Lambda Definition and 110 Threads

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. T

    What does lambda in nuclear decay mean if it is big?

    I am thinking about lambda, the nuclear decay constant and what it actually means. I have built spreadsheet models looking at decay using lambda to determine the decay for each time period and then comparing the number left to that determined by using e ˆ- lamda x time. These are my...
  2. M

    Finding the eigenspace for this value of lambda

    For this, I don't understand how they solved, Because we would have to take the inverse of both side which would give the inverse of the matrix ##2 \times 2## matrix on the left hand side which dose not have an inverse. Dose anybody please know how they did this? Many thanks!
  3. M

    Finding the value of lambda so that two lines are parallel

    For this (ii), The solution is ##\lambda = \frac{4}{3}##, however when I tried solving the problem I did not get their answer. Dose somebody please guide me to their solution and tell me what I did wrong with my method below: ##\textbf {PR} = -3\hat i + 6\hat j - 2\hat k## ##\textbf {RS} =...
  4. ergospherical

    Python Speed of function vs lambda calls in python

    An observation I made earlier- something like def f(...): ... return ... def g: ... = f(...) was quite a bit slower than doing def g: f = lambda ... : ... ... = f(...) any reasons why?
  5. E

    Probability of Negative Value in Sz 1/2 Spin System w/ Lambda 1 & 2

    Will the probability to provide a negative value of a Sz 1/2 spin system always be 0? If lambda 1 = hbar/2 and lambda 2 = -h bar/2 ?
  6. Evo

    COVID Lambda variant shows vaccine resistance

    Well, if the Delta variant wasn't enough, now this seems to be rearing it's head. Also continued https://news.yahoo.com/delta-infections-among-vaccinated-likely-192553854.html
  7. A

    A Understanding Integrating Lambda with l1(y) and l0(y)

    I have the following function l1(y)=c1. Integrating lambda(t) = l1(y + a1t) from 0 to t gives (I/a1) (L1(y + a1t) - L1(y)), where L'1(x) = l1(x). Now I don't understand why that is. Similarly, I have the following function l0(y)=c0/y. Integrating lambda(t) = l0(y - a0t) from 0 to t gives -...
  8. C

    Finding inverses of two functions in Lambda Notation

    I found the following functions ( In lambda notation ) to be injective, and now I am trying to find the inverse functions for them ( the inverse for the Image of ## f ## ) but I am stuck and I need help: 1. ## f = \lambda n \in \mathbb{N}. (-1)^n + n^2 ## 2. ## f = \lambda g \in \mathbb{R}...
  9. J

    Find the phase difference in terms of d, lambda, theta

    So in figure 4.8 the path difference between the two waves is d*sin(theta), then is the phase difference just (d*sin(theta)*2*pi)/lambda?
  10. lola1227

    Beats and Resonance - How to Find the Length With only Frequency?

    So, my thinking was that we use the formula V=f(lambda) and substitute the f so, V = 440(lambda) but then i don't have another number to cancel or rearrange by. And since closed air columns have the fractions of 1/4, 3/4, and 1 1/4 (5/4), we could divide by those?
  11. P

    Evanescent Waves in near field for aperture > lambda (diffraction)?

    We have two different accepted formulas for the far field and near field respectively. I want a numerical program that works for both, furthermore I want to use it to calculate power through the aperture after confirming it in the far field vs near field. I start off by treating the far field...
  12. S

    Find the linear charge density lambda and the radius of a charged semicircle

    Electric field for the semi-circle $$E = - \frac {πKλ} {2R} $$ In this case E is equals to 10 N/C Electric field for the straighten wire $$E = 2Kλ * ( 1 - \frac {2y} {\sqrt{4y^2 + L^2}})$$ In this case E is equals to 8 N/C What I'm searching is R, λ, and the length of the wire, so I think...
  13. H

    Formula for calculating the wavelength of sound in interference

    Here is a diagram of experiment: Here is the results: Average distance between nodes (cm) Frequency (hz) Line 1 Line 2 Line 3 500 253 176 105 1000 333 438 None My analysis: ƛ/2=D ∴ƛ=2D where ƛ=wavelength (cm) D=distance between nodes/antinodes (the average,cm) 500hz: Line 1...
  14. T

    I Lambda CDM Model and Spatial Flatness

    [Moderator's note: Spun off from previous thread due to topic/level change.] Which current model? Doesn't "spatially infinite" imply Euclidean flatness which as far as I'm aware of requires ##\Omega = 1##? The theories of inflation don't predict that. They predict a value for ##\Omega## which...
  15. V

    I Understanding q: Lambda & S in the Equation

    What is this formula? q=λ⋅S⋅∪_x What does s and lambda mean?
  16. Davephaelon

    I Particle track resolution of the positive lambda particle

    The positive lambda has a quark composition udc, and a lifespan of 2 x 10 minus 13 seconds. When this particle is created in a collision, inside a modern detector, how long will its track be? At near the speed of light, its lifetime would allow it to traverse less than a tenth of a millimeter...
  17. A

    MHB Best procedure to determine Lambda to calculate Poisson probability

    What is the best procedure to determine Lambda to calculate the Poisson probability? Say I want to calculate P(X ≥1) of an accident occurring next day. For this I would calculate the average of daily accidents and divide it by 10. The question is, should I take the previous 10 days? Or calculate...
  18. DoobleD

    I Why is the number of wavelets in a slit = slit length / lambda

    Hi folks, Huygens principle is not really new to me but I just realized there is something I don't understand with it. Take a single 1D slit with a coherent incident plane wave. It seems that the number of wavelets in the slits is ##n = l/\lambda##, where ##l## is the length of the slit, and...
  19. Z

    Finding Eigenvalues: List of possible solutions for Lambda

    Homework Statement I got a solution for finding eigen values. It evaluates to: (Lambda)^3 -12(lambda) -16=0, Then it that the list of possible integer solutions is: +-1, +-2, +-4, _-8, +-16 (i.e. plus minus 1, plus minus 2 and so on). I can't understand, why he says list of possible solution...
  20. R

    Lagrange multipliers: help solving for x, y and lambda

    Homework Statement Find the local extreme values of ƒ(x, y) = x2y on the line x + y = 3 Homework Equations ∇ƒ = λ∇g The Attempt at a Solution 2yxi+x^2j = λi + λj [2yx=λ] [x^2=λ] [x+y=3] [2yx=x^2] & [(2y)+y=3] [2y=x] & [y=1]...
  21. M

    A What is the significance of the variable lambda in Bell's locality assumption?

    A side question. Can one be a bit more specific about what ##\lambda## is? He says that it doesn't matter and it could be many things, and he treats it as a single continuous variable, but then he integrates over it. So whatever the set of lambdas is, it has to be at least a measure space, no...
  22. Cocoleia

    Lambda decay, momentum of the pion and proton

    Homework Statement I have a lambda decaying into a pion and a proton. The lambda is moving with velocity 0.9c and I know the mass of the lambda as well as the pion and proton (these are known constants). I need to find the momentum of the pion and the proton after the decay happens. Homework...
  23. S

    Y-intercept of a lambda square VS tension of standing wave

    Hi all! I am doing an experiment where we create a standing wave by attaching a string to a hanging mass at one end and to a string vibrator at the other (the string passes through a pulley). When plotting the graph, the slope is inevitably 1/(u*f^2) where u is the linear density and f the...
  24. Iftekhar Uddin

    How an Electric Field is affected by an Insulator

    I looked through this forum post for an answer to my problem. It gave me enough insight to try and come to some conclusions but I'm still confused on some parts here and there about how I got my final answer. 1. Homework Statement A uniformly charged, straight filament 7.70 m in length has a...
  25. V

    Parity violation in lambda baryon decay

    Homework Statement In the weak decay of the lambda baryon to a proton and pion, parity is not conserved, allowing for s and p waves in the orbital wave function of the pion-proton system. Using non-relativistic wavefunctions, find the angular distribution of the protons relative to the...
  26. CMJ96

    What happens at the lambda point of superfluid Helium?

    Homework Statement 2. Homework Equations are given in the above picture 3. The attempt at the solution In part a) I simply rearranged the other expressions given and subbed them into the relationship for relative velocity and came out with Vns= Qdot/ρsT(1- ρn/ρs).Then in part b) I started by...
  27. T

    I Semileptonic Lambda baryon decay suppression

    Hi there, I'm currently studying the decay modes of the Lambda baryon (uds). According to literature, the decay mode with leptons (e.g. Lambda -> p + e- + anti ve) is suppressed against the decay modes with pions (e.g. Lambda -> p + pi-) by a factor of about 10^-4. I was looking for the reason...
  28. Chronos

    I Einstein & Lambda: 1917 Static Model Review

    This paper; https://arxiv.org/abs/1701.07261, Einstein's 1917 Static Model of the Universe: A Centennial Review, offers an informative insight into the mind of Einstein and, to large extent, his motivation for adding the cosmological constant to his field equations. Interestingly, both the...
  29. K

    I PDE, heat equation lambda =,<,> 0 question

    So I have been studying solving separation of variable, heat equation and came across 2 set of lambda equation. and lambda = 0 have the same equation. Is it different?
  30. F

    I Suppression of semileptonic lambda decays

    Confused by the branching ratio of uds ---> proton + e- + neutrino compared to uds ---> proton + pion (or neutron + pion). In both cases an W boson is being produced as the strange quark changes flavour, and it is either decaying to leptons or first generation quarks - why is the leptonic...
  31. wolf1728

    Radioactive decay - the difference between "lambda" and "k"

    When reading about radioactive decay, I see two types of decay constants: λ and "k". From what I have interpreted, k = ln (.5) / half-life whereas λ = ln (2) / half-life. Have I defined these correctly? If this is so, the difference between the two is slight. When putting these into equations...
  32. X

    I Find Lambda Baryon Decays Cross Section Ratio

    I've been asked to find the ratio between the cross sections of the two folowing decais: Using the CKM matrix and the feynman diagrams for both decays, I reach the conclusion that the Ratio is exactly 1. However, consulting this document...
  33. G

    I Could "dark matter" be regions where Lambda is lower?

    We assume that Lambda, the cosmological constant or "dark energy" is constant in all of spacetime (at least all of space). But what if it was not? A lower value of Lambda in a certain region of space would mean that space's tendency to expand there is lower, and that might have the appearance...
  34. BiGyElLoWhAt

    Python Solve Lambda Error in Python Homework

    Homework Statement Somewhat irrelevant, but we need to simulate the redshift for a star system. Pretty open ended. Single star, binary, whatever. The problem is this: TypeError: <lambda>() takes at most 1 argument (5 given) And upon searching, most people who get this error have a function that...
  35. annoyingdude666

    Why infinite conducting rod - Gauss's Law , uses lambda?

    hi, i still don't understand why infinite thin-walled cylindrical shell or conducting rod use lambda rather than sigma ? lambda = C/m ,,, sigma = C/m^2 i mean when we look at conducting rod, the charges inside the conductor is zero, so the charges spread on the surface of conducting rod(have...
  36. M

    Determine the change in path length

    Homework Statement A ripple tank is setup and a point selected on the second nodal line. determine the change in path length from two wave sources if they are in phase and separated by 2cm and the wave length is 5cm Homework Equations not really sure of what equations to use? The Attempt at a...
  37. lep11

    Derive error formula for Lambda (25 C)

    In physics lab course I measured equivalence conductivity of NaCl in infinite dilution Λ0 as a function of temperature T. So I have observations (T, Λ0) and fitted a line using the least squares method in Ms excel (lol :oldbiggrin:). The formula of the line is Λ0(T)=c0+c1T, where c0 and c1 are...
  38. B

    Find Lambda from this arbitrary triangle

    Folks, I am puzzled how one obtains equation 3.2.31 based on the schematic as attached! Can you help? Is there an online source I can refer to to learn how to obtain angles and magnitudes of complex schematics? Thanks
  39. HanningWu

    How could this,Sigma0 decay into Lambda and gamma, happens?

    I found an article, titled Electromagnetic Decay of the Σ0(1385) to Λγ , in the arXiv telling that the reaction Σ0→Λ+γ can happen through electromagnetic interaction. However, if I examine the conservation of parity. Parity on the left side is even(P(Σ0)=+), but that on the right side is...
  40. J

    MHB Β reduce a redex - Lambda Calculus.

    As far as I understand it to reduce the formula is: $(\lambda x.M)N -> β M[N\x]$ Where: $β M[N\x]$ means M with every free x replaced by N. I'm stuck on this one though. $(\lambda x. \lambda y.yx)(\lambda x.xy)$ I know that the answer should be $\lambda z.z(\lambda x.xy)$ but I can't get it.
  41. marcus

    Simple no-pressure cosmic model gives meaning to Lambda

    The size of the universe (any time after year 1 million) is accurately tracked by the function $$u(x) = \sinh^{\frac{2}{3}}(\frac{3}{2}x)$$ where x is the usual time scaled by ##\sqrt{\Lambda/3}## That's it. That's the model. Just that one equation. What makes it work is scaling times (and...
  42. Jameson

    MHB If matrix lambda is diagonal with entries 0,1 then lambda squared is lambda

    This is part of a proof I am working on involving idempotent matrices. I believe it is true that for any real symmetric matrix A ($n \times n$ for this), even with repeat eigenvalues, it can be decomposed into the form $A=Q \Lambda Q^{T}$. For the matrix I'm working on, we assume that all...
  43. C

    Why was the flat, no Lambda Universe previously favoured?

    In this paper they state that a flat universe with no dark energy (##\Lambda = 0##) was favoured before the measurement results -- as they convey in the paper -- implies that the universe can not be flat and have a zero cosmological constant simultaneously. What reasons were there, before this...
  44. DiracPool

    Understanding Lambda Mu Nu Prime and Its Indices

    I'm trying to do some GR self-instruction through a variety of video lectures and thought this would be a good place to seek clarification on the inevitable thorny issues. I've tried this before and didn't make it too far, but I'm trying to get back on the horse, so to speak, and give it...
  45. H

    Nernst equation - Lambda Sensor

    Hello everyone, I am not sure if this question is comfortable in the chemistry section but I will try my luck. I have been dealing with lambda sensors a little bit and when I look at the characteristic voltage lambda curve I keep asking myself why it flatens out when getting into the rich...
  46. reddvoid

    Cadence Inverter layout lambda based design

    I am creating layout of cmos inverter in cadence virtuoso using 0.18um technology. channel length is 2Lambda = 0.18um I read that contact should be 2Lamda X 2Lambda that is 0.18um X 0.18um right but my LVS Check is throwing error telling that contact must be 0.22umX0.22um whats might be the...
  47. morrobay

    Disconnect With Inequality Realism Assumption And Bells' Lambda

    Bell, QM Ideas - Science 177 1972 :" Strictly, however. a hidden variable theory could be non-deterministic; the hidden variable could evolve randomly (possibly even discontinuously) so that their values at one instant do not specify their values at the next instant" From the locality...
  48. C

    What kinds of particles can decay to Lambda hyperons?

    Such as ##\Sigma^0 \to \bar{\Lambda}\gamma\gamma##. I want to make a complete collection of all these decay modes, i.e. ##X \to \Lambda / \bar{\Lambda} + \cdots##. At least some major channels.
  49. J

    MHB Value of lambda in quadratic equation

    If $a,b,c$ are the length of the sides of an scalene triangle, If the equation $x^2+2(a+b+c)x+3\lambda\left(ab+bc+ca\right) = 0$ has real and distinct roots, Then the value of $\lambda$ is given by Options:: (a) $\displaystyle \lambda < \frac{4}{3}\;\;\;\;\; $ (b)$\displaystyle...
  50. TheDemx27

    Where Can I Learn Lambda Calculus?

    If anyone knows of any sites that have lectures on lambda calculus it would be very helpful if you could post them. Wikipedia is a bit too rigorous for me on this subject. Thanks.
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