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. T

    Car on a banket - maximum speed formula derivation

    Hi, This is not related with a specific homework question. I was studying this topic and have noticed that I didn't understand some bits.The car is negotiating a bend with a speed of V. The slope of the banket is θ The coefficient of friction is η Weight of the car if mg Radius of the bend is R...
  2. snoopies622

    Seeking derivation of real scalar field Lagrangian

    Here and there I come across the following formula for the Lagrangian density of a real scalar field, but not a deriviation. \mathcal{L} = \frac {1}{2} [ \dot \phi ^2 - ( \nabla \phi ) ^2 - (m \phi )^2 ] Could someone show me where this comes from? The m squared term in particular...
  3. G

    The easiest derivation of rod's moment of inertia?

    Homework Statement Derive the formula for rod's moment of inertia: I = ml2/12 Homework Equations I = ml2/12 The Attempt at a Solution The only one derivation I know of is dividing the rod into two parts and then integrating from 0 to l/2. However' I'd love to know if there's some...
  4. ElijahRockers

    Imaginary Numbers Derivation

    Homework Statement Derive the following relation, where z1 and z2 are arbitrary complex numbers |z1z2*+z1*z2| ≤ 2|z1z2| The Attempt at a Solution I found the expression |z1z2*+z1*z2| = |2(a1a2+b1b2)| = √(4[a12a22 + 2a1a2b1b2 +b12b22]) But that is where I get stuck. How does the...
  5. B

    First-Order Perturbation Theory Derivation in Griffiths

    Homework Statement On page 251 of Griffiths's quantum book, when deriving a result in first-order perturbation theory, the author makes the claim that <\psi^0|H^0\psi^1> = <H^0\psi^0|\psi^1> where H^0 is the unperturbed Hamiltonian and \psi^0 and \psi^1 are the unperturbed wavefunction and its...
  6. A

    P(t) = V(t)I(t) derivation

    I kindly ask for assistance in derivation of the equation for instantaneous power in an electric circuit, P(t) = V(t) I(t). I want to derive it as rigorously as possible. Here's what I got: We start with P = {\bf F} \cdot {\bf v}, where {\bf v} = \frac{d\bf r}{dt} We know that the force...
  7. NanaToru

    Use geometry -Redshift derivation?

    "use geometry"--Redshift derivation? 1. Use geometry to derive z=v/c where c is the speed of light and z = [v(obs)-v(em)]/v(em). Homework Equations None given... Though I am assuming that I am constant. The Attempt at a Solution I believe it has to do with the Doppler effect which...
  8. D

    Derivation of the Biot-Savart Law from Coulomb's Law?

    The title says it all--I'm working through The Feynman Lectures, and came across the assertion that a magnetic field can be thought of as a relativistic-transformation of an electric field (and vice-versa). This makes sense to me, since the magnetic field of a moving point-charge can easily be...
  9. H

    Reversal of limits of integration in the derivation of probability current density

    In working out the derivation of the probability current density, I see (based on the definition of j(x,t)) that the limits of integration are changed from d/dt∫(b to a) P(x.t) dx = iħ/2m[ψ*(x.t)∂/∂xψ(x.t) - ψ(x.t)∂/∂xψ*(x.t)](b to a) to d/dt∫(b to a) P(x.t) dx =...
  10. JJBladester

    Ripple Voltage Derivation (Full-Wave Rectifier)

    Homework Statement Derive the ripple voltage of a full-wave rectifier with a capacitor-input filter. Homework Equations Where V_{r(pp)} is the peak-to-peak ripple voltage and V_{DC} is the dc (average) value of the filter's output voltage. And V_{p(rect)} is the unfiltered peak rectified...
  11. Y

    Please verify my derivation on elliptical polarization of EM wave

    This is not a home work, it is part of the textbook on elliptical polarization. Attached is a page in Kraus Antenna book, I cannot verify the equation on the last line. Here is my work E_y=E_2(\sin{\omega} t \cos \delta \;+\; \cos \omega {t} \sin \delta) , \sin\omega {t} =\frac {E_x}{E_1}\;,\...
  12. Mandelbroth

    Derivation of the Antiderivative of the Gaussian Distribution

    I'm in a high school pre-calculus class and a statistics class. For the latter, we are given z-tables for some of our tests. I don't like these z-tables. Thus, I decided that a more direct approach (fundamental theorem of calculus) would be more accurate and, more importantly, more fun. My...
  13. Mandelbroth

    Deriving Quantum Numbers from the Schrodinger Equation

    Can someone explain to me how one gets the values of n, l, and ml (principle quantum number, azimuthal quantum number, magnetic quantum number, respectively) from the Schrodinger equation for use in chemistry involving distribution of electrons in a hydrogen atom?
  14. N

    Doubt regarding derivation of bound charges in dielectric

    In Griffiths, for deriving the bound charges for a given polarization P , the formula used is the general formula for dipoles .i.e ( equation 4.9) {Here the potential at r is calculated due to the dipole at r' ) V(r) = ∫\frac{x.P(r')}{X^2}d\tau' Here X = r - r' , and x = unit vector in...
  15. A

    Derivation of the thermodynamic potentials using Legendre transformations

    Hello guys, I'm studying Thermodynamics and I don't totally see how you introduce the potencials using Legendre transformations. I have seen a non formal explanation showing how you can interpret them, but not a rigorous demonstration of how you get them via the Legendre transformations...
  16. S

    Derivation of the Geodesic equation using the variational approach in Carroll

    Hello Everybody, Carroll introduces in page 106 of his book "Spacetime and Geometry" the variational method to derive the geodesic equation. I have a couple of questions regarding his derivation. First, he writes:" it makes things easier to specify the parameter to be the proper time τ...
  17. D

    How do I calculate Lie derivation of a metric?

    Homework Statement I've searched everywhere, and I cannot find an example of calculation of Lie derivation of a metric. If I have some vector field \alpha, and a metric g, a lie derivative is (by definition, if I understood it): \mathcal{L}_\alpha g=\nabla_\mu \alpha_\nu+\nabla_\nu...
  18. M

    Derivation of Euler-Lagrange equation?

    Homework Statement Problem 1: Derive the Euler-Lagrange equation for the function ##z=z(x,y)## that minimizes the functional $$J(z)=\int \int _\Omega F(x,y,z,z_x,z_y)dxdy$$ Problem 2: Derive the Euler-Lagrange equation for the function ##y=y(x)## that minimizes the functional...
  19. C

    Derivation of the kinetic energy equation in terms of distance.

    I have seen the derivation of the kinetic energy equation using F=M*v' and E=F*x And I can see how this works, however if you try to do this without thinking about velocity, and only thinking about the rate of change of distance, and the rate of change of rate of change of distance, then the...
  20. D

    DU/dt = 0 for oscillating spring, help with derivation

    U = energy In the book: \frac{dU}{dt} = \frac{d}{dt} (\frac{1}{2} mv^2 + \frac{1}{2} kx^2) then we have m \frac{d^{2}x}{dt^2} + kx = 0 because v = \frac{dx}{dt} however they get rid of \frac{dx}{dt} . They are ignoring the case where v = 0, because then m \frac{d^{2}x}{dt^2} + kx...
  21. T

    Deriving SHM: Help Needed for Challenging Problem in Textbook

    This is actually the problem in the textbook. I'm trying to derive the harmonic oscillator differential equation for this system, but It seems like it's very very challenging. could anyone help me out? Following is the question and figure from the textbook. Homework...
  22. G

    Don't understand critical part of derivation in textbook.

    I've been working my way through Intro to Electrodynamics (Griffiths), and in Chapter 3, one of the derivations comes out to ∫sin(n\piy/a) sin(n'\piy/a) dy ={ 0 if n'\neqn a/2 if n'=n where the function is...
  23. K

    MHB Derivative of f:R->R with f'(x)=[x^2/1+(x^2))], f(0)=0 and its Bounds on R

    f:R->R is differentiable and f'(x)=[x^2/1+(x^2))] and f(0)=0. check whether 0<=f(x)<=x for all x belonging R. Thanks.
  24. I

    Newton's derivation of Kepler's laws

    Introduction This is not a homework or coursework question (if it were it would be of the project type), and I am looking for hints not spoilers. Hi, I recently passed by kepler's laws again in a science class (this time Earth science), and am concurrently taking calculus in my math class...
  25. 0

    Derivation of Instantaneous Velocity

    Find the instantaneous velocity where r is the position vector as a function of time: r(t)=(3.0m/s^2)t\hat{x}+(4.0m/s)t\hat{y} I attempted to find the derivative of this to find instantaneous velocity, but the book's solution was different. I think the author of the book may have made a...
  26. Jalo

    Archived Partial Derivatives and Constant Variables in Thermodynamics

    Homework Statement Consider the following equality: (\frac{∂S}{∂V})T = (\frac{∂P}{∂T})V If I rearrange the equality so that I write: (\frac{∂S}{∂P})? = (\frac{∂V}{∂T})? What variables will be constant in each side? I'm having some trouble in a few thermodynamics problems because...
  27. N

    How Is Normal Strain Derived in Continuum Mechanics?

    http://imgur.com/SnHyP What are the mathematical steps and assumptions to reach the conclusion that length(ab) ≈ dx + ∂u/∂x*dx ? If you consider the the squares of the gradients to be negligible, you still have a square root and multiplication by the constant "2". What other assumptions do...
  28. N

    Derivation of normal strain

    http://imgur.com/SnHyP What are the mathematical steps and assumptions to reach the conclusion that length(ab) ≈ dx + ∂u/∂x*dx ? If you consider the the squares of the gradients to be negligible, you still have a square root and multiplication by the constant "2". What other assumptions do...
  29. F

    Momentum balance derivation in equations

    I'm a little confused, in my fluid mechanics course we've covered many equations and they are all derived using an x-direction fluid flow. If I was to use these in a system in which fluid flowed in the y-direction would I have to re-derive them? Or would it be more of a case of using a...
  30. C

    Thermodynamic Derivation of Wien's Law?

    Can someone tell me how I can derive Wien's law, i.e., \lambda_{max} T = constant where \lambda_{max} is the peak wavelength and T is the absolute temperature of the black body, using the equation, P=\frac{U^{*}}{3} where U^{*} is the energy density. Note: I'm not looking for...
  31. B

    Stuck on derivation of Euler's equations in rigid body dynamics

    i was reading about derivation of Euler's equations for rotational dynamics (john taylor, classical mechanics, chapter 10) when i got stuck on one of the reasonings essentially it refers to the moment of inertia tensor, since the tensor itself about a point is dependent on the position of the...
  32. J

    Astronomical telescope: derivation - greatest magnification (detail) formula

    Homework Statement I am seeking a derivation of the formula for greatest detail or maximum resolution of an astronomical telescope, which is: Homework Equations M = fo/foe where: M: magnification fo: focal length of objective lens foe: distance of primary image from the eyepiece...
  33. P

    Is there a connection between energy derivation and Newton's Law of Motion?

    Hey guys, I was trying to reverse engineer Einstein's formula for energy, E=γmc^2 by re-engineering Newton's Law of motion, F=ma. I was talking with my physics prof about deriving energy from this because I got two different answers but it gets weird because the incorrectly derived formula...
  34. M

    Simple derivation for elastic collisions, where is my mistake?

    Homework Statement http://postimage.org/image/j2ccrtjp1/ Here is a scan of my work. The problem is on the scan. Just trying to derive the velocity of the target in an elastic collision, as sketched in the image... Can't seem to find the problem for the life of me.
  35. A

    Stiffness Equation for Spring Dimensions: How is it Derived?

    Equation attached. For those who can't see the image here it is in text form, k=(Gd^4)/(8D^3 n ) It is the equation for the stiffness of a spring in terms of its dimensions: G - shear constant d - wire diameter D - coil average diameter n - number of active coils (total coils -2 as...
  36. A

    Simplest derivation of Lorentz Transformation

    I'm just getting started on relativity. I watched this a couple of day ago - But I didn't like the way Lorentz Transformation was derived (the assumption about the nature of the final transformations, to be more specific). I tried reading Einstein's original paper for a better derivation but...
  37. W

    General question about a derivation

    I just have a question of "why/how?" I know that for instance \mathbf v=\omega \hat k \times \mathbf r where \mathbf v is my vector for velocity, \omega is my angular velocity and \mathbf r is my position vector from a point on the axis of rotation of a wheel to a point on the outer edge of the...
  38. F

    Derivation of Acceleration from Velocity with Partial derivatives

    Homework Statement I'm taking a fluid mechanics class and I'm having an issue with acceleration and background knowledge. I know this is ridiculous, but I was hoping someone might be able to explain it for me. Homework Equations I definitely understand: ##a=\frac{d\vec{V}}{dt}## And I...
  39. P

    How was the Lorentz factor derived?

    So I know about the lorentz factor and how it describes time dialition, mass increasing etc.. but I was wondering how it was derived in the first place?
  40. U

    How do I derive the particle flux for a cylindrical vessel?

    Homework Statement Consider a cylindrical vessel with cross-sectional area 1m^2 Derive the particle flux (1/4n\bar{v})Homework Equations I have the solid angle: \Omega = 2π(1-cosθ) The Attempt at a Solution I'm assuming that the solid angle represents the full area that the particles can...
  41. S

    Wave Function Doubt and Derivation

    Homework Statement I was reading up on the Wave Function used in the Schrodinger Wave Equation. However one source said that ψ(x,t)=e^(-i/hbar*(px-Et)) Another source had this ψ(x,t)=e^(i/hbar*(px-Et)) Which one of these is true and could someone give a derivation for the correct...
  42. C

    Derivation of pressure differences in a stream.

    Homework Statement I tried to reach the Bernoulli principle this way: Two pipes are connected, one has a cross-sectional area of S_{1} and speed of v_{1}; S_{2} and v_{2} for the other. The pipes are horizontal, the connecting wall between them at the crossing from one pipe to the other is...
  43. G

    Betatron, derivation of expressions

    Hi! I've got a problem with question 5 on this paper: http://www.freeexampapers.com/past_papers.php?l=Past_Papers%2FAEA%2FPhysics%2F2006/ Download AEA-PHYS-PP-MayJune-2006-AEA-Paper-1342.pdf. Starting from b) i), we got that: ε=Δ∅/Δt → W=εe Where W is denotes work, ε is...
  44. Jalo

    Parcial derivation of two variable function

    Homework Statement Given the function f(x) defined as: (x^3-y^3)/(x^2+y^2) if (x,y)≠(0,0) 0 if (x,y)=(0,0) Find the parcial derivatives of the function at the point (0,0). Is the function f differentiable? Homework Equations The Attempt at a Solution d/dx [...
  45. M

    Understanding the Disappearance of 2*A^*<A> and 2*B^*<B> in Derivations

    Hello guys, Check the attachment please. How is it what's written after "HENCE"? Where did 2*A^*<A> term go? the same thing for 2*B^*<B>??
  46. K

    Derivation of Maxwell's relations

    In thermodynamics one of the maxwell relations is: \left( \frac{\partial S}{\partial V} \right)_T = \left( \frac{\partial P}{\partial T} \right)_V When I try to derive it from dU = TdS - PdV i get: T = \left( \frac{\partial U}{\partial S} \right)_V P = -\left( \frac{\partial...
  47. C

    Derivation of mass invariance using Lorentz transformation

    Homework Statement As the title suggests, I need help finding resources that clearly shows the step by step process of the derivation of the rest or invariant mass using the Lorentz transformation. Homework Equations Energy-momentum relation The Attempt at a Solution Not looking...
  48. S

    Meaning and derivation of 4-vector

    Meaning of ct in Lorentz transformation - In Lorentz transformation matrix, the first column is defined as - ct, not t itself. Is it because ct satisfies the units of x, y, z? Or, simpler Lorentz transformation matrix will be derived? The idea of 'ct', instead of t, is quite abstract for me...
  49. D

    Derivation of the equilibrium saturation ratio equation?

    Homework Statement S=1+(a/r)-(b/r^3) Homework Equations need to find r=sqrt(3b/a) and S=1+ sqrt((4a^3)/(27b))) from a derivation of the above formula in #1. The Attempt at a Solution 0=(3b/r^4) - (a/r^2)
  50. H

    Understanding the Derivation of E=hf and its Significance in Quantum Physics

    What is the derivation for E=hf and why did experimental observation of black bodies show that quantization of light was neccessary?
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