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. abby11

    A Derive Radial Momentum Eq. in Kerr Geometry

    I am trying to derive the radial momentum equation in the equatorial Kerr geometry obtained from the equation $$ (P+\rho)u^\nu u^r_{;\nu}+(g^{r\nu}+u^ru^\nu)P_{,r}=0 \qquad $$. Expressing the first term in the equation as $$ (P+\rho)u^\nu u^r_{;\nu}=(P+\rho)u^r u^r_{;r} $$ I obtained the...
  2. christang_1023

    Derivation about the wave interference

    Starting from the simple case, there is a single wave ##e=a\cos(2\pi ft+\frac{2\pi}{\lambda}x+\phi_0)##, and integrate in such a way, where ##T_{eye}## stands for the response time of human eyes' response time towards energy change: $$I=\int_{0}^{T_{eye}}e^2dt$$ The calculation includes...
  3. J

    Derivation of Lagrangian in the calculus of variations

    Hello. In a chapter of a book I just read it is given that ##\frac {d} {d\epsilon}\left. L(q+\epsilon \psi) \right|_{\epsilon = 0} = \frac {\partial L} {\partial q} \psi ## While trying to get to this conclusion myself I've stumbled over some problem. First I apply the chain rule...
  4. J

    Sinking Object Motion Equations

    Hi guys! I am currently learning about fluid dynamics, and I am stuck on a certain equation derivation. It's about sinking motion which considers only gravity force, buoyant force, and viscous resistance. The link attached has the details...
  5. tjholi

    Derivation of the Emptying Time for a buoyant box to drain

    Problem Statement: I am having trouble deriving the expression from the initial equations. (Calculate the emptying time considering Volume conservation) Relevant Equations: Q=A*sqrt(b(H-h(t)) And we have dh/dt =Q/S (conservation equation) and we have to obtain h/H = 1-(1-t/te)^2 with te=...
  6. R

    Derivation of ideal magnetic dipole field strength

    For reference, this is from Griffiths, introduction to quantum mechanics electrodynamics, p253-255 When deriving the ideal magnetic dipole field strength, if we put the moment m at origin and make it parallel to the z-axis, the book went from the vector potential A $$ A=...
  7. jk22

    B Deriving Lorentz Transformation: Wave Eq Invariance & General Relativity

    I read the Lorentz transformation can be obtained by solving the requirement of invariance of the wave equation. If one considers linear transformations this the same as the spacetime interval squared to be invariant. What are the other nonlinear transformations keeping the wave equation...
  8. B

    Question about the derivation of linear magnification

    I tried assumed ##\theta \approx sin \theta \approx tan \theta##. By Snell's law(after approximation), $$n_1 \tan( i_1)= n_2 \tan( i_2)$$ If ##\tan (i_1)=\frac {h_o}{ u}## and ##\tan (i_2)=\frac {h_i}{ v}##,then $$m=\frac {h_i}{h_o}=\mod{\frac {v n_1}{un_2}}$$ Which is the expected...
  9. berlinspeed

    A Derive 4-Velocity Components: Anyone Know How?

    Anyone know how to derive ##u^0=\frac {dt} {d\tau}=\frac {1} {\sqrt {1-\mathbf {v}^2}}## and ##u^j=\frac {dx^j} {d\tau}=\frac {v^j} {\sqrt {1-\mathbf{v}^2}}##?
  10. K

    I Derivation of the Lorentz transformations

    It seems that there is a considerable number of ways of deriving the Lorentz transformations. Does anyone know how many ways are there?
  11. W

    Bernoulli's Principle -- correct derivation

    In this scenario I'm assuming that there is a shared velocity of water within the pipes, as well as a shared pressure and that water is non-compressible. If I understand correctly when someone says that pressure at a point is P at some point, it is the same as saying that if I put a small cube...
  12. I

    I Where did the extra 8 come from in the derivation for density of states?

    I was looking for a derivation for the density of states and I came across this page: https://ecee.colorado.edu/~bart/book/book/chapter2/ch2_4.htm I followed the derivation and came up with: g(E) = (1/L3)dN/dE = (1/L3)L3/∏2*k2 * dk/dE =K2/∏2 * dk/dE =K2/∏2 * g(E) =...
  13. MathematicalPhysicist

    A A derivation in Stoner's "The Demagnetizing Factors for Ellipsoids"

    In the attachment in eq. (1.6) I don't understand why is ##H-B = B/(1-D)##? Where does this relation come from?
  14. berlinspeed

    A How Do You Derive the Riemann Component?

    Can someone please show how to write as ?
  15. mertcan

    I Derivation of the Variance of Autocorrelation

    Hi everyone in this link (https://stats.stackexchange.com/questions/226334/ljung-box-finite-sample-adjustments) I see the variance of autocorrelation related to specific lag is demonstrated in the following: $$ Var(r_k) = \frac {\sum_{t=k+1}^n a_t*a_{t-k}} {\sum_{t=1}^n a_t^2}$$ where ##r_k## is...
  16. W

    Need help regarding the derivation of a 2-particle wavefunction

    I have an issue trying to understand the derivation of equation 3.40 (screenshot attached) of Blundell's QFT book. Here's my attempt. ##| x,y \rangle = |x\rangle \otimes |y\rangle = \Big( \int dp' \phi_{p'}(x)|p'\rangle \Big) \otimes \Big( \int dq' \phi_{q'}(y)|q'\rangle \Big)## which gives...
  17. sergiokapone

    I Derivation of Geodesics Eq from EM Tensor of Point Particle

    The energy-momentum tensor of a free particle with mass ##m## moving along its worldline ##x^\mu (\tau )## is \begin{equation} T^{\mu\nu}(y^\sigma)=m\int d \tau \frac{\delta^{(4) }(y^\sigma-x^\sigma(\tau ))}{\sqrt{-g}}\frac{dx^\mu}{d\tau}\frac{dx^\nu}{d\tau}.\tag{2} \end{equation} The covariant...
  18. V

    A Derivation of the differential Chapman-Kolmogorov Equation

    The integral equation is T(x_3,t_3|x_1,t_1)=\int \text{d}x_2T(x_3,t_3|x_2,t_2)T(x_2,t_2|x_1,t_1) where T(x_3,t_3|x_1,t_1) is the probability density of a Markov process taking the value x_3 at time t_3 given that it took the value of x_1 at time t_1. So far so good. To derive the differential...
  19. F

    Derivation of the Optical Law of Reflection

    Problem Statement: Derive the optical law of reflection. Hint: Let light go from the point A (x1, y1) to B (x2, y,2) via an arbitrary point P = (x, 0) on a mirror along the x axis. Set dt/dx = (n/c) dD/dx = 0, where D = distance APB, and show that then theta = phi. Relevant Equations: t = nD/c...
  20. MathematicalPhysicist

    Derivation of eq. (N.10) on page 791 of Appendix N in Ashcroft's SSP.

    Well as always start with the definition of scalar product: $$\sum_f (\Phi_i,A\Phi_f)(\Phi_f ,B\phi_i) = \sum_f \int \Phi_i^*A\Phi_f \int \Phi_f^* B\Phi_i=\int \int \Phi_i^* \sum_f A\Phi_f \Phi_f^* B\Phi_i$$ How to continue from the last equality? Thanks.
  21. J

    Understanding the derivation for Elastic Potential Energy.

    Elastic Potential Energy of a Strained Body (A) Using ## Y = \frac {stress}{strain}## we get ##F = \frac {AY}{L} * x## where ##F## is the restoring force, ##x## is the distance the body is stretched by. Since Work = PE (spring force/ stress is conservative?) Thus ##W = \int_{0}^{x} \frac...
  22. W

    Derivation of the wave equation on a curved space-time

    I'm confused by this question, from minimal coupling shouldn't the answer simply be ## \nabla^a \nabla_a F_{bc} = 0 ##? Any help would be appreciated. EDIT: I should also point out ##F_{ab}## is the EM tensor.
  23. D

    MHB Stuck on Derivation (Natural Deduction)

    1. ((N ⊃ P) ⊃ (I ⊃ P)) ⊃ ((P ⊃ I) ⊃ P) P 2. (I v X) ≡ (R ⊃ P) P 3. R ⊃ (I ⊃ (N ^ V)) P 4. R A 5. Reiteration of 3 6. I ⊃ (N ^ V) 3,4 ⊃E 7. I A 8. I v X 7, vI 9. Reiteration of 2...
  24. ManishN

    Why are the E-L-Equations the Same Old Song in the Music Industry?

  25. SamRoss

    I Why wasn't this symbol "swapped"?

    In a certain derivation, the author begins with $${g(-t)=}\frac 1 {2\pi}\int_{-\infty}^\infty {G(\omega)}e^{-i\omega t}d\omega$$ and then says he will replace ##t## with ##\omega## and ##\omega## with ##t##. He then writes $${g(-\omega)=}\frac 1 {2\pi}\int_{-\infty}^\infty {G(t)}e^{-it\omega...
  26. Z

    I Derivation of Divergence in Cartesian Coordinates

    In section 1-5 of the third edition of Foundations of Electromagnetic Theory by Reitz, Milford and Christy, the authors give a coordinate-system-independent definition of the divergence of a vector field: $$\nabla\cdot\mathbf{F} = \lim_{V\rightarrow 0}\frac{1}{V}\int_S\mathbf{F\cdot n}da$$...
  27. SamRoss

    I Is there an algebraic derivation of the area element in polar coordinates?

    There is a simple geometric derivation of the area element ## r dr d\theta## in polar coordinates such as in the following link: http://citadel.sjfc.edu/faculty/kgreen/vector/Block3/jacob/node4.html Is there an algebraic derivation as well beginning with Cartesian coordinates and using ##...
  28. S

    I Running through a complex math derivation of plasma frequency

    Background of problem comes from Drude model of a metal (not necessary to answer my problem but for the curious): Consider a uniform, time-dependent electric field acting on a metal. It can be shown that the conductivity is $$\sigma = \frac{\sigma_0}{1-i\omega t}$$ where $$\sigma_0 =...
  29. B

    I Issue With Derivation of Gravitational Time Dilation

    Why do we use the equation ##\frac {1}{2}mv^2 = \frac {GmM}{r}## to derive potential velocity, and then put that in the Lorentz factor in order to derive gravitational time dilation? Shouldn't we be using the relativistic definition of kinetic energy -> ##mc^2(\gamma - 1)## to derive the...
  30. Z

    The Energy of a Continuous Charge Distribution (Griffiths EM Sect. 2.4.3 3rd ed)

    I'm working through Griffiths EM 3rd ed. in section 2.4.2 (point charge distribution) and 2.4.3 (continuous charge distribution). I understand from the section on point charge distributions that when we add up all the work (excluding the work necessary in creating the charge itself), one clever...
  31. mertcan

    I AICc value derivation (Akaike information criteria for finite samples)

    Hi everyone, initially let me introduce a concept widely used in ARIMA in the following. $$AICc = AIC + \frac {2k^2+2k} {n-k-1}$$ where n denotes the sample size and k denotes the number of parameters. Thus, AICc is essentially AIC with an extra penalty term for the number of parameters. Note...
  32. R

    Derivation from simultaneous equations (Fabry-Perot etalon)

    Here are three equations: $$E_{2}=rE_{1}+itE_{3} \tag{1}$$ $$E_{4}=rE_{3}+itE_{1} \tag{2}$$ $$E_{2}=\tau\exp\left(i\varphi\right)E_{4} \tag{3}$$ I started by substituting Eqn. 3 into Eqn. 2, $$\frac{E_{2}}{\tau}\exp\left(-i\varphi\right)=rE_{3}+itE_{1}, \ \therefore E_{3} =...
  33. Pencilvester

    I Lorentz Transformation Derivation: Assumptions Req'd?

    In deriving the Lorentz transformation, is it required to assume that the transformation to get from coordinate system ##\bf {x}## to ##\bf {x’}## should be the same as that to get from ##\bf {x’}## to ##\bf {x}## (with the simple correction of flipping the velocity)? If no, could someone...
  34. P

    A Relativistic derivation of E=1/2MV^2 from QFT or Diriac or other

    It is easy to derive E=1/2mv^2 from the Schroedinger equation for the nonrelativistic one dimensional case where e^ipx-iEt/\hbar is the free traveling wave function: i\hbar x -iE/\hbar x e^ipx-iEt/\hbar = - - \hbar^2/2m x p^2/2m x e^ipx-iEt/\hbar which reduces to E=1/2mv^2 Where should I start...
  35. J

    I Relation between spectral radiance and density of cavity

    Hi, my teacher showed us how we can derive de relation between spectral radiance and density of cavity (of a black hole), but I have a doubt. This is the equation of the energy that are coming from definited directions by the intervals of angles θ and Φ with frequency in a determined interval...
  36. T

    I Typo in elliptical orbit energy derivation?

    I'm reading through a derivation for the energy of a satellite in an elliptical orbit. Shouldn't EO-2 read as: ... and not as shown in the following?
  37. benorin

    B Can Atomic Clocks Yield the Same Time Dilation Equation as Light Clocks?

    Ok so I've got a question after walking through the time dilation derivation that used 'light clocks' (think a beam of light bouncing back and forth between mirrors) to derive ##\delta t^\prime = \frac{\delta t}{\sqrt{1-\frac{v^2}{c^2}}}##. So my Q is could you derive the same equation if you...
  38. A

    MHB Calc Male & Female Cattle Pop Growth Rates: 30 Heifers, 100% Fert/Surv

    I want to estimate the number of male and female cattle produced over a period of time (say, five years and ten years) from an initial stock of 30 heifers, all 18 months of age at which age they are first joined (mated). Assume that the first calf is born when the mother is 27 months old...
  39. merlyn

    Fourier series equation derivation

    Hi all. Could someone work out for me how equation 21 in attachment left side becomes right side. Please show in detail if you could. It's for exponential Fourier series. Drforbin thank you
  40. T

    What's the derivation in a moving magnet & conductor problem?

    In the Wikipedia page of the moving magnet and conductor problem, it asserts "This results in: E' = v x B", but does not elaborate why. What's the full derivation?
  41. Arman777

    Is This a Valid Derivation of Kinetic Energy from Work?

    I am trying to derive the kinetic energy from the work and can I derive it like this ? $$W=\int Fdr$$ $$W=\int \frac {dp} {dt}dr=\int (dp) \frac {dr} {dt}=\int (mdv)v=1/2m[v_f^2-v_i^2]$$
  42. JulioHC

    Derivation of blackbody radiation equations for stars

    Good evening, As part of my course, I had this week two lectures about the blackbody radiation and its relation to the stars. While I do understand how to use results such as the Stefan-Boltzmann law and Wien's Law I'm lost in other parts. I think the only parts that I don't understand yet are...
  43. ikihi

    Math Derivation: Solve for t - Calc 1 Help

    Homework Statement solve for t Homework Equations A = P (1+r)t + c[ ((1 + r)t+ 1 - (1 + r)) / r ] The Attempt at a Solution I've taken calc 1, but I've been away from math for years. I'm having trouble solving this for t
  44. TeethWhitener

    I Derivation of Crooks's Fluctuation Theorem

    I'm reading through Crooks's paper: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.60.2721 as well as a review paper by Mansour et al.: https://aip.scitation.org/doi/10.1063/1.4986600 trying to figure out their derivation of the fluctuation theorem (section II of both papers). I had a...
  45. E

    I Derivation of the Onsager symmetry

    Derivation of the Onsager symmetry in many textbooks and papers is as follows: First, assume that the correlation function of two state variables,##a_i## and ##a_j## satifsies for sufficiently small time interval ##t## that $$\langle a_i(t) a_j(0) \rangle = \langle a_i(-t) a_j(0) \rangle =...
  46. Cathr

    I How to derive a symmetric tensor?

    Let ##Q_ik## be a symetric tensor, so that ##Q_ik= \frac{m}{2} \dot x_i \dot x_j + \frac{k}{2} x_i x_j## (here k is also a sub, couldn't do it better with LaTeX). How do we derive such a tensor, with respect to time? And what could such a tensor mean in a physical sense? It really looks like the...
  47. M

    Assumptions in the derivation of the kinetic theory of gases

    When deriving the kinetic theory of gases, we take the change in momentum of a particle as it hits one side of a box and divide it by the time over which the collision takes place. The time is derived by taking the total distance the particle traveled in the box (i.e. from one end, off the side...
  48. R

    Why Centrifugal Force in the Derivation of Curvature Drift

    Homework Statement This is a question about a pretty basic plasma physics derivation. In the standard derivation of the Curvature Drift of a charged particle in a magnetic field with curvature, the force that they use is the "imaginary" centrifugal force (or the force the guiding center sees in...
  49. H

    A Derivation of the Noether current - Lorentz Transformation

    We make an infinitesimal Lorentz transformation of the Lagrangian and require it to be invariant. We then arrive at the following expression. $$\epsilon^{\mu\nu}j_{\mu\nu} = P_{\mu}\epsilon^{\mu\nu}X_{\nu}$$ which can be written as $$\epsilon^{\mu\nu}j_{\mu\nu} =...
  50. binbagsss

    GR, small expansion, (perihelion derivation)

    Homework Statement Hi I am looking at the attached as part of the derivation and am stuck on how we go from 18 to 19 [/B]Homework Equations Above below The Attempt at a Solution [/B] I'm pretty stuck. Lambda is small and not sin so can't see why one would expand out sine in a Taylor...
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