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. rosaliexi

    Derivation Constants/Rate of Change

    Hi, I'm working on a process control question about a tank system at steady state. The part I'm having problems with is where I have derived a second order differential equation to model the system and have replaced the concentrations with derivation constants in that : Actual Concentration at...
  2. H

    Why Is Bloch's Theorem Derived Using Complex Methods?

    Why are the solutions satisfying ##\psi(x+l)=\lambda\,\psi(x)## (4.191) the only physically admissible solutions? (##l## is the period of the periodic potential.) We may argue that the probability of finding an electron at ##x##, ##|\psi(x)|^2##, must be the same at any indistinguishable...
  3. J

    Derivation of moment of inertia of a solid sphere

    Homework Statement I need to know why my derivation does not work. I am attempting to derive I=2/5 mR^2Homework Equations I have seen people derive it using disks but my question is why do the shells not work? Where in my set up did I go wrong? Thanks The Attempt at a Solution I am attempting...
  4. I

    Graphical Derivation of x = Asin(ωt)

    Homework Statement Deriving the equation for simple harmonic motion, x = Asinωt, graphically. Homework Equations ω = 2πf, where f = 1/T 2. The attempt at a solution Take a sine curve as the simple harmonic motion (displacement, x, on y-axis; time, t, on x-axis), then transform it. The...
  5. M

    Derivation of wave equation using tension of a string

    Homework Statement I'm currently following the textbook Advanced Engineering Mathematics by Erwin Kreyszig. I'm learning the derivation of the Wave equation using the method shown in the book, but when I reached the final part of the derivation, the working just confuses me. (1/Δx)[ (u/dx)|...
  6. weezy

    Doubt regarding derivation of De Broglie relation

    For someone who's familiar with the de Broglie relation it's easy to say that for k=0 we have p=0 but how would we know that before deriving the result? In this image the author derives de Broglie relation by considering a wave packet in motion. As you can see where I have star-marked the author...
  7. T

    Derivation of acceleration in rotating coordinates

    I was just trying to write out the derivation for an object's trajectory from an inertial coordinate system if the object is rotating in another coordinate system (e.g. finding Coriolis, centrifugal acceleration). I seem to have gotten something close to what I was looking for, but after...
  8. H

    Derivation of the momentum-to-the-power-of-n operator

    Homework Statement Homework Equations The Attempt at a Solution First substitute ##\Phi(p,t)## in terms of ##\Psi(r,t)## and similarly for ##\Phi^*(p,t)##, and substitute ##p_x^n## in terms of the differentiation operator ##< p_x^n>\,=(2\pi\hbar)^{-3}\int\int...
  9. Titan97

    Derivation of induced charge on a dielectric

    Homework Statement Show the the induced charge density on a dielectric placed inside a capacitor is given by $$\frac{k-1}{k}\sigma$$ where ##\sigma## is the charge density of the capacitor plates and ##k## is the dielectric constant. Homework Equations $$E=\frac{E_0}{k}$$ The Attempt at a...
  10. H

    Derivation of Schrodinger's equation in momentum space

    Homework Statement How do you get from (3.171) to (3.172)? In particular, why is ##\int e^{-ip.r/{\hbar}}\frac{p_{op}^2}{2m}\Psi(r,t)\,dr=\int\frac{p_{op}^2}{2m}[e^{-ip.r/{\hbar}}\Psi(r,t)]\,dr##? ##\,\,\,\,\,##-- (1) Homework Equations The Attempt at a Solution For (1) to be true, it...
  11. K

    Discrete Fourier series derivation

    Hello,*please refer to the table above. I started from x(n)=x(n*Ts)=x(t)*delta(t-nTs), how can we have finite terms for discrete time F.S can anyone provide me a derivation or proof for Discrete F.S.?
  12. wololo

    [itex](\frac{\partial U}{\partial P})_T[/itex] derivation

    Homework Statement Homework Equations Maxwell relations The Attempt at a Solution Here is how I proceeded. Am I allowed to go from line 1 to 2? It almost seems too simple. dU=TdS-PdV \\ (\frac{\partial U}{\partial P})_T=T(\frac{\partial S}{\partial P})_T-P(\frac{\partial V}{\partial P})_T...
  13. O

    Work-Energy Derivation question: F(x(t)) = F(t) ?

    Does this derivation: ...imply: My best guess is that x(t) ≠ t So I would also guess that F(x(t)) ≠ F(t) But then how can this derivation be explained? How can F(x(t)) = m(a(t))? What does that actually mean? How come it's not: F(x(t)) = m(a(x(t))) ? Why/How does the x just cancel...
  14. A

    I Question in linear algebra, derivation of a certain relation

    Hello good people, please refer to this: (notice the mistake in 9.31: cos(psi) switches places with cos(phi)sin(psi) to the best of my understanding) Now, I am trying to derive 9.30 and for this, according to the book, we solve 9.32. The problem is I can not understand 9.32, the meaning of...
  15. W

    Derivation of formula of centroid

    Homework Statement what is y ′and y bar ? why y ′ is changed to y bar ? why are they = 0 ? Homework EquationsThe Attempt at a Solution
  16. AwesomeTrains

    Question about the derivation of the energy momentum tensor

    Hey I'm trying to follow the derivation given here: http://lampx.tugraz.at/~hadley/ss1/studentpresentations/Bloch08.pdf Homework Statement As it says in the pdf: "Based on Noether's theorem construct the energy-momentum tensor for classical electromagnetism from the above Lagrangian. L=-1/4...
  17. C

    Derivation of momentum for the complex scalar field

    The conserved 4-momentum operator for the complex scalar field ##\psi = \frac{1}{\sqrt{2}}(\psi_1 + i\psi_2)## is given in terms of the mode operators in ##\psi## and ##\psi^{\dagger}## as $$P^{\nu} = \int \frac{d^3 p}{(2\pi)^3 }\frac{1}{2 \omega(p)} p^{\nu} (a^{\dagger}(p) a(p) +...
  18. Odious Suspect

    Binomial Coefficient Factorial Derivation

    A few decades ago my algebra teacher showed how to construct the expression for binomial coefficients. If I start with Pascal's recursion, and propose C(n,k)=n!/k!(n-k)!, I can prove it to be so through induction. But that doesn't give me that happy feeling that comes with understanding. It...
  19. DiracPool

    Metric in polar coordinate derivation

    At time 1:11:20, Lenny introduces the metric for ordinary flat space in the hyperbolic version of polar coordinates? Is that what he is doing here? d(tau)^2 = ρ^2 dω^2 - dρ^2. He then goes on to say that this metric is the hyperbolic version of the same formula for Cartesian space, i. e...
  20. Y

    How is Fick's First Law derived?

    How do you derive it? I'm looking for the form J = -D(dC/dX) From the image, I am assuming left side is of higher concentration. N represents the number of molecules. My work: Mass balance Net molecules in from concentration gradient = Net = N(x) - N(x+Delta X) Net concentration in =...
  21. K

    Boltzmann distribution derivation.

    please check the video at 5:33. how can we find the partial derivative w.r.t n1 n2 and on? isn't each state (n1, n2 and on) one discrete state not a continuous variable? is it because we can have multiple particles in the given energy state? However its a finite discrete number. as far as I...
  22. K

    Derivation of Electric Field with Gauss's Law

    I did everything I could to solve the following problem: A solid ball of radius rb has a uniform charge density ρ. What is the magnitude of the electric field E(r) at a distance r>rb from the center of the ball? E(r) = My third attempt went like this: qencl=[ρ(4/3)(π)rb3]...
  23. gracy

    Questions based on derivation of electrical potential energy

    Consider a system of two charges ## q_1## and ##q_2## separated by distance ##r_1##.This configuration is associated with a potential energy ##U_1##.When the separation is increased to ##r_2##.Potential energy becomes ##U_2## ##dW_E##=##\vec{F}##.##\vec{dr}##...
  24. Dusty912

    Really with lab derivation -- Rolling objects down an incline

    Homework Statement So I attached the page from the lab with the directions for the derivation. It may be easier to view that document. The lab was set up was taking two objects and rolling them down an incline. The time was measured using photo gates. Basically, I need to use conservation of...
  25. T

    Missing something obvious in this derivation

    Hi, I've attached a file displaying a derivation to make the kinetic energy of a two-body problem into a kinetic energy only involving the reduced mass. When plugging 8.3 into 8.1, I just don't quite see how this derivation makes sense. Shouldn't there be a $$ \mu^2$$ term? Since when squaring...
  26. PWiz

    Christoffel symbols derivation

    I've attempted to derive an expression for the Christoffel symbols (of the 2nd kind) solely in terms of the covariant and contravariant forms of the metric by only using the definition of the Christoffel symbols. I would like to know if my approach is correct or not. The Christoffel symbols are...
  27. saybrook1

    Alternative Derivation of sin integral

    Homework Statement Hi guys; I'm just dealing with Fourier series and they evaluate integrals such as ∫sin(nπx/L)dx from 0 to L as (L/nπ)[1-(-1)^n]. Can someone please tell me how to get to this conclusion or point me in the direction of a resource that will show me? Additionally I need to solve...
  28. K

    Derivation of Fermi-Dirac distribution

    http://ecee.colorado.edu/~bart/book/book/chapter2/pdf/ch2_5_5.pdfcan you please tell me where f/(f(gi,fi) is from? and also how to get to (2.5.13)
  29. wololo

    How Can dv/dx Be Determined to Solve for dv/dt?

    Homework Statement Homework Equations Chain rule, partial derivation The Attempt at a Solution dv/dt=dv/dx*dx/dt+dv/dy*dy/dt dx/dt=-4t -> evaluate at (1,1) =-4 dv/dt=-4dv/dx+4(-2) dv/dt=-4dv/dx-8 How can I find the missing dv/dx in order to get a value for dv/dt? Thanks!
  30. shounakbhatta

    Deriving 8πG/c^4 in General Relativity

    Hello All, In GR the factor 8piG/c^4. I want to understand how the term is derived? I mean to say that is this related to Friedmann Equation. How the factor actually comes into Einstein's field equation? I am sorry if I am unable frame the question properly. Thanks. -- Shounak
  31. N

    Rayleight scattering derivation

    Homework Statement I have a problem understanding derivation of particular equation in a textbook on Optical Waveguide Theory (Snyder, Love) - see attached. The equation 5.79 is the starting point. Explanation of 5-80 are clear and derivation of 5-81 likewise. I am stuck, however with 5-82...
  32. S

    Derivation of Lorentz algebra commutation relation

    Homework Statement 1. Show that the Lorentz algebra generator ##J^{\mu \nu} = i(x^{\mu}\partial^{\nu}-x^{\nu}\partial^{\mu})## lead to the commutation relation ##[J^{\mu \nu}, J^{\rho \sigma}] = i(g^{\nu \rho}J^{\mu \sigma} - g^{\mu \rho}J^{\nu \sigma}-g^{\nu \sigma}J^{\mu \rho}+g^{\mu...
  33. P

    The physical derivation of annihilation operator?

    From P. Meystre's book elements of quantum optics (Many labels of equations are wrong:H) Page 83, the annihilation operator and creation operator, which are helpful to discuss harmonic oscillator, are defined as ## a=\frac{1}{\sqrt{2\hbar\Omega}}(\Omega q+ip),\\...
  34. S

    Peskin and Schroeder - Derivation of equation (2.45)

    I'm having trouble deriving equation (2.45) on page 25. In particular, in the derivation of ##i\frac{\partial}{\partial t}\pi({\bf{x}},t) = -i(-\nabla^{2}+m^{2}) \phi({\bf{x}},t)##, I need to show that ##\frac{1}{2}\pi({\bf{x}},t) \phi({\bf{x'}},t)(-\nabla^{2}+m^{2}) \phi({\bf{x'}},t) -...
  35. Geofleur

    Derivation from Landau and Liffshitz, vol 6

    I have starting working through section 134 of Landau and Lifshitz, vol 6, and it seems I have entered some kind of twilight zone where all my math/physics skills have left me :cry: The derivation starts with the energy-momentum tensor for an ideal fluid: ## T^{ik} = wu^i u^k - p g^{ik} ##...
  36. K

    Derivation of PV=nRT: Exploring Logic Behind the Ideal Gas Law

    http://quantumfreak.com/derivation-of-pvnrt-the-equation-of-ideal-gas/please check eq.(7) pressure equation is P=F/A which means, in any region over the surface, pressure will be the same. for example, if we assume all the particles have the same mean squared velocity, pressure of one cube will...
  37. P

    Deriving the Equation for Projectile Motion: t = 2(vi)/g*sin(theta)

    1. Derive this equation t = 2(vi)/g*sin(theta) where vi isinitial velocity, and g is acceleration due to gravity 2. Implicit differentiation, possibly gravity as a constant.The Attempt at a Solution t = 2(vi)/v*sin(theta) dt/d(theta) = 2(vi)/g * dt/d(theta)(sin(theta)) dt/d(theta) = 2(vi)/g *...
  38. I

    Derivation of 1st order correction to energy degenerate spec

    Hello there ! I need to derive the formula of first order correction to the energy in the case of discrete level of wave function with descrete spectrum.
  39. L

    Can The Joule Coefficient be Derived Using the First Law and Maxwell Relation?

    The Joule coefficient, μJ, is defined as μ = (∂T/∂V)U. Show that μJ CV = p – αT/κ Relevant equations Cv=(∂U/∂T)v κT=-1/V*(∂V/∂p)T α=1/V*(∂V/∂T)p dV(T,p)=(∂V/∂T)pdt+(∂V/∂p)TdpWhat I have attempted was to make μ = (∂T/∂V)U=(∂T/∂U)V(∂U/∂V)T=(∂U/∂V)T*Cv-1. Then α/κT=(∂V/∂T)p/(∂V/∂p)T because the...
  40. T

    Understanding derivation of delta-y transform

    Hi, I was just looking over my textbook, and it mentions a ## \Delta##-y and y-## \Delta## transformation that is helpful for dealing with circuits in these configurations. The equations can be found here...
  41. C

    Question regarding the derivation of the wave equation

    Homework Statement There's a derivation here that I'm looking at, and I've hit a snag. At (1) about 15 lines down the page, the author divides by Δx and takes the limit as Δx goes to 0. I understand what he did on the right side of the equation, but on the left side of the equation, by what...
  42. Amr Elsayed

    Derivation of orbital velocity formula

    Is there some mathematical derivation for calculating the orbital velocity based on altitude and acceleration without using calculus? I thought of equations of motion, but I always get problems. Is there a way to derive it using laws of gravitational potential and kinetic energy ? Are the...
  43. S

    Time averaged intensity, derivation and vector plot

    Homework Statement I'm trying to graph this equation: [/B] I'm trying to use the champ command in scilab to graph this from -π to π on the kx and ky axes. But this requires the x and y components of the vector as arguments. How do I get those components, is there a command for that? There's...
  44. M

    Intuitive ways to think of integration and second derivative

    Hi, I feel sometimes when I'm doing calculus I lose the logic and intuition behind what I'm doing, especially when integrating. I have yet to find a way to think about it in a way it makes sense to me why the definite integral would tell us the area under a curve. Same with why the second...
  45. G

    Tangent of function and its limit position

    Homework Statement Find tangent line of y=xe^{\frac{1}{x}} at point x=\alpha and it's limit position when \alpha \rightarrow +\infty. Homework Equations Tangent of y=f(x) at point M(x_0,f(x_0)): y-y_0=f^{'}(x_0)(x-x_0) The Attempt at a Solution Applying the above equation for tangent of...
  46. P

    Maximizing x-component of force

    A charge Q is placed at a distance a = 3m and a charge q is placed at a distance b For what value(s) of b is the x-component of the force maximized? I know to maximize the force we need to maximize F_Qq = k Qq b/(3^2 + b^2)^{3/2}. To do this we need to set the first derivative to zero and...
  47. pabilbado

    Harmonic oscillator derivation

    I was wondering how to derive the sinusoidal equation for the simple armonic oscillator. But I am currently trying to understand this step in this webpage: I don't get where do P and Q come from and why it is summing pe^iwt + qe^-iwt. please I need some help. The rest of it pretty much makes...
  48. H

    Index Notation, taking derivative

    Can anyone explain how to take the derivative of (Aδij),j? I know that since there is a repeating subscript I have to do the summation then take the derivative, but I am not sure how to go about that process because there are two subscripts (i and j) and that it is the Kronecker's Delta (not...
  49. B

    Help with probably basic integral?

    In some reading I came across this equation P/P1=(T/T1)^-g/aR which can apparently be derived from dp/P=(-g/RT)dh when T=T1 + a(h-h1). I don't really understand how they could have taken the a out of the integral in order for it to be part of the exponent once you get rid the the ln on both...
  50. C

    Orbital and Spin Angular momentum of light derivation

    Homework Statement The momentum carried by an electromagnetic field is [;\vec{P}(\vec{x}, t) = \frac{1}{4\pi c} \int d\vec{x}\vec{E}(\vec{x},t) \times \vec{B}(\vec{x},t);] show that for a finite field extension [;\vec{J}(\vec{x}, t) = \frac{1}{4\pi c}\int -i...
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