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. genxium

    Why is stress tensor (in this derivation) symmetric?

    First by "this derivation" I'm referring to an online tutorial: http://farside.ph.utexas.edu/teaching/336L/Fluidhtml/node9.html It's said in the above tutorial that the ##i-th## component of the total torque acting on a fluid element is ##\tau_i = \int_V \epsilon_{ijk} \cdot x_{j} \cdot F_{k}...
  2. R

    How would one describe the universe in which

    there are no electromagnetic waves? All I know is that there is a modified version of the Maxwell equations (in differential form) for such a universe, such as (the arrows represent vector arrows): →∇x →B = μ0 →j + μ0 ε0 ∂→B/∂t instead of having ∂E/dt in the last term (which would be the case...
  3. D

    How to find combined velocity after impact in a mallet and stake collision?

    Homework Statement A heavy mallet of Mass M (see Attached file) is dropped and moves through vertical distance y before it hits the top of a tent stake of mass m, driving it into the ground a distance d. Assume that the ground offers a a constant resistance to the motion of the tent stake and...
  4. Buzz Bloom

    Derivation of Gott's formula for size of observable universe

    I understand that Gott derived a formula for calculating the size of the observable universe, and the value of the diameter based on current obsrvations is 93 Gly. Can someone please show the mathematical derivation of Gott's formula, or give a reference to a source which shows this derivation?
  5. P

    Checking derivation of the curvature tensor

    Homework Statement I am trying to derive the curvature tensor by finding the commutator of two covariant derivatives. I think I've got it, but my head is spinning with Nablas and indices. Would anyone be willing to check my work? Thanks Homework Equations I am trying to derive the curvature...
  6. Devin

    Derive Lorentz Transformations w/ Special Relativity

    Hope this derivation helps someone!
  7. Devin

    Taylor Exansion Series Derivation

    My derivation of Taylor expansion. Hope someone struggling with it gets use!
  8. Devin

    Lorentz Transformations with Special Relativity Derivation

    Any advice on my derivation layout?
  9. fluidistic

    Derivation of Fresnel equations / minus sign

    Homework Statement For an s-polarized wave (E and B fields are orthogonal to the plane of incidence) passing from medium to medium 2, I'm not understanding a minus sign. The matching conditions are ##\hat n \times (\vec E_2 - \vec E_1)=\vec 0## and ##\hat n \times (\vec H_2 - \vec H_1 )=\vec...
  10. C

    MHB Stefan-Boltzman law derivation and integral tricks

    HI people, I was trying to derive the stefan-boltzman law from the planc's formula, I kind of got stuck with an integral $$ \int_{0}^{\infty} \frac{x^3}{e^x -1} dx $$ I tried simplifying it with $$ \int_{0}^{\infty} x^3 e^{-x} \sum_{n=0}^{\infty} e^{-nx} dx $$ Now I don't know what to do...
  11. K

    Derivation of T1 term in Bloch equations

    I always see the contribution of semiclassical scattering to the Bloch equations for a two-level system justified heuristically, using Fermi's Golden Rule to calculate the scattering rates. The resulting time evolution of the density matrix is clearly in the Lindblad form, but is it possible to...
  12. bananabandana

    Superposition of Two Travelling Waves, Different Amplitudes

    Homework Statement I'm looking at an E&M textbook - "Time-Harmonic Electromagnetic Fields". They state: "A more general ##x ## polarized field is one consisting of waves traveling in opposite directions with unequal amplitudes - i.e : (1) $$ E_{x} = Ae^{-jkz} +Ce^{jkz}$$ Let ## A ## and...
  13. toforfiltum

    Confused abt derivation of centripetal acceleration

    A comparison of corresponding parts of these two similar isosceles triangles yields velocity triangle displacement triangle where |-vo| = |vf| = v In a small time interval Δt, the arc length s → c. Okay, so I got this from Physics LAB, and I don't understand the last statement that...
  14. C

    Archimedes Derivation: Law of the lever

    Hi, I'm watching a talk about Archimedes Law of the lever, and I was wondering: Does anyone know how the formula d=w/2w/b-a) was derived from the lecture drawing at 9.00 min in? The speaker just skips the algebraic derivation.
  15. S

    Derivation of non decaying mode in cosmology

    Homework Statement Derive the following result : \phi_k=-C_1(k)\frac{\dot{H}(t)}{H(t)} . Homework Equations \phi_k=C_1(k)\Bigg(1-\frac{H}{a}\int\limits^{t}a(t)dt\Bigg) a(t)= a(t_i)\exp\Bigg(H_i(t-t_i)+\dot{H}_i\frac{(t^2-t_i^2)}{2}\Bigg) The Attempt at a Solution So I stuck a(t) into...
  16. B

    Electromagnetic fields derivation

    Homework Statement In a book I find the following derivation: \int (J \cdot \nabla ) \frac{\bf{r} - \bf{r}'}{|\bf{r} - \bf{r}'|^3} d^3\mathbf{r'}= -\sum_{i=1}^3 \int J_i \frac{\partial}{\partial r_i'} \frac{\bf{r} - \bf{r}'}{|\bf{r} - \bf{r}'|^3} d^3\mathbf{r'} \\ = -\sum_{i=1}^3 \int J_i...
  17. J

    Derivation of Kirchhoff's Formula in Gravitational Radiation

    I am trying to understand the formula's for Gravitational Radiation. At one point in the derivation, every source I have seen comes up with Kirchhoff's Formula but they never derive it. They always just say its a well known result from Electromagnetic Radiation. I have been able to determine...
  18. P

    Einstein-Cartan Field Equations Derivation

    I'm looking for a derivation of the Einstein-Cartan Equations from varying the Einstein-Hilbert Action. I've looked around the internet but can't seem to find one, so if anyone knows of a pdf or book reference that goes through the derivation, that would help a lot. The wikipedia page for...
  19. orion

    Tangent vector as derivation question

    I have a question concerning the tangent space. Consider a manifold Mn and take Mn to be ℝn with the Euclidean metric for the purposes of this question. The directional derivative of a function in the direction of a vector v is (a) vf = ∑ vi(∂f/∂xi) where the sum runs from 1 to n. The...
  20. C

    How Does Zee Simplify Integrals in QFT Derivations?

    On page 12 of Zee's QFT in a nutshell, he rewrites an integral from dirac notation to a mixture of schrodinger/dirac My question is, since , what happened to the integrals, and shouldn't there be four wave functions instead of two? I tried writing out the integrals explicitly, thinking maybe...
  21. 24forChromium

    Someone verify my answer to this question about rotation?

    Homework Statement A lever with one end on a pivot point, a point mass on the lever's shaft with a certain arm length (d), it is also the only relevant mass body (m). A torque (Tauapp.) is applied to the lever, an angular acceleration (alpha) transpired. Find the relationship between the force...
  22. S

    How was the van der Waals equation derived?

    the equation (P+a(n/V)^2)(V-nb)=nRT was derived in this manner: The pressure of a real gas is affected by intermolecular forces and so the a(n/V)^2 term must be added to the measured pressure to obtain the ideal pressure where Pmeasured+a(n/V)^2=Pideal On the other hand when they explained...
  23. P

    Derivation of Time Dependent Schrodinger Equation

    Hi All, I have problem in understanding one step in the derivation of the time dependent Schrodinger Equation. Please see attached file page 2 (marked in red). Most grateful if someone can help! Peter Yu (This is from Quantum Mechanics The Theoretical Minimum Page 99-102)
  24. kzf

    Kinematics derivation of conservation of angular momentum

    Homework Statement A welding robot consists of an arm (thin rod) that can rotate about the origin point O, and a welding tip, which can freely move along the rod, from the outermost point of the arm A all the way to the center point O. The design invokes two electric motors, one to turn the...
  25. C

    MHB Derivation of snedecors F distribution

    derive f distribution as x1 and x2 are independent random variables having a chi-square distribution with n1 and n2 degrees of freedom.. aslo mgf and find raw moments ... and finds its mean and variance.?prove it ?help me guys?
  26. popopopd

    Spectroscopy hookes law, derivation?

    hi, i am a lillte confused why the equation for hookes law is 1/(2pi*c)*sqrt(k/m_reduced)? where does c come from? http://www.massey.ac.nz/~gjrowlan/intro/lecture5.pdf - slide 8. also, is there any particular reason why we use reduced mass?
  27. L

    Why Does My Kohn Effect Derivation Differ from Ziman's Model?

    I'm working through a derivation of the [Kohn Effect](http://en.wikipedia.org/wiki/Kohn_effect), as presented in Ziman's 'Principles of the Theory of Solids.' However, I find myself getting a somewhat different result. The book states that calculating $$\epsilon(\mathbf{q}, \omega) = 1+...
  28. Shahab Mirza

    How to interpret this Wave Equation (Derivation) Help ?

    Hi dear people , Hello I waw studying super position of two Sound Waves , traveling in same medium with same frequency , same wavelength and same amplitude while differing in phase . quick derivation : Wave 1 displacement y1= A sin (kx-vt ) and wave 2 displacement y2= A sin (kx-vt-phase...
  29. K

    Center of mass - cant find error in derivation

    First of all, I am sorry if this is in the wrong subforum; I'm not sure if astrodynamics should be under astronomy. The post is also fairly long. My problem is that in my derivation of the center of mass of a binary system, I get a conflicting result for the distances of the center of mass to...
  30. AwesomeTrains

    Derivation of orbital period - Hydrogen

    Hey everyone! 1. Homework Statement I've been giving the equation for a gaussian wave packet and from that I have to derive this formula: T_{Kepler}=2\pi \bar n ^3 by doing a first order taylor series approximation at \bar n of the phase: f(x)=f(\bar n)+\frac{df}{dx}|_{\bar n}(x-\bar...
  31. Drafter

    The Derivation of Several Triginometric Identities

    I would like to know how can I derive the double, half, product to sum, and sum to product identities of trigonometry using simple algebraic means. And which books (which I prefer) should I pickup at the library on this subject to actually learn these derivations? Or at the very least some...
  32. eifphysics

    Insights A Partial "Derivation" of Gauss's Law - Comments

    eifphysics submitted a new PF Insights post A Partial "Derivation" of Gauss's Law Continue reading the Original PF Insights Post.
  33. T

    Moment of Inertia of a Sphere derivation?

    Hi, Is there a way to derive the moment of inertia of a sphere without using the M of I of a cylinder? In other words, is it possible to find a sphere's from scratch? Please include a derivation in your answer, unless there isn't one of course.
  34. G

    Differentiation with respect to a function

    Hi. A very long problem brought me to a derivative in the form \frac{\mathrm{d}f(x)}{\mathrm{d}g(x)} I'm assuming that \mathrm{d}g(x)=\left(\frac{\mathrm{d}g(x)}{\mathrm{d}x}\right)\mathrm{d}x So, is it correct to say that...
  35. PratyashAstro

    Derivation of self inductance formula in an LC circuit

    My observation is to verify self inductance formula by measuring the resonant frequencies of different coils in an LC circuit.For this, I am asked to use this formula by my mentor : L = 1/(4π^2 . f^2 . C) Here, f = different resonant frequencies, C = capacitance of the capacitor in the LC...
  36. D

    Is there any derivation of Newton's second law?

    is there any derivation of Newton second law?
  37. R

    Stuck on last part of class derivation (proof) K-G Eqn

    Mentor note: fixed formulas so they get displayed properly If we take the K-G eqn and the following term for the wave function $$( \partial^2 + \frac{m^{2}c^{2}}{\hbar^{2}})\Psi =0 \\\\\Psi = Re^{-i\omega t + i k_{i}x_{i}}$$We worked through to this ##\hbar \omega = \pm \sqrt{\hbar^{2}...
  38. D

    Help! EM Exam: Covariant LW Fields Derivation Questions

    Hi I am doing some exam revision for an EM class and I'm trying to understand a few things about this derivation. Specifically in equation 18.23 why do we not consider the derivative of the four velocity i.e ##\partial^{\alpha}U^\beta## Then going from 18.23 to 18.25 why is...
  39. resurgance2001

    Deriving E(ave)=kT: Is it Correct?

    I have attached a photo of a page from a book that I am studying. The author is showing a derivation of E(ave) = kT However, I can't follow this derivation. He says that you need to use integration by substitution and I am OK with that. But when he actually does the substitution it looks...
  40. B

    Coloumbs constant's derivation

    I want to know how coloumbs constant was derived without using gausses law
  41. S

    Derivation of a cinematic formula

    I'm really happy about every hint! Homework Statement There is a ball on hight h which is dropped on a table. With every Impact the ball loses velocity v by a factor a<1. I Need to Show the following: The time T after the ball stopps bouncing is: T = \frac{1+a}{1-a} (\frac{2h}{g})^\frac{1}{2}...
  42. M

    Derivation of the equations of APF

    I am working to use the artificial potential field method for path planning of mobile robot; actually I found in one of references the following description about this method: the artificial potential field method uses a scalar function called the potential function. This function has two...
  43. B

    Derivation of coloumbs law without Gauss's law

    Whenever I try searching on how coloumbs law is derived Gauss's law is always used,for this reason when I search for Gauss's law it is always derived from coloumbs law :frown:.could you guys guys help me out by telling me which camfirst and how it was derived Coloumbs law- F=Q1Q2/r2ε Gauss's...
  44. F

    Derivation of electromagnetic waves

    I've seen derivations for c=E/B and c=1/√μ0ε0, but I don't seem to get the directions right. i.e. I end up with a negative sign in one of the equations. The derivations I've seen do not use vector calculus. One derivation I've seen is in http://Derivation[/PLAIN] of Electromagnetic Waves from...
  45. vrble

    Derivation of the Area Formula for Triangles Using Axioms

    From Apostol's Calculus Volume I, "Area as a Set Function" 1. Homework Statement : Right triangular regions are measurable because they are constructed from the intersection of two rectangles. Prove that all triangular regions are measurable and have an area of the product of one-half, their...
  46. acdurbin953

    Astronomy derivation, leading to question about oscillations

    Homework Statement The sun experiences a vertical gravitation acceleration of g=-4πGρz, where ρ is the density of the disk of our Galaxy. a) Assuming that d2z/dt2=-kz, express k in terms of ρ and G. b) Find the general expression for z and w=dz/dt as a function of time. c) If the total mass...
  47. binbagsss

    Tod & Hughston GR Intro: FRW Metric Derivation w/ R=6k or R=3k?

    I'm looking at Tod and Hughston Introduction to GR and writing the metric in the two forms; [1]##ds^{2}=dt^{2}-R^{2}(t)(\frac{dr^{2}}{1-kr^{2}}+r^{2}(d\theta^{2}+sin^{2}\theta d\phi^{2}))## [2] ##ds^{2}=dt^{2}-R^{2}(t)g_{ij}dx^{i}dx^{j}## where...
  48. binbagsss

    Proving Total Covariant/Total Partial Derivative EFE Derivation

    I'm trying to prove that ##\sqrt{-g}\bigtriangledown_{\mu}v^{\mu}=\partial_{\mu}(\sqrt{-g}v^{\mu}) ## So i have ##\sqrt{-g}\bigtriangledown_{\mu}v^{\mu}=\sqrt{-g}(\partial_{\mu}v^{mu}+\Gamma^{\mu}_{\mu \alpha}v^{\alpha}) ## by just expanding out the definition of the covariant derivative...
  49. anandzoom

    How do I correctly derive the formula d = vt + 1/2 at^2?

    d=vt+1/2at^2 Derive me this formula please... When I do I get 1/2(vt+at^2)...i know that I'm doing a mistake by not considering the initial velocity... So how do I correct it?
  50. Y

    Strain Gauge Formula Derivation

    Using R = ρL/A, I am trying to get this formula, which is the change in resistance due to change in length, area, and resistivity. ΔR = (∂R/∂L)ΔL + (∂R/∂A)ΔA + (∂R/∂ρ)Δρ I understand the above conceptually, but I am confused about why we are multiplying by terms ΔL, ΔA, and Δρ. Intuitively, I...
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