What is Lambda: Definition and 110 Discussions

Lambda (; uppercase Λ, lowercase λ; Greek: λάμ(β)δα, lám(b)da) is the 11th letter of the Greek alphabet, representing the sound /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. In Modern Greek the name of the letter, Λάμδα, is pronounced [ˈlam.ða].
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 put the angle at the lower-left.
The HTML 4 character entity references for the Greek capital and small letter lambda are Λ and λ respectively. The Unicode code points for lambda are U+039B and U+03BB.

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  1. harrylin

    Problem with Bell's lambda - again

    I have been bugged for a long time by EPR-Bell's hidden function "lambda" (Bell1964: lambda is a hidden 'variable or a set, or even a set of functions'). Here's my latest problem with it. Triggered by some recent discussions which brought up papers, in which is argued (and claimed to be proved)...
  2. Jim Kata

    Turing Completeness Lambda Calculus

    I have been kind of trying to teach myself some ideas from CS. What does Turing completeness mean exactly? For example, Lambda Calculus is Turing complete. What does that mean and how do you prove that?
  3. S

    Simply Typed Lambda Calculus question - Beta Reduction

    Homework Statement Under the assumption that BETA is a closed term show that (λx.α)(β) and α[x→β] are logically equivalent. Homework Equations I'm sure I have to use β-reduction but I'm not sure how in this case: ⊢(λx.x)(β→α[x→β] The Attempt at a Solution
  4. T

    Coulomb Gauge invariance, properties of Lambda

    Homework Statement A gauge transformation is defined so as to leave the fields invariant. The gauge transformations are such that \vec{A}=\vec{A'}+\nabla\Lambda and \Phi=\Phi'-\frac{\partial\Lambda}{\partial t}. Consider the Coulomb Gauge \nabla\cdot\vec{A}=0. Find out what properties the...
  5. W

    PDE's Find the values of lambda (eigenvalues)

    the problem stays to find the values of Lambda for which the given problem has nontrivial solutions. Also to determine the corresponding nontrivial eigenfunctions. y''-2y'+\lambday=0 0<x<\pi, y(0)=0, y(\pi)=0 r^{2}-2r=-\lambda r=1±i\sqrt{\lambda+1}...
  6. M

    Characteristics of Feynman diagrams for correlators at a given order of lambda

    I've been given an action of S = -\frac{1}{2}m^2\phi^2 - \frac{\lambda}{3!}\phi^3 and the question then require drawing the feynman diagrams for the <\phi\phi> at order \lambda^2. I am told that there are 2 connected diagrams at one-loop order and one disconnected two-loop diagram and...
  7. marcus

    Reuter takes hit, Hamber says Lambda can't run

    As I see it, observational early universe cosmology is the main arena for testing quantum models of the start of expansion and the two main rival lines of research are Asym Safe QG and Loop. In the Asym Safe safe approach to quantum geometry both G and Lambda run with scale. In particular...
  8. O

    Lifetimes of kaon and lambda baryon in a bubble chamber

    Lifetimes of kaon and lambda particles in a bubble chamber (updated) Statement of the problem: This isn't quite a homework problem. I'm just having trouble with the concepts of this lab. I'm working on a lab report dealing with analysis of bubble chamber photographs of the decay of a kaon...
  9. L

    Are Mu and Lambda the Key to Solving this Line Intersection Problem?

    the lines l2[/SUB and l3 are given by l1 : r = 10i + j + 9k + μ(3i+j+4k) l2: x= (y+9)/2= (z-13)/-3 l[SUB]3 r= -3i-5j-4k + λ(4i+3j+k) where mu and lambda are parameters. d) Show that AC=BC A(4,-1,1) this was given, I calculated and got B as (5,-1,-2) and C (1,-2,-3) This I...
  10. F

    How to calculate CBR lambda vs age of universe?

    hello, I'm wondering how to calculate, even approximately for the relatively mature universe, what the CBR wavelength was as a function of age of the universe. I get that the CBR began during recombination, though have read different values for the black body temperature at that...
  11. G

    The role of lambda in Bell (1964) and experiments

    Moved from https://www.physicsforums.com/showthread.php?t=590249&page=3 to avoid confusion with the classical example in its OP. ThomasT and I are mainly discussing Bell (1964) here. The example discussed relates to 2 spin-half particles in the original EPR-Bohm example, see Bell (1964). The...
  12. R

    Find Lambda for Simple Walk on Z (Markov Chain)

    Homework Statement Find \lambda= \{\lambda_i\} with \lambda_0 = 1 if P(X_n=i+1|X_n=i) = p, P(X_n = i-1|X_n = i) = 1 - p, i \in Z, 0<p<1 Homework Equations \lambda P = \lambda The Attempt at a Solution I used my relevant equation to write out: (1-p)\lambda_0 + P\lambda_{-2} =...
  13. marcus

    What would happen to black holes if Lambda increased?

    Evidence has been mounting that cosmic acceleration behaves as if simply due to a constant of nature Lambda, a small intrinsic curvature term (reciprocal area) which appears naturally in the Einstein equation. For more about this, google "prejudices against constant" and have a look at the...
  14. H

    How Do You Integrate Complex Functions with Logarithmic Terms?

    Homework Statement Suppose a complex integral of the form \int_{-\infty}^{\infty}(\frac {1}{\alpha+i\lambda}-\frac{1}{\beta +i \lambda}) log(-i\mu\lambda) d\lambda where \alpha,\beta are arbitrary positive parameters and the sufficient condition for integrability (nonlatttice, etc) is...
  15. P

    What is the Significance of the Lambda Symbol in Transformation Matrices?

    Does the lambda symbol \Lambda_{\nu}^{\mu} refer specifically to the Lorentz transformation matrix or to any transformation matrix? Also, is it essential that it's enclosed in brackets \left(\Lambda_{\nu}^{\mu}\right) to indicate the entire matrix and not a particular component? Does it matter...
  16. marcus

    How close to constraining DE to simply be Lambda?

    what recent papers have you seen that deal with this question? Here is one I found by Paolo Serra et al (2009) http://arxiv.org/abs/0908.3186 No Evidence for Dark Energy Dynamics from a Global Analysis of Cosmological Data Paolo Serra (UC Irvine), Asantha Cooray (UC Irvine), Daniel E. Holz (Los...
  17. C

    Proving: If A is \lambda ^* -measurable, Then x+A is \lambda ^* -measurable

    Homework Statement Prove: If A is \lambda ^* -measurable and x\in \mathbb{R} ^n then x+A is \lambda ^* -measurable. My attempt at the proof is below, but i feel like it is not a correct proof. Homework Equations Notation: \lambda ^* is the lebesgue outer measure The Attempt at...
  18. S

    What is the difference between Lambda -> n + pi^0 and Lambda -> p + pi^- decay?

    The \Lambda baryon (quark content uds) decays into n + \pi^0 or p + \pi^-. In the case \Lambda \to p + \pi^-, the s quark decays into a u quark, releasing a W^- in the process (which subsequently decays into a \pi^- meson). What happens in the \Lambda \to n + \pi^0 case? (I tried Google, but...
  19. L

    Sign of Lambda cosmology homework

    In question 4 of this paper, I am trying to find the sign of \Lambda Since we have the vacuum einstein eqns G_{\mu \nu}=-\Lambda g_{\mu \nu} we can just contract to get R-\frac{4}{2} R=-4\Lambda \Rightarrow \Lambda=\frac{R}{4} So \Lambda will have the same sign as R Now given the...
  20. G

    3 linear equations, for what value lambda no solutions etc.

    Homework Statement \lambda x_1 +x_2=1 x_1 +2\lambda x_2+x_3=2 x_2 +\lambda x_3=1 The Attempt at a Solution The determinant is 0 for Lambda=0 and 1, found the infinite solutions associated with those to be (1,0,1)+t(-1,1,-1) and (0,1,2)+t(1,0,-1) I need to show a...
  21. C

    Do not understand setting lambda = 1 in proof of Euler's homogeneous function theorem

    As the title suggests, I do not understand why people set lambda = 1 in proofs of Euler's homogeneous function theorem. Euler's homogeneous function theorem is: i. Definition of homogeneity. Given a differentiable function, f(\vec x), that function is said to be "homogeneous of degree...
  22. K

    Sentences described in Lambda terms

    Homework Statement In a sentence like "Tina is tall", "Tina" is an entity (type e), "is" is an identity function and "tall" is an function of entities to truth values (e-> t or et). The denotations are something like this: Tina = Tina' , is = \lambdax.x and tall = tall'. So in lambda terms the...
  23. M

    Understanding the Airy Disk Equation: Lambda in Medium or Vacuum?

    hi the airy disk equation is d= 1.22 lambda / NA my question is: lambda is the wavelength in medium or in vacuum? thanks in advance
  24. A

    Were There Any Proposed Non-Expanding Cosmological Models Without Lambda?

    In most cosmology books it says that historically there is only two(some include here also the Minkowski spacetime but I'd rather leave it aside since it is a flat spacetime) non-expanding cosmological models with lambda, the Einstein 1917 model and the de Sitter model, this last was afterwards...
  25. M

    Calling all knights of the lambda

    i'm really going nuts here. I don't know much about lisp. however, I do know a thing or two about C. Knowing a lot about C and trying to learn lisp is like (to me) trying to learn italian when completely wasted out of your mind whilst taking a trip to italy but speaking fluent english anyway...
  26. D

    Understanding the Semantics of Lambda Calculus

    I do not understand the following extract on the semantics in the wikipedia article on lambda calculus: Is D supposed to represent the semantics of the lambda calculus? If so, how? I would really appreciate an explanation of the whole text. They say the set of functions from D into D has...
  27. L

    GRAVITATION by MTW: p.49, lambda or tau?

    At the very bottom of the page they have that the straight line, using the definition of a vector as the derivative of the worldline is given as: P(0) + \lambda(\frac{dP}{d\tau})_o But since the worldline, P(\tau) is paramtrized by \tau and not \lambda, then shouldn't the equation be...
  28. J

    Quark Structure of Baryons: Sigma & Lambda

    Hi this isn't actually a homework question more my own curiosity/confusion. They have the same quark constituents and http://en.wikipedia.org/wiki/File:Baryon_octet.png" for both but mass and decay rate are different, please explain. (if the lambda is an excited state of the sigma why isn't it...
  29. S

    Inductive reactance – Circular loop with N lambda standing wave

    Has anyone come across, or may be able to point me in the direction of a method for evaluating the inductive reactance of a circular loop when the wavelength of the applied signal is significantly less than the conductor length of the loop - and more particularly when; A. The driven...
  30. S

    Inductive reactance – Circular loop with N lambda standing wave

    Has anyone come across, or may be able to point me in the direction of a method for evaluating the inductive reactance of a circular loop when the wavelength of the applied signal is significantly less than the conductor length of the loop - and more particularly when; A. The driven wavelength...
  31. R

    Minimising for Lambda; Differentiation?

    Hi, so first post on this forum so I hope I'm doing everything good-as-gold! I've been twisting my head around a derivation of the uncertainty principle and I'm a little stumped on something that I feel I really should know. Hope someone would like to help. Certain things are defined at...
  32. I

    Wedge interference - solving for 'separation of fringes' without lambda

    Homework Statement plane plates of glass are in contact along one side and held apart by a wire 0.05mm in diameter, parallel to the edge in contact and 20cm distant. using filtered green mercury light, directed normally on the air film between plates, interference fringes are seen. calculate...
  33. C

    Eliminating Lambda to Solve Question 2(b) of Physics Homework

    Homework Statement Hello , Please look at question 2 (b). http://phstudy.technion.ac.il/~wn114101/hw/wn2010_hw05.pdf I got that the lagragian is the potential energy (as in part a of the question) How Do I eliminate the lamda so I can write the U (wave) as requested? Or In Other word...
  34. H

    Phase differences of light and multiples of lambda

    Hello All, My new physics professor literally talks about nothing but his childhood and women during lecture halls. We seriously have taken half of a page of notes throughout this entire semester, and our book doesn't explain the content very well. I was wondering if any of you could help me...
  35. I

    Finding Lambda 4 for mechanical harmonics

    Homework Statement I am trying to find the equation for lambda four for mechanical harmonics. Homework Equations I know that lambda1=2L, lambda2=L, lambda3=2L/3, but neither google nor my textbook have the equation for lambda4! The Attempt at a Solution I have searched my physics...
  36. R

    Solving a 3x3 Matrix with Lambda: A Tutorial

    Homework Statement I am having trouble figuring out lambda for the 3x3, I have only done 2x2. My matrix: 4 1 4 1 7 1 4 1 4 The Attempt at a Solution I know that when I add lambda (L) in it looks like 4-L 1 4 1 7-L 1 4 1 4-L When I do a 2x2, I would just cross multiply as...
  37. F

    QCD \Lambda Parameter: Definition & Its Role in Non-Perturbative QCD

    I have a simple sounding question about QCD and its scale parameter \Lambda: The general consensus amongst field theorists is that QCD is not a well defined theory by its Lagrangian and the quantization procedure alone. One needs an additional parameter \Lambda, which sets the scale of...
  38. M

    Find Thickness of Oil Film on Water, \lambda = 550 nm

    Homework Statement A thin film of oil (n = 1.50) floats on water (n = 1.33). If the film appears yellow-green (\lambda = 550 nm) when viewed at normal incidence, how thick is it? Given: n_{f} = 1.50 n_{water} = 1.33 \lambda_{0} = 550 nm \theta_{i} = 0 Required: Thickness (d)...
  39. B

    Type Lambda Bar in Word 07: Quick & Easy Way

    Wasn't sure which forum to put this in... Is there a way to type lambda bar in word 07? Really basic thing. I'm sure there must be a way to do it. I have just been using \lambda and then formatting it with strikethrough. It doesn't look very professional though. The bar should be a little...
  40. S

    Finding Uncertainty in Lambda Using Michelson-Interferometer

    I'm during an experiment involving the Michelson- Interferometer, now i need to find the uncertainty for lambda using the equation. 2 (path length difference) = N (lambda) Now I no the above equation can be changed to 2(path length difference)/ N = Lambda; and from their the corresponding...
  41. T

    Another attempt to understand min/max value of lambda

    i read and translated this "article" from a book that shows a new concept to me. infinity small and infinitely large function. can you explain to me using those terms http://img262.imageshack.us/img262/1610/97335712sc3.gif why in certain case we use maximum as the value for lambda...
  42. H

    How Can Lambda Calculus Implement List Tripling with Recursive Functions?

    Homework Statement I have two lambda expressions. Triblelist should trible every element in a list eg 1234 to 111222333444. N_th_list should do it n times. The problem is to give some value of n to n_th_list to receive triblelist. How can you do it? Help is really appreciated! Homework...
  43. stevebd1

    How Does the Cosmological Constant Λ Define the Cosmic Scale of Space-Time?

    Apparently, one way to understand the effects of Λ on space-time is to apply the following equation which provides the invariant cosmological length-scale (while Planck length is the invariant quantum length-scale that replaces zero), length-scale being a measure of the space-time sheet-...
  44. rocomath

    What is the significance of Eigenvalues in a 2 by 2 matrix?

    Assuming 2 by 2. Ok, I'm asked to find the Eigenvalues. How do I know which should be lambda 1 and lambda 2? I can find the lambda's easily, but does it matter which is 1 or 2? It becomes important when I'm asked to diagonalize. A=S\Lambda S^{-1}
  45. G

    Solving a Wave Equation with 0 < \lambda < 1

    Homework Statement if 0<\lambda<1 and f(x) = x for 0<x<\lambda\pi and f(x) = (\lambda/(1-\lambda))(\pi-x) for \lambda\pi<x<\pi show that f(x)= 2/(\pi(1-\lambda))\Sigma(sin( n\lambda\pi)sin(nx)(/n^{}2 Homework Equations The Attempt at a Solution am i right in saying that...
  46. K

    Gel electrophoresis - eco r1 digest with lambda

    just want to know why if there are six fragments present in an Eco R1 digest of lambda then why are there only five bands visible on a .8% agarose gel? so where have the 21.2 kbp gone? is it to big to migrate therefore has not show up on the gel? can someone explain to me please? thankyou
  47. jal

    Research on Lambda Evolution: Collider Physics & Cosmology

    Does lambda evolve? Some people have been working on this question. http://arxiv.org/abs/0801.1334 Collider Physics and Cosmology Authors: Jonathan L. Feng (Submitted on 8 Jan 2008) ==== http://arxiv.org/abs/0707.3778v1 Renormalization group running cosmologies - from a scale...
  48. E

    Edward Witten on LQG for lambda > 0, QG does not exist in any dimension

    Edward Witten on LQG "for lambda > 0, QG does not exist in any dimension" arxiv.org/abs/0706.3359 - page 6 "for lambda > 0, QG does not exist in any dimension" ...the reason... "cannot provide precise observables" As I understand Edward Witten, deSitter space is not stable but metastable, and...
  49. P

    Lambda Warp Drive: Locally Manipulating for Alcubierre Warp Bubble

    Lambda Warp Drive... Here's an interesting paper, http://arxiv.org/abs/0712.1649 It's about "locally manipulating lamdba" to get something similar to the Alcubierre warp "bubble". I love wild stuff like this...
  50. C

    Decay equations: Given A0 &amp;amp;amp; At, find half-life, lambda and N0

    [SOLVED] Decay equations: Given A0 &amp;amp;amp; At, find half-life, lambda and N0 Homework Statement This is from Advanced Physics by Adams & Allday, spread 8.13 Question 5. The activity of a particular source falls from 5E8 Bq to 2E7 Bq in 20 minutes. a) What is the half-life and decay...
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