Derivation Definition and 1000 Threads

In cryptography, a key derivation function (KDF) is a cryptographic hash function that derives one or more secret keys from a secret value such as a main key, a password, or a passphrase using a pseudorandom function. KDFs can be used to stretch keys into longer keys or to obtain keys of a required format, such as converting a group element that is the result of a Diffie–Hellman key exchange into a symmetric key for use with AES. Keyed cryptographic hash functions are popular examples of pseudorandom functions used for key derivation.

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  1. E

    Question about the Derivation of the Gravitational Law

    The derivation of the law have been put up in the forums but I have a question regarding its derivation. I understood everything from the assumptions to the application of Newton's Third Law, but I got stocked at this step: \frac{m}{k} = \frac{M}{k'} . This is similar to \frac{C}{M} =...
  2. S

    Derivation of Bernoulli's equation via Newton's second law

    In the derivation on Wikipedia, it says the following ## \frac{dv}{dt}=\frac{dv}{dx}\frac{dx}{dt}=\frac{dv}{dx}v = \frac{d}{dx}[\frac{v^2}{2}] ## How do they go from the second to last to last equation? I've been trying to understand, but I think I'm just looking over something incredibly simple.
  3. Fosheimdet

    Stuck on the derivation of pV^gamma=c

    I have been tearing my hair out for a while over a step in the proof of the relation pV^{\gamma}=constant. The textbook has assumed that we are dealing with an ideal gas undergoing an adiabatic process. Therefore dQ=0 and we get $$C_vdT + (c_p-c_V)\left(\frac{\partial T}{\partial...
  4. M

    Bjorken Drell derivation - Lorentz transformation

    I'm trying to derive (14.25) in B&J QFT. This is ##U(\epsilon)A^\mu(x)U^{-1}(\epsilon) = A^\mu(x') - \epsilon^{\mu\nu}A_\nu(x') + \frac{\partial \lambda(x',\epsilon)}{\partial x'_\mu}##, where ##\lambda(x',\epsilon)## is an operator gauge function. This is all being done in the radiation...
  5. koustav

    Derivation of Wiens Displacement & Distribution Laws from Thermodynamics

    derivation of wiens displacement law and wiens distribution law from thermodynamic principle.but not from Plancks law
  6. A

    Deriviation for law of conservation of energy

    I'm a bit confused about how the work-energy theorem for a single particle can be extended into the general law of conservation of energy for the macroscopic system, particularly the point where we divide the kinetic energy of the system into macroscopic kinetic energy and internal kinetic...
  7. DivergentSpectrum

    Helmholtz theorem derivation question

    http://en.wikipedia.org/wiki/Helmholtz_decomposition#Derivation how do we go from to also on the next step ∇' just means the gradient with respect to r', right? Also, why do i have to use the dirac delta function? i thought it was only used to deal with discontinuities? also when we say...
  8. U

    Deriving Equation 4.8 in Special Relativity: Tips and Tricks

    Taken from Steane's "Relativity made relatively easy" equation 4.8 I have been trying to show (4.8) using these relations earlier on in the book: Tried most means (rearranging, taking dot products) but can't seem to make it work. Is there an easy method I'm missing out?
  9. freddie_mclair

    Relativistic kinetic energy derivation (from Work expended)

    Hi, I'm trying to get the relativistic kinetic energy, ## T ##, from the work expended, ## W ##, (assuming that the body is at rest initially) and I'm doing it like this (in 1D): \begin{equation} W = T = \int F ds = m \int \frac{d(\gamma u)}{dt}u dt = m\int u d(\gamma u) \end{equation} Where...
  10. S

    A direct derivation of the speed transformation formula?

    In SR the speed transformation formula (in response to a change of inertial frame of reference) is usually derived from the Lorentz transformation of space and time coordinates. I would like to find a direct derivation starting from the existence of a maximum speed limit (c) in respect to any...
  11. S

    Derivation Problem (Magnetic Field)

    Homework Statement Hi, I'm having trouble solving this problem: I can't seem to get to the right derived formula. The one selected is wrong. I'm still attempting to solve this. Homework Equations B= 8 M0 N (I - I0) 1251/2 a e = 2V m B2 R2 The Attempt at a Solution...
  12. R

    Quick question regarding a step in a bra ket derivation

    In class we went through the derivation of the energy of a perturbed system, I've dug my old notes out and found a bra ket derivation of the same thing, there's just one step that doesn't look right and was wondering if someone could tell me if its a misprint or actually correct (and why)...
  13. PcumP_Ravenclaw

    Derivation of mapping for isometric rotation about i

    Homework Statement 2. Find the formulae as in (3.4.1) for each of the following: (a) the rotation of angle π/2 about the point i ; Homework Equations The equation 3.4.1 is given below. ## f(z) → z*a + b ## where a, b and z are all complex numbersThe Attempt at a Solution I have attached my...
  14. SalfordPhysics

    Derive Entropy Change for Ideal Monatomic Gas

    A Monatomic gas passes from state 1 (pressure p1, volume V1) to state 2 (p2, V2). Derive an expression for the change in entropy of a monatomic ideal gas. The required final equation is: ΔS = Cv ln(T2/T1) + nRln(V2/V1) In my attempt, I am retrieving ΔS = Cv ln(T2/T1) + Rln(V2/V1) i.e.; the...
  15. PcumP_Ravenclaw

    Derivation of rotation isometry on the complex plane

    Dear all, can you please verify if my derivation of the algebraic formula for the rotation isometry is correct. The handwritten file is attached. The derivation from the book (Alan F beardon, Algebra and Geometry) which is succinct but rather unclear is given below. Assume that f (z) = az + b...
  16. C

    Rüchardt experiment equation derivation

    Homework Statement The piston is initially at the top of the tube and the air pressure is equal to P0 (ambient pressure). After it is released and drops to location x, the pressure can be computed as follows. Assuming the air is an ideal gas with constant specific heats and assuming the process...
  17. S

    Derivation of Sabine's formula for reverberation time

    https://courses.physics.illinois.edu/phys406/Lecture_Notes/P406POM_Lecture_Notes/Derivation_of_the_Sabine_Equation.pdf I can't understand anything from the above link. Is there any alternative way to derive Sabine's formula. I searched in google but coundn't find anything.
  18. J

    Derivation of Vibration equation

    Can somebody please tell me what should be present in the free body diagram for this system below. Also please mention the arrow details like which direction each force in the free diagram should be acting in. I really need to understand this concept...
  19. V

    Understanding Planck Scale Derivation: Energy, Length, and Uncertainty

    I see that Planck scale of mass-energy is related to the corresponding length scale by application of the uncertainty principle. What is not clear for me is how we find either energy or length scale to compute the other one? What goes wrong if we assume a higher energy level than the Planck...
  20. F

    Derivation of Planck Radiation Formula

    I am having some issues with the derivation of the Planck Radiation Formula, as for instance given in http://hyperphysics.phy-astr.gsu.edu/hbase/mod6.html . My point is that the assumption of cavity modes implies the formation of standing waves inside the cavity walls. In most situations in...
  21. A

    Understanding the Larmor Formula: The Role of Field Line Connections

    Homework Statement I need to derive this formula, and I'm basing it upon the following method (this has the diagram which I will be talking about below) http://isites.harvard.edu/fs/docs/icb.topic1214926.files/Purcell-appendix-B.pdf The Attempt at a Solution I'm fine with everything apart from...
  22. K

    How Do I Apply Multivariable Calculus to Thermodynamics Problems?

    Homework Statement Homework Equations au/as=T au/av=p S/R=ln[(v-b)(u+a/c)^2] The Attempt at a Solution 1/T=1/au/as=as/au S=ln[(v-b)(U+a/v)^2]R as/au=[(v-b)2(U+a/v)(1)]R/[(v-b)(U+a/v)^2]=2R/(U+a/v)=1/T T=(U+a/v)/2R U=2RT-a/v au/av=-P au=-Pav integrate au to get u=-pv+c u=-pv+c=2RT-a/v...
  23. M

    Radius of convergence derivation

    Hi, I am likely just missing something fundamental here, but I recently just revisited series and am looking over some notes. In my notes, I have written that if ## \lim_{x \to +\infty} \frac{a_{n+1}}{a_n} = L ## Then ## | x - x_o | = 1/L ## But shouldn't the correct expression be $$ | x -...
  24. L

    Derivation of waveguide condition for two light rays

    How did they derive equation (6)? I don't like how they say -Φm instead of Φm, but that aside, I get that both rays 1A and 2A' travel the same distance, but AC incurs a phase change due to total internal reflection (-Φm) and it travels AC from there. Meanwhile, A'C is the distance the other...
  25. M

    Derivation of parametric Equations?

    Homework Statement Hi, so confused abou this question that I probably haven't even posted it in the correct section.Here's the question. A wheel of radius ,r, is situated at the top of a ramp having an angle θ = π/6 rad. At t= 0 the wheel is at rest with its centre at coordinates (0,r) and...
  26. GoodTimes

    Deriving Velocity and Acceleration from Position Vector r(t)

    Hello, I am new here, glad I found this Forum :0) I am german and english is not my mother-tongue, so sorry in advance for any language-related mistakes 1. Homework Statement i don't know how to make a vector arrow on a letter so I declare a v for vector as the following...
  27. L

    Where does the equation for Gaussian beam divergence come from?

    For a Gaussian beam, which has 86% of its power within its beam diameter (spot size 2w0), I've read that beam (angular) divergence is given by 2θ = 4λ/(π[2w0]) Where does this come from? I hate memorizing equations. It makes me feel stupid.
  28. H

    W=F.dx rate of change of x approaches to zero?

    In the integration of Force with respect to displacement (W=∫F.dx), is that true if the rate of change of displacement approaches to zero? My teacher said the one which approaches to zero is the rate of change of time. But If I arrange the formula, I will get F=dW/dx then F= lim Δx→0 ΔW/Δx...
  29. B

    Confused on escape velocity derivation

    I'm confused on how you get the formula v=root(2GM/R²). I know you can use work=forcexdisplacement (W=Fd) so F=W/d. W=½mv² and R=d. Hence, F=½mv²/R Equate that to F=GmM/R² and rearrange to get v=root(2GM/R²). That makes sense as it involves the kinetic energy needed/work done in reaching orbit...
  30. I

    Thermodynamics: derivation for q @ constant P

    general equation of q in terms of S,T $$q=d(ST)=SdT+TdS$$deivation of ΔS at constant pressure(in terms of heat cap C_p: $$dq=C_{p}dT=TdS$$ $$\frac{C_{p}}{T}dT=dS$$ $$C_{p}ln(T_{f}/T_{i}=ΔS$$ why do we keep T constant on TdS side?
  31. thegreengineer

    Derivative as a rate of change exercise

    Homework Statement A police car is parked 50 feet away from a wall. The police car siren spins at 30 revolutions per minute. What is the velocity the light moves through the wall when the beam forms angles of: a) α= 30°, b) α=60°, and c) α=70°? This is the diagram...
  32. C

    The simplest derivation of position operator for momentum space

    Might be simple but I couldn't see. We can easily derive momentum operator for position space by differentiating the plane wave solution. Analogously I want to derive the position operator for momentum space, however I am getting additional minus sign. By replacing $$k=\frac{p}{\hbar}$$ and...
  33. kq6up

    Straightforward and Rigorous Rocket Thrust Derivation

    I have noticed many of the thrust derivations in textbooks I have seen do not do a straightforward derivation of rocket thrust. The all seem to use the same trick with infinitesimals in a sort of binomial form. For reference: Taylor, "Classical Mechanics" Pg. 85. I am working on a rigorous...
  34. F

    Derivation of fluctuations in canonical ensemble

    Homework Statement Statistical Mechanics by Pathria. Problem 3.1 Homework Equations (1) <(△nr)2>=<nr2>-<nr>2=(wrd/dwr)(wrd/dwr)lnΓ, for all wr=1 How to derive above equation from these equations? <nr>=wrd/dwr(lnΓ), for all wr=1 <nr2>=(1/Γ)(wrd/dwr)(wrd/dwr)Γ, for all wr=1 (2) Also, if you...
  35. A

    Derivation of the CHSH inequality

    Bell's 1971 derivation The following is based on page 37 of Bell's Speakable and Unspeakable (Bell, 1971), the main change being to use the symbol ‘E’ instead of ‘P’ for the expected value of the quantum correlation. This avoids any implication that the quantum correlation is itself a...
  36. J

    How Does Calculus Explain the Changes in Notation in Rocket Equation Derivation?

    Homework Statement Hi, need some help trying to understand calculus derivation of the rocket equation. If someone who be so kind as to look at the attachment where it is all laid out. Homework Equations All equations are listed in the attachmentThe Attempt at a Solution I have had a good go...
  37. genxium

    [Special Relativity]Questions on Maxwell Equations' Derivation

    In Einstein's paper section 6 (I'm reading an English version online: https://www.fourmilab.ch/etexts/einstein/specrel/www/), it's said that one of the Maxwell Equations in frame K \frac{1}{c}\frac{\partial X}{\partial t} = \frac{\partial N}{\partial y} - \frac{\partial M}{\partial z}, where <X...
  38. _N3WTON_

    How Do You Solve an Annuity Differential Equation?

    Homework Statement Solve the annuity problem: \frac{dS}{dt} = rS + d S(0) = S_0 Homework Equations Integrating factor method equation Future value of an annuity equation (this should be the final answer): S(t) = S_0e^{rt} + \frac{d}{r}(e^{rt} - 1) The Attempt at a Solution Ok, I am...
  39. 3

    Angular momentum - kleppner and kolenkow - derivation or definition?

    I am reading "An Introduction to Mechanics" by Kleppner and Kolenkow (2014). On page 241 is the definition of the angular momentum: "Here is the formal definition of the angular momentum $$\vec{L}$$ of a particle that has momentum $$\vec{p}$$ and is at position $$\vec{r}$$ with respect to a...
  40. J

    Two Blocks and a pulley (Equation derivation)

    Homework Statement Look at the figure below. Derive the formula for the magnitude of the force F exerted on the large block (mC) in the figure such that the mass mA does not move relative to mC. Ignore all friction. Assume mB does not make contact with mC. Homework Equations F = ma...
  41. D

    Implicit differentiation; reproducing textbook derivation

    Homework Statement (The fourth equation is the central one) first, we have \frac{1}{r}=\frac{a}{b^2}(1+ecosθ) and b^2=a^2(1-e^2) now using these two, we transform acosψ=ae+rcosθ into (1-ecosψ)(1+ecosθ)=\frac{b^2}{a^2} we want to find dθ/dψ, and the author performs an inplicit...
  42. B

    What Does Derivation Mean in a General Relativity Context?

    Homework Statement This seems like a simple question but I've never asked it and I'm stuck haha For my general relativity course we are asked to derive the change in a vector under parallel transport. My professor references his lecture notes on his course web page in the statement of the...
  43. C

    Derivation of Schwinger function in Di Francesco

    This is a question for anyone who is familiar with Di Francesco's book on Conformal Field theory. In particular, on P.108 when he is deriving the general form of the 2-point Schwinger function in two dimensions. He writes that the most general form of the tensor is $$S_{\mu \nu \rho \sigma} =...
  44. P

    Physical Pendulum Formula Derivation

    Homework Statement A physical pendulum, consisting of a uniform rod (of mass M and length L) with an attached blob, can oscillate about an axis that goes through one end of the rod. The mass of the blob is also M. The distance of the blob to the rotation axis is x. The aim is to derive a...
  45. C

    Derivation of Planck's law and the shape of the cavity

    When Planck's law is derive a cubical cavity is often used (for example in: http://disciplinas.stoa.usp.br/pluginfile.php/48089/course/section/16461/qsp_chapter10-plank.pdf) However, the result is applied generally. But in general, it seems like the wave lengths of the standing waves will...
  46. P

    Derivation of Stefan-Boltzmann Law from Wien's Law

    Homework Statement Derive Stefan-Boltzmann Law from Wien's Law. Hint: You can use (without proof) R(T)=∫(-∞ to ∞) R(λ,T)dλ, p(λ,T)= 4/c R(λ,T). Homework Equations Stefan-Boltzmann Law:P=AσT^4 Wien's Law: λmax=(2.898*10^-3 m*K)/T. The Attempt at a Solution Let λmax=(2.898*10^-3...
  47. D

    Derivation step in ODE solution in textbook

    This is not homework but is part of the solution process of an ODE and I cannot understand how the author made a derivation step. After a change of variable in the original ODE, the ODE in the new independent variable has a standard method of solution. But instead of using this method, the...
  48. A

    What is the explanation for the confusion in Griffiths' energy derivation?

    In Griffiths section 4.4.3, he derives the energy in a dielectric system as W=0.5∫D.Edτ. Part of the derivation involves the relation 0.5Δ(D.E)=0.5Δ(εE2)=ε(ΔE).E=(ΔD).E for infinitesimal increments, using D=εE. Now the part 0.5Δ(εE2)=ε(ΔE).E loses me so I was wondering if anybody could explain...
  49. C

    The derivation of Ito formula and Stratonovich formula

    The differential form of a stochastic variable can be expressed as $$dx=a(x)dt+b(x)dw(t)$$, here w(t) presents the Wiener process and satisfies ##(dw)^2=dt##. For the function f(x), the derivation of its differential form in the book by Gardiner is...
  50. L

    Derivation of the Laue Equation -- Problem with path difference

    Hi everyone Homework Statement I'm trying to understand the Laue equation but I have problems unterstanding the derivation, especially one part in my textbook about the path difference (see attachment) The Attempt at a Solution My textbook says that the path difference here is...
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