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 letter Lamed Image:Phoenician lamedh.png. 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.^[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 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.

Symbol

Upper-case letter Λ

• Lambda can mean the empty set in mathematics, though other symbols are more commonly used, such as <math>\varnothing</math>.
• 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 first-order logic.
• Lambda was used as a shield pattern by the Spartan Army. This stood for Lakedaimon, the name of the region of Sparta.
• 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 (mathematics).
• 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. (The Spartan army used a capital lambda on its shields.)
• In electrochemistry, lambda denotes the "equivalent conductance" of an electrolyte solution.
• In cosmology, lambda is the symbol for the cosmological constant.
• In optics, lambda denotes the grating pitch of a Bragg reflector.

Lower-case letter λ

Lower-case lambda

• Lambda indicates the wavelength of any wave, especially in physics, electronics engineering, and mathematics.
• Lambda indicates the 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.
• 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 an anonymous function expressed with the concepts of lambda calculus.
• Lambda is a non-SI metric unit of measure of volume (symbol λ) equal to one microliter (1 μL) or one cubic millimeter (1 mm³). This always rare 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 multi-dimensional calculus.
• In solid-state electronics, lambda indicates the channel length modulation parameter of a MOSFET.
• There is a lambda phage virus in biology.
• 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).
• In formal language theory and in computer science, lambda denotes the empty string.
• 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.
• 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 stoichiometric air-to-fuel ratio in the exhaust gases of an internal-combustion engine.
• The Lambda (rocket) is a version of a large booster rocket in Japanese outer-space technology.
• 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 is the symbol of the musician Richard D. James or Aphex Twin.
• 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").^[3]
• 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.
• Lambda is used as a recurring symbol for the human resistance in the Valve computer game series Half-Life.

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.^[5]
• 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

• 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.^[6]
• 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. Conversely, the name of the band Λucifer (pronounced lucifer) is sometimes spelt Aucifer.

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.^[7][8]

See also

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

References

• 1. Herbert Weir Smyth. A Greek Grammar for Colleges. I.1.c
• 2. Poinikastas: Epigraphic Sources for Early Greek Writing
• 3. Wankat Separation Process Engineering 2nd ed, Prentice Hall
• 4. http://www.lambda.org/symbols.htm
• 5. http://msdn.microsoft.com/en-us/library/bb397687.aspx
• 6. "Imperial Lambda-class shuttle". Star Wars Databank. Lucasfilm. http://www.starwars.com/databank/starship/lambdashuttle/index.html. Retrieved 2010-10-12.
• 7. Read, David (July 15, 2010). "Earth Symbol". Propworx. http://stargateartifacts.com/2010/07/15/exclusive-wallpaper-earth-symbol/. Retrieved 2010-10-12.
• 8. "Official Stargate Website". Metro-Goldwyn-Mayer. http://stargate.mgm.com/. Retrieved 2010-10-13.