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Lambda

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Lambda (/ˈlæmdə/ ;[1] uppercase Λ, lowercase λ; Greek: λάμ(β)δα, lám(b)da) is the eleventh letter of the Greek alphabet, representing the voiced alveolar lateral approximant IPA: [l]. In the system of Greek numerals, lambda has a value of 30. Lambda is derived from the Phoenician Lamed. Lambda gave rise to the Latin L and the Cyrillic El (Л). The ancient grammarians and dramatists give evidence to the pronunciation as [laːbdaː] (λάβδα) in Classical Greek times.[2] In Modern Greek, the name of the letter, Λάμδα, is pronounced [ˈlam.ða].

In early Greek alphabets, the shape and orientation of lambda varied.[3] 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 put the angle at the lower-left.

The Greek alphabet on a black figure vessel, with a Phoenician-lamed-shaped lambda. The gamma has the shape of modern lambda.

Symbol

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Upper-case letter Λ

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Examples of the symbolic use of uppercase lambda include:

Lower-case letter λ

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Lower-case lambda

Examples of the symbolic use of lowercase lambda include:

Litra symbol

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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 ⟨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[36] 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).[37]

Unicode

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Unicode uses the (Modern Greek-based) spelling "lamda" in character names, instead of "lambda", due to "the pre-existing names in ISO 8859-7, as well as preferences expressed by the Greek National Body".[38] Latin versions of lambda were added to Unicode in 2024 for the Salishan and Wakashan languages in Canada.[39]

  • U+039B Λ GREEK CAPITAL LETTER LAMDA (Λ)[40]
  • U+03BB λ GREEK SMALL LETTER LAMDA (λ)
  • U+1D27 GREEK LETTER SMALL CAPITAL LAMDA
  • U+2C96 COPTIC CAPITAL LETTER LAULA
  • U+2C97 COPTIC SMALL LETTER LAULA
  • U+A7DA LATIN CAPITAL LETTER LAMBDA
  • U+A7DB LATIN SMALL LETTER LAMBDA
  • U+1038D 𐎍 UGARITIC LETTER LAMDA
  • U+1D6B2 𝚲 MATHEMATICAL BOLD CAPITAL LAMDA[a]
  • U+1D6CC 𝛌 MATHEMATICAL BOLD SMALL LAMDA
  • U+1D6EC 𝛬 MATHEMATICAL ITALIC CAPITAL LAMDA
  • U+1D706 𝜆 MATHEMATICAL ITALIC SMALL LAMDA
  • U+1D726 𝜦 MATHEMATICAL BOLD ITALIC CAPITAL LAMDA
  • U+1D740 𝝀 MATHEMATICAL BOLD ITALIC SMALL LAMDA
  • U+1D760 𝝠 MATHEMATICAL SANS-SERIF BOLD CAPITAL LAMDA
  • U+1D77A 𝝺 MATHEMATICAL SANS-SERIF BOLD SMALL LAMDA
  • U+1D79A 𝞚 MATHEMATICAL SANS-SERIF BOLD ITALIC CAPITAL LAMDA
  • U+1D7B4 𝞴 MATHEMATICAL SANS-SERIF BOLD ITALIC SMALL LAMDA
  1. ^ The MATHEMATICAL characters should only be used in math. Stylized Greek text should be encoded using the normal Greek letters, with markup and formatting to indicate text style.

See also

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References

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  1. ^ "lambda". Oxford English Dictionary (Online ed.). Oxford University Press. (Subscription or participating institution membership required.)
  2. ^ Herbert Weir Smyth. A Greek Grammar for Colleges. I.1.c
  3. ^ "Epigraphic Sources for Early Greek Writing". Poinikastas.CSAD.ox.ac.uk. Retrieved 2011-10-03.
  4. ^ Philodemus (2003). On Poems. Oxford University Press. p. 212. ISBN 9780199262854.
  5. ^ Deza, Elena (2023). Perfect and amicable numbers. Selected chapters of number theory : special numbers. New Jersey: World Scientific. p. 79. ISBN 978-981-12-5962-3. The von Mangold function Λ(n) is defined as…
  6. ^ Broughan, Kevin A. (2024). Equivalents of the Riemann hypothesis. Volume 3: Further steps towards resolving the Riemann hypothesis / Kevin Broughan (University of Waikato, New Zealand). Encyclopedia of mathematics and its applications. Cambridge, United Kingdom New York, NY, USA Port Melbourne, VIC, Australia New Delhi, India Singapore: Cambridge University Press. p. 63. ISBN 978-1-009-38480-3. Now we can give the definition of the de Bruijn–Newman constant Λ.
  7. ^ Everitt, Brian (2011). An introduction to applied multivariate analysis with R. Use R! Ser. Torsten Hothorn. New York, NY: Springer New York. ISBN 978-1-4419-9649-7. In the current case of one-way MANOVA, it can be shown that the LR test statistic is a monotone function of what is called Wilks' lambda (Λ, capital Greek letter lambda):
  8. ^ Wilkinson, John (2016). The Solar System in Close-Up. Astronomers' Universe Ser. Cham: Springer International Publishing AG. p. 7. ISBN 978-3-319-27627-4. American planetary scientists Alan Stern and Harold Levison introduced a parameter Λ (lambda) to express the likelihood of a body "clearing the neighborhood around its orbit".
  9. ^ Kuhn, Reinhard; Hoffstetter-Kuhn, Sabrina (1993). Capillary electrophoresis: principles and practice. Springer Laboratory. Berlin Heidelberg: Springer. p. 12. ISBN 978-0-387-56434-0. According to the first Kohlrausch law, anions and cations contribute independently to the conductance, which means that the equivalent conductance Λ is the sum of the…
  10. ^ Liddle, Andrew R. (2015). An introduction to modern cosmology (Third ed.). Chichester, West Sussex: John Wiley and Sons, Inc. p. 55. ISBN 978-1-118-50214-3. The cosmological constant Λ appears in the Friedman equation as an extra term,
  11. ^ Pal, Bishnu, ed. (2010). Frontiers in Guided Wave Optics and Optoelectronics. Erscheinungsort nicht ermittelbar: IntechOpen. p. 352. ISBN 978-953-7619-82-4. The circular Bragg grating on the bottom DBR gives high reflection for Bragg wavelength which is decided, for first order grating in slab hollow waveguide [25], by the following equation… where Λ is grating pitch.
  12. ^ Nelkon, Michael (1977). Fundamentals of Physics. St. Albans, Hertfordshire: Hart-Davis Educational. p. 329.
  13. ^ Baragona, Roberto (2011). Evolutionary statistical procedures: an evolutionary computation approach to statistical procedures designs and applications. Statistics and computing. Francesco Battaglia, Irene Poli. Berlin: Springer. p. 16. ISBN 978-3-642-16217-6. … ,and λ is the number of offsprings at each generation:
  14. ^ Panik, Michael J. (2005). Advanced statistics from an elementary point of view. Boston: Elsevier/Academic Press. p. 260. ISBN 978-0-12-088494-0. Since λ is the mean number of occurrences per unit time of the Poisson process,
  15. ^ Tabatabaian, Mehrzad; Rajput, R. K. (2018). Advanced thermodynamics: fundamentals, mathematics, applications. Dulles, Virginia Boston, Massachusetts New Delhi: Mercury Learning and Information. p. 434. ISBN 978-1-936420-27-8. A gas of atoms reaches quantum degeneracy when the matter waves of neighbouring atoms overlap – i.e. when the thermal de Broglie wavelength, λ, which means as the temperature falls,…
  16. ^ Ito, Kazufumi (2008). Lagrange multiplier approach to variational problems and applications. Advances in Design and Control. K. Kunisch, Society for Industrial and Applied Mathematics. Philadelphia, Pa: Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104). pp. xii. ISBN 978-0-89871-649-8. Here the Lagrange multiplier λ is treated like an independent variable just like y and u.
  17. ^ Wiegerink, Remco J. (1993). Analysis and synthesis of MOS translinear circuits. The Kluwer international series in engineering and computer science ; Analog circuits and signal processing. Boston: Kluwer Academic. p. 21. ISBN 978-0-7923-9390-0. Channel length modulation in an MOS transistor causes the drain current to be dependent on the drain voltage.… and λ the channel-length modulation parameter.
  18. ^ Li, Xue-Zhi; Yang, Junyuan; Martcheva, Maia (2020). Age Structured Epidemic Modeling. Interdisciplinary Applied Mathematics. Cham: Springer International Publishing AG. p. 7. ISBN 978-3-030-42495-4. λ* is called the Malthusian parameter or intrinsic growth rate.
  19. ^ Tourlakis, George J. (2024). Discrete mathematics: a concise introduction. Synthesis lectures on mathematics & statistics. Cham: Springer. p. 37. ISBN 978-3-031-30487-3. The symbols prevalent in the literature used to denote the empty string are ϵ or λ. We will choose λ…
  20. ^ International Phonetic Association (2021). Handbook of the International Phonetic Association: a guide to the use of the international phonetic alphabet (22. printing ed.). Cambridge: Cambridge University Press. p. 179. ISBN 978-0-521-63751-0. λ lambda voiceless dental or alveolar lateral fricative Not IPA usage
  21. ^ Bierens, Herman J. (2004). Introduction to the mathematical and statistical foundations of econometrics. Themes in modern econometrics. New York: Cambridge University Press. p. 19. ISBN 978-0-521-83431-5. This function λ is called the Lebesgue measure on ,...
  22. ^ Leong, Frederick; Austin, James T. (2024). The psychology research handbook: a guide for graduate students and research assistants (Third ed.). Thousand Oaks London New Delhi Singapore: Sage. p. 280. ISBN 978-1-4522-1767-3. If the independent and dependent variables are nominal, the contingency coefficient, Cramer's V, or Goodman–Kruskal's λ may be chosen.
  23. ^ Ribbens, William B. (2017). Understanding automotive electronics: an engineering perspective (8th ed.). Oxford: Elsevier/Butterworth-Heinemann, an imprint of Elsevier. p. 215. ISBN 978-0-12-810434-7. As a result, one of the most significant automotive engine sensors in use today is the exhaust gas oxygen (EGO) sensor. This sensor is often called a lambda sensor from the Greek letter lambda (λ), which is commonly used to denote the equivalence ratio (as defined in chapter 4):
  24. ^ "Encyclopedia Astronautica: Lambda". Astronautix.com. Archived from the original on 2012-10-22. Retrieved 2012-12-18.
  25. ^ Geng, Hwaiyu (2021). Data center handbook: plan, design, build, and operations of a smart data center (2nd ed.). Hoboken: Wiley. p. 278. ISBN 978-1-119-59753-7. Commonly, the failure rate is assumed to be constant and written as λ.
  26. ^ Farrington, David; Kazemian, Lila; Piquero, Alex R., eds. (2019). The Oxford handbook of developmental and life-course criminology. The Oxford handbooks in criminology and criminal justice. New York, NY: Oxford University Press. p. 74. ISBN 978-0-19-020137-1. In order to evaluate acceleration and deceleration in criminal activity over the life-course, it is first necessary to determine the individual crime rate, or lambda (λ), for each offender of interest.
  27. ^ Wankat Separation Process Engineering 2nd ed, Prentice Hall
  28. ^ "Half-Life on Steam". store.steampowered.com. Valve. Retrieved 2017-01-02.
  29. ^ "Half-Life 2 on Steam". store.steampowered.com. Valve. Retrieved 2017-01-02.
  30. ^ Rapp, Linda (2004). "Gay Activists Alliance" (PDF). glbtq.com.
  31. ^ "1969, The Year of Gay Liberation". The New York Public Library. June 2009. Retrieved 17 November 2018.
  32. ^ Goodwin, Joseph P. (1989). "It Takes One to Know One". More Man Than You'll Ever Be: Gay Folklore and Acculturation in Middle America. Indiana University Press. p. 26. ISBN 978-0253338938.
  33. ^ Rapp, Linda (2003). "Symbols" (PDF). glbtq.com.
  34. ^ Haggerty, George E., ed. (2000). Gay Histories and Cultures: An Encyclopedia (Encyclopedia of Gay Histories and Cultures, Volume II) (1 ed.). London: Garland Publishing. p. 529. ISBN 0-8153-1880-4. OCLC 750790369.
  35. ^ Weisstein, Eric W. "Golomb-Dickman Constant Continued Fraction". mathworld.wolfram.com. Retrieved 2025-01-31.
  36. ^ Unicode Ancient Greek Numbers block.
  37. ^ "Thesaurus Linguae Graecae" (PDF). Stephanus.TLG.UCI.edu. Archived from the original (PDF) on 2011-07-16.
  38. ^ "Unicode Mail List Archive: RE: Greek letter "LAMDA"?".
  39. ^ Humchitt, Robyn; Jacquerye, Denis; King, Kevin (2023-07-17). "L2/23-191: Proposal to Encode 3 Additional Latin Characters for Wakashan and Salishan Languages to the Unicode Standard" (PDF).
  40. ^ "HTML 4.01 Specification. 24. Character entity references in HTML 4". World Wide Web Consortium.