC CAPITAL LAMDA 
MATHEMATICAL BOLD ITALIC SMALL LAMDA 

Encodings  decimal  hex  decimal  hex  decimal  hex  decimal  hex  decimal  hex  decimal  hex 
Unicode  120498  U+1D6B2  120524  U+1D6CC  120556  U+1D6EC  120582  U+1D706  120614  U+1D726  120640  U+1D740 
UTF8  240 157 154 178  F0 9D 9A B2  240 157 155 140  F0 9D 9B 8C  240 157 155 172  F0 9D 9B AC  240 157 156 134  F0 9D 9C 86  240 157 156 166  F0 9D 9C A6  240 157 157 128  F0 9D 9D 80 
UTF16  55349 57010  D835 DEB2  55349 57036  D835 DECC  55349 57068  D835 DEEC  55349 57094  D835 DF06  55349 57126  D835 DF26  55349 57152  D835 DF40 
Numeric character reference  𝚲  𝚲  𝛌  𝛌  𝛬  𝛬  𝜆  𝜆  𝜦  𝜦  𝝀  𝝀 
Character  𝝠  𝝺  𝞚  𝞴  

Unicode name  MATHEMATICAL SANSSERIF BOLD CAPITAL LAMDA 
MATHEMATICAL SANSSERIF BOLD SMALL LAMDA 
MATHEMATICAL SANSSERIF BOLD ITALIC CAPITAL LAMDA 
MATHEMATICAL SANSSERIF BOLD ITALIC SMALL LAMDA 

Encodings  decimal  hex  decimal  hex  decimal  hex  decimal  hex 
Unicode  120672  U+1D760  120698  U+1D77A  120730  U+1D79A  120756  U+1D7B4 
UTF8  240 157 157 160  F0 9D 9D A0  240 157 157 186  F0 9D 9D BA  240 157 158 154  F0 9D 9E 9A  240 157 158 180  F0 9D 9E B4 
UTF16  55349 57184  D835 DF60  55349 57210  D835 DF7A  55349 57242  D835 DF9A  55349 57268  D835 DFB4 
Numeric character reference  𝝠  𝝠  𝝺  𝝺  𝞚  𝞚  𝞴  𝞴 
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.
See also
 Greek letters used in mathematics, science, and engineering
 Л, л  El (Cyrillic)
 Fraser alphabet#Consonants
References
 ^ Herbert Weir Smyth. A Greek Grammar for Colleges. I.1.c
 ^ "Epigraphic Sources for Early Greek Writing". Poinikastas.csad.ox.ac.uk. Retrieved 20111003.
 ^ World Wide Web Consortium W3C. HTML 4.01 Specification, 24. Character entity references in HTML 4. [1]
 ^ Nelkon, Michael (1977). Fundamentals of Physics. St. Albans, Hertfordshire: HartDavis Educational. p. 329.
 ^ "Encyclopedia Astronautica: Lambda". www.astronautix.com. Retrieved 20121218.
 ^ Wankat Separation Process Engineering 2nd ed, Prentice Hall
 ^ "HalfLife on Steam". store.steampowered.com. Valve. Retrieved 20170102.
 ^ "HalfLife 2 on Steam". store.steampowered.com. Valve. Retrieved 20170102.
 ^ "Article 11". SMPhillips.8m.com. Retrieved 20160918.
 ^ Unicode Ancient Greek Numbers block.
 ^ Thesaurus Linguae Graecae.
 ^ Read, David (July 15, 2010). "Earth Symbol". Propworx. Retrieved 20101012.
 ^ "Official Stargate Website". MetroGoldwynMayer. Retrieved 20101013.
 ^ "Imperial Lambdaclass shuttle". Star Wars Databank. Lucasfilm. Retrieved 20101012.
 ^ "Ʌ". Aarrcc.bandcamp.com. Retrieved 20111003.
 ^ "Dr. Gordon Freeman". Valve Developer Community. Valve. Retrieved 20170102.
 ^ Balich, Garrett; Aschenbach, Conrad (4 May 2004). The Gasoline 4Stroke Engine for Automobiles (PDF). Department of Aerospace and Mechanical Engineering University of Notre Dame Notre Dame, IN 46556. p. 37. Retrieved 27 September 2016.
 ^ http://www.unicode.org/mailarch/unicodeml/y2010m06/0063.html