What is Derivation: Definition and 1000 Discussions

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. 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!
  2. 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...
  3. 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)...
  4. 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...
  5. Y

    Asymmetric bending principle of second moment of A derivation

  6. 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...
  7. 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...
  8. 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...
  9. 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...
  10. 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
  11. 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...
  12. 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...
  13. 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...
  14. 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 +...
  15. 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.
  16. 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)...
  17. U

    Derivation of torque on general current distribution

    How do I simplify the expression...
  18. 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...
  19. 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...
  20. 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?
  21. 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...
  22. 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}...
  23. 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...
  24. 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##...
  25. 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.
  26. 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...
  27. 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...
  28. 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...
  29. 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}...
  30. 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)...
  31. 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)?
  32. 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...
  33. 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...
  34. 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.
  35. 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...
  36. 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...
  37. 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...
  38. N

    I Question about The derivation of Lorentz equation in “The Behaviour of Measuring rods and clocks in motion”

  39. person123

    Derivation of Griffith's Criterion

    I did my derivation for a beam as shown with Young's Modulus ##E##, width ##w##, crack length ##a##, and surface energy density ##\gamma##. I understand that a crack will propagate when the free energy ##G## decreases with increase crack length ##a##. Free energy is the combination of the...
  40. phun_physics

    I Derivation of Average Square Energy Fluctuation in a Canonical System

    The canonical ( Boltzmann) distribution law for a canonical system is described the probability of state ##v## by ##P_v = Q^{-1} e^{-\beta E_v} ## where ##Q^{-1}## is the normalization constant of ##\sum_v P_v = 1## and therefore ##Q = \sum_{v}e^{-\beta E_v}##. Chandler then derives ##...
  41. E

    Can anyone explain this derivation of the variable mass equation?

    This question stems from one of the recent homework threads. I'm familiar with the derivation given here regarding mass accretion and ejection, where the general idea is to define a system around body and all of the incoming/leaving mass so that we can once again apply NII to the whole thing. I...
  42. MathematicalPhysicist

    I Inquiry about a derivation in "A First Course in GR" by Schutz

    on page 269 it's written in the second edition of Schutz's textbook that ##(10.69)p_c/\rho_c=\beta (2-5\beta)^{-1}##. Demanding that this be less than ##1/7## gives: ##(10.70) 0<\beta < 1/6## Now, if I am not mistaken on page 268 in equation (10.57) the condition should be ##p_c/\rho_c >1/7##...
  43. Jorzef

    How can I solve for the x force component in this force expression?

    Hello everyone, I'm stuck doing this problem, I've tackled the partial derivative but i can't figure out the derive for x component part, i solved the partial derivative part, i came to this result: What do can i do from here on, thank you!
  44. T

    In short circuit condition, what is wrong with following derivation

    V=ir considering the whole circuit Now we knowV=E-ir Then ir=E-ir Therefore i=E/2r Therefore,V=E/2
  45. Replusz

    I Fermi's golden rule derivation a bit hazy

    My thought is following: However this would give me w=E_m + E_n instead of E_m-E_n I guess something relating to hermiticity or adjointing something has gnoe wrong in my version. Can someone point me in the right direction please? :) Thank you in advance!
  46. W

    Engineering Derivation of the error due to a finite load attached to a potentiometer

    x = fraction of potentiometer connected to load Vp in parrallel with VL = x/(Rp/RL.x.(1-x) + 1) If RL = infinite, then Ro = x and Vo = x.Vs If RL = finite, then Ro = x/(Rp/RL.x.(1-x) + 1) and Vo = x.Vs/(Rp/RL.x.(1-x) + 1) Therefore error is x.Vs - x.Vs/(Rp/RL.x.(1-x) + 1) Trying to break the...
  47. patric44

    Derivation of the Bloch theorem

    hi guys our solid state professor gave us a series of power point slides that contains the derivation of Bloch theorem , but some points is not clear to me , and when i asked him his answer was also not clear : in the first part i understand the he represented both the potential energy and the...
  48. O

    I Is this PDF file the correct derivation?

    My work is in the following pdf file:
  49. patric44

    Derivation of the velocity of bloch electrons

    Hi guys I saw that equation of the velocity of electrons In a periodic potential $$ v = (1/h) grad E(k) $$ in my textbook we use in our solid state physics course without any proof or any thing and when I searched for it I found that its derived in Ashcroft book appendix E : Is there is any...
  50. MathematicalPhysicist

    A mathematical derivation in Peskin and Schroeder on page 722.

    My attempt at solution is in the HW template, though this is not an HW question.
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