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. romsofia

    I More rigorous Euler-Lagrange derivation

    Sorry if there are other threads on this, but after a discussion with a friend on this (im in the mountains, so no books, and my googlefu isn't helping), I realize that my understanding of the variational principles arent exactly... great! So, maybe some one can help. Start with a functional...
  2. L

    How can one derive an expression for \( w^2 / k \) using \( b, p, l \) only?

    The total energy of the particle is ##u^2 / 2 - k/R##. When ##u^2 \gg 2k/R##, we take the total energy to be ##u^2/2## only. By the conservation of energy, we have: $$ \frac{u^2}{2} = \frac{w^2}{2} - \frac{k}{p} $$ Take the angular momentum expression ##l = bu##, we can replace ##u## with...
  3. A

    Semi empirical mass formula derivation help

    Can somebody please derive for me an example of the Binding energy from the Semi Empirical mass formula? I am trying myself but always there is a difference between the database binding energy and my own result. I am calculating the BE of Niobium 93. For the mass formula I used the coefficients...
  4. A

    I Deriving Contravariant Form of Levi-Civita Tensor

    The covariant form for the Levi-Civita is defined as ##\varepsilon_{i,j,k}:=\sqrt{g}\epsilon_{i,j,k}##. I want to show from this definition that it's contravariant form is given by ##\varepsilon^{i,j,k}=\frac{1}{\sqrt{g}}\epsilon^{i,j,k}##.My attemptWhat I have tried is to express this tensor...
  5. redtree

    I Derivation of the Helmholtz equation

    I am trying to understand the Helmholtz equation, where the Helmholtz equation can be considered as the time-independent form of the wave equation. It seems to me that the Helmholtz equation can be derived from the Fourier transform, such that it is part of a larger set of equations of varying...
  6. ArisMartinez

    Taking the derivative of a function of a function

    Summary:: According to Yale’s University PHYS: 200: v*(dv/dt) = d(v^2/2)/dt Could someone explain how has he reached that conclusion? He claims to be some standard derivation rules, but I can’t find anything about it. As much as I can tell: (dv/dt)* v = v’ * v = a* v thanks! [Moderator's...
  7. MathematicalPhysicist

    A Some questions about the derivation steps in the Gravitational deflection of light section in Schutz

    In the screenshots below there are the equations (11.49) and (11.53). I don't understand how did he derive equation (11.53) from Eq.(11.49)? From (11.49) I get: ##d\phi/dy= d\phi/du du/dy = (1/b^2-u^2+2Mu^3)^{-1/2}(1+2My)##. It seems he neglected the ##2Mu^3## since ##Mu\ll 1##, so ##y\approx...
  8. steve1763

    A Derivation of recovery channel for bit flip error

    In general, if R is the recovery channel of an error channel ε, with state ρ, then and according to these lecture slides, we get the final result highlighted in red for a bit flip error channel. I am simply asking how one reaches this final result. Thank you (a full-ish derivation can be found...
  9. M

    I Derivation of an angular momentum expression

    Hello! I found this formula in several places for the total angular momentum of a particle with intrinsic spin 1/2 and angular momentum l=1 in the non-relativistic limit: $$\frac{1}{\sqrt{4 \pi}}(-\sigma r /r )\chi$$ where ##\sigma## are the Pauli matrices and ##\chi## is the spinor. Can someone...
  10. U

    Help in understanding the derivation of Einstein equations

    There are two parts to my question. The first is concerns the variation of the Reimann tensor. I am trying to show $$\delta...
  11. S

    I Fluids: Bernoulli's Equation Derivation Question

    I figure that either the Force F2 is applied in the opposite direction because of some kind of resistance, but I'm not sure. Thanks!
  12. stevendaryl

    I A short derivation of the relativistic forms of energy and momentum

    I've been noodling around with derivations of the relativistic energy and momentum, and I almost got it down to just a few lines. But not quite. I'm going to work in one spatial dimension, for simplicity (even though some derivations require a second spatial dimension) Let's assume that there...
  13. alya

    Help Needed: Deriving Formula for Computer Undergrad's Final Project

    My mentor wants the derivation of this formula. Me a computer undergrad, unable to figure it out, and my final project are on a halt due to this, any help from the community is greatly appreciated!
  14. bhobba

    B Simple Derivation Of Euler's Formula And Applications

    Here is a simple way to get Euler's relation for those learning pre-calculus/calculus, so the trigonometric addition formula and the derivative of sine and cosine are easy. We will assume some basic knowledge of complex numbers and properties of Euler's number, e. Consider a small segment of...
  15. T

    I Derivation of Eigenfunctions/Eigenvalues of the Momentum Operator

    Good afternoon all, In David Griffiths' "Intro to Quantum Mechanics", I'm looking through Example 3.2 on page 115 that shows how to get the eigenfunctions and eigenvalues of the momentum operator. I completely understand everything up until this part: ##\int_{-\infty}^{\infty} f_p'^*(x)...
  16. snoopies622

    Confusion about the derivation of the speed of sound

    I've having trouble understanding a derivation of the speed of sound waves, which is actually similar to another derivation I found a couple days ago. Let's suppose the sound is moving through water in a long cylindrical horizontal pipe. The premises of the derivation are 1.) For a given...
  17. Y

    Asymmetric bending principle of second moment of A derivation

  18. T

    I Question on Harmonic Oscillator Series Derivation

    Good afternoon all, On page 51 of David Griffith's 'Introduction to Quantum Mechanics', 2nd ed., there's a discussion involving the alternate method to getting at the energy levels of the harmonic oscillator. I'm filling in all the steps between the equations on my own, and I have a question...
  19. patric44

    Derivation of the density of states?

    hi guys i have a question about the derivation of the density of states , after solving the Schrodinger equation in the 3d potential box and using the boundary conditions ... etc we came to the conclusion that the quantum state occupy a volume of ##\frac{\pi^{3}}{V_{T}}## in k space and to...
  20. L

    Elastic collision formulas -- Derivation blunder

    https://en.wikipedia.org/wiki/Elastic_collision μα+mβ=μx+my, μα^2+mβ^2=μx^2+my^2 I want x in relation of all variables except y, therefore I need to replace-eliminate y: μα+mβ=μx+my =>y=(μα+mβ-μx)/m μα^2+mβ^2=μx^2+my^2=>y=((μα^2+mβ^2-μx^2)/m)^0.5 and it is eliminated if I equate these two parts...
  21. N

    I 9-point Laplacian stencil derivation

    Hey there I'm currently taking a course on numerical methods for solving differential equations, and atm we are working with the discrete laplacian operator. In particular the 9-point stencil: However unlike the 5-point stencil, this one is getting to me. I have tried several things, in...
  22. P

    I Why is my derivation of the catenary wrong?

    Important note: I only derived the differential equation, I did not solve it. What I think caused the mistake: - the tangent approximation (tan(theta+dtheta) ~ tan theta + d theta
  23. D

    Question about Ampere's Force Law derivation

    I'm reading about the derivation of ampere force law formula, which is $$ F=k_A \iint \frac{i'ds' \times (ids \times \vec{r})}{\vec{r}^2}$$ where K_A is mu_0/4pi. In the article that I read, they have assumed such these paths: And according to ampere's conclusion that he had from observation...
  24. N

    Magnetohydrodynamics - Derivation of PDE

    Summary:: partial differential equation (PDE) to describe the potential distribution φ in the system Hey, I need some help with the following question: We have a stationary electrolyte, a magnetic field "B" and a Current density "j" (2D). Derive the partial differential equation (PDE) to...
  25. M

    Control Theory: Derivation of Controllable Canonical Form

    Hi, I was recently being taught a control theory course and was going through a 'derivation' of the controllable canonical form. I have a question about a certain step in the process. Question: Why does the coefficient ## b_0 ## in front of the ## u(t) ## mean that the output ## y(t) = b_0 y_1...
  26. yucheng

    Incorrect derivation of tangential acceleration in polar coordinates

    I am trying to derive the tangential acceleration of a particle. We have tangential velocity, radius and angular velocity. $$v_{tangential}= \omega r$$ then by multiplication rule, $$\dot v_{tangential} = a_{tangential} = \dot \omega r + \omega \dot r$$ and $$a_{tangential} = \ddot \theta r +...
  27. Strand9202

    Velocity of an Object given its position as a function of time

    Attached is the problem and my work through the problem. I got the problem correct, but my teacher said this could be done quicker on a calculator. Any idea how it could be done quicker.
  28. SebastianRM

    Relating volumetric dilatation rate to the divergence for a fluid-volume

    in class we derived the following relationship: $$\frac{1}{V}\frac{dV}{dt}= \nabla \cdot \vec{v}$$ This was derived though the analysis of linear deformation for a fluid-volume, where: $$dV = dV_x +dV_y + dV_z$$ I understood the derived relation as: 1/V * (derivative wrt time) = div (velocity)...
  29. U

    Derivation of torque on general current distribution

    How do I simplify the expression...
  30. Leo Liu

    Confusion about the derivation of acceleration relative to rotating frames

    This derivation is found in Kleppner's mechanics book. It shows how to find the acceleration in rotating coordinates by differentiating ##\vec v_{in}=\vec v_{rot}+\vec\Omega\times\vec r##; subscripts IN and ROT stand for inertial and rotation respectively. My question is what the term...
  31. greg_rack

    Derivation of the Euler equation for a streamline

    Hi guys, in the derivation of the Euler equation we apply Newton's 2nd law to a gas flowing through a streamline. To do so, we consider a "box" with sides ##dx## ##dy## and ##dz##: as such; Here, with reference to the image, I can't understand where does that '##+dp##' comes from, and hence...
  32. I

    I Derivation of E=pc & E=MC2: Which Came First?

    I have seen E=pc used to derive E=MC2. I have seen E=MC2 used to derive E=pc. This is circuitous. Which came first and how is E=pc derived?
  33. patric44

    Derivation of the Child-Langmuir law?

    hi guys i was trying to understand the derivation of the child Langmuir law that govern the current flow between the two plates of vacuum tubes and saw this derivation online : and i am stuck at couple of points : when i saw the derivation it seem like a direct application of the Poisson's...
  34. G

    Problem about the derivation of divergence for a magnetic field

    Summary:: I am trying to derive that the divergence of a magnetic field is 0. One of the moves is to take the curl out of an integral. Can someone prove that this is addressable Biot Savart's law is $$B(r)=\frac{\mu _0}{4\pi} \int \frac{I(r') \times (r-r')}{|r-r|^3}dl'=\frac{\mu _0}{4\pi}...
  35. M

    A Claimed derivation of Weinberg angle, Higgs/W mass ratio

    https://arxiv.org/abs/2010.15621 Superselection of the weak hypercharge and the algebra of the Standard Model Ivan Todorov [Submitted on 29 Oct 2020] I haven't had time to study this paper yet. But a few curiosities: It talks about Clifford algebras. But in fact it builds on work due to...
  36. Hamiltonian

    Derivation of the orbital analysis equation and its physical significance

    $$cos\theta = \frac {s}{1-s} = \frac{p-1}{p}$$ in this equation ##\theta## is the bond angle and ##s## and ##p## are the fractional s-character of the orbital and p-character of the orbital. This is equation is used rigorously in showing that the s-character of the axial orbitals in a ##sp^3d##...
  37. K

    I Help - Derivation of Pulsating Star Euler ODE

    to I am a bit clueless on how to get break the ##r X(r)## from inside the derivative.P.S. I tried to copy from Symbolab instead of pasting the picture, but it didn't let me.
  38. Hamiltonian

    B Doubt on the derivation of an equation for a surface integral

    this method of derivation is approximating the function using a polyhedron. concentrating on one of the surfaces(say the L'th surface which has an area ##\Delta S_l## and let ##(x_l,y_l,z_l)## be the coordinate of the point at which the face is tangent to the surface and let ##\hat n## be the...
  39. jisbon

    Engineering 2-bit Bin Full Adder Truth Table Derivation

    Hi all, I am having some troubles deriving the truth table of the following: I don't understand how does one gets to the highlight parts. For example, 10 10, when the carry is low, shouldn't the output be 0 0 1? I fully understand how to add if it is a single bit, but now with 2 bits, it is a...
  40. patric44

    Is this a valid derivation of the Uncertainty Principle?

    Homework Statement:: i saw this simple derivation of the uncertainty principle in my college introductory quantum book Relevant Equations:: Δp.Δx = h hi guys i saw this derivation of the uncertainty principle in my college quantum book , but the derivation seems very simple and sloppy , i...
  41. cwill53

    Specific Heat Capacity Derivation

    The specific heat capacity at constant volume and the specific heat capacity at constant pressure are intensive properties defined for pure, simple compressible substances as partial derivatives of the functions u(T, v) and h(T, p), respectively, $$c_v=\left ( \frac{\partial u}{\partial T}...
  42. J

    Radiative cooling time derivation (for ambient temperature = 0 °K)

    as T_∞ = 0 , I use Q=−F\epsilon A\sigma T^4 for this problem as the integration is much easier, so we start with mcdTdt=−F\epsilon A\sigma T^4 rearrange so T is on one side and t is on the other: −mcF\epsilon A\sigma T^4dT=dt on the left side I integrate from the initial temperature (Ti)...
  43. J

    Derivation of 3pt forward formula

    f(x+2h) = f(x) + 2hf’(x) + .5(2h)^2f”(x) f(x+h) = f(x) + hf’(x) + .5h^2f”(x) f(x+2h) - f(x+h)? f(x+2h) - 2f(x+h)?
  44. Leo Liu

    A mistake in the derivation of escape velocity

    In the last step of the derivation of escape velocity, the two sides of the equation seem to have opposite signs. $$-1/2mv_0^2=-mgR_e^2\,\lim_{r\to\infty}(1/r-1/R_e)$$ $$-1/2mv_0^2=mgR_e^2 \frac{1}{R_e}$$ Since the mass and the square of the velocity are positive, the left side of the equation...
  45. T

    Determine for which x the derivative exists of: ##f(x)=\ln|\sin(x)|##

    Hi there. I have the following function: $$f(x)=\ln|\sin(x)|$$ I've caculated the derivative to: $$f'(x)=\frac{\cos(x)}{\sin(x)}$$ And the domain of f(x) to: $$(2\pi n, \pi+2\pi n ) \cup (-\pi + 2\pi n, 2\pi n)$$ And the domain of f'(x) to: $$(\pi n, \pi+\pi n )$$ I want to determine for...
  46. T

    A Questions about derivation of GR and applications of it

    Hello friends. I have this question about how the Einstein field equations were derived, the assumptions behind them and the possible applications of them. What could their solutions be?Also, how are they used in cosmology and in the big bang theory?What about astrophysics? Thank you very much.
  47. J

    Question about the derivation of Exact Differentials in thermo

    What I don't understand is why ##dS## is expanded in only the two differentials ##dV## and ##dT.## Why doesn't it look more like: $$dS = \left(\dfrac{\partial S}{\partial V}\right)_{T,P,U} \ dV + \left(\dfrac{\partial S}{\partial T}\right)_{V,P,U} \ dT + \left(\dfrac{\partial S}{\partial...
  48. W

    What is the algebra concept used to derive time dilation formula?

    Hi this is my first post the forum, nice to meet you all. I am trying to derive the time dilation formula following the image attached. However I am unsure of the algebra being used toget from the 2nd line of working to the 3rd line. Can someone please tell me what the name of the algebra...
  49. Eipi

    Derivation of Lorentz Time Transformation

    I have to derive the Lorentz time transformation given the equation for gamma and the equation for the Lorentz space transformation. I started by using relevant equations from the Space derivation done in class (also the one that Ramamurti Shankar does). Here is a picture of what I have tried...
  50. N

    I Is x Equal to x' and t Equal to t' in Lorentz Transformations?

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