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. L

    Derivation of Height Function given an angle

    Hey everyone, I'm currently doing research at a University, I've been working on a problem for a few hours and wrote up a quick paper that shows my derivation of a certain height based on an angle. Basically the experiment is looking at optical properties of graphene, but for this to happen we...
  2. T

    Students t-distribution Derivation

    I have attempted a derivation of the Students t-distribution probability distribution function in the attached pdf. I defined T to be Z/sqrt(W/v) where Z has standard normal distrubution and W has chi squared distribution with v degrees of freedom. I know that Z and W need to be independent, but...
  3. tomwilliam2

    Derivation of relativistic E_kin

    In my textbook there is a derivation of relativistic kinetic energy starting from an integral of the force applied over the distance required to take the particle's speed from 0 to v. There's one stage of the derivation I don't understand on mathematical grounds, which is going from: $$E_k =...
  4. R

    MATLAB Skin effect derivation and plotting in Matlab

    This is driving me crazy. The derivation of the current distribution in a long cylindrical wire is extremely straightforward, giving J(r) = J(a) \frac{J_0(k r)}{J_0(k a)} where J is the current density, a is the radius of the wire, and k is the complex wave vector, which in a metal (with...
  5. A

    Analytic derivation of quantum SHO

    In Griffith's derivation of the quantum SHO, he uses some funny math: first he considers asymptotic behavior to get ψ=Ae-(ε^2/2) then he 'peels off the exponential part' to say that ψ=h(ε)e-(ε^2/2) then he hopes that h(ε) will have simpler form than ψ(ε) I can kind of understand the first...
  6. C

    Trouble understanding this derivation of Faraday's law

    I am having trouble understanding part of the derivation of Faraday's law given in this lecture at around 57:00 So the first goal is to calculate the change in magnetic flux through a changing closed loop in a dynamic magnetic field, and it's given by the following \phi(t+\Delta...
  7. U

    Small oscillation equation derivation

    Hi guys, I have been trying to find the "floppy" resonant mode frequency of a simple oscillator. The displacement is in the order of nanometers, while the dimensions of the oscillator is in cm. I think small angle approximations apply here. I got to the point of the equation of motion, but I...
  8. R

    Prandtl stress function derivation

    Can someone explain to me how the Prandtl stress function is derived? The book only briefly describes how the Airy stress function is derived.
  9. I

    Thermodynamics: Einstein solid (simple step in derivation)

    S=kln(\frac{eq}{N})N --->= S=Nkln(\frac{q}{N}+1) i understand that the e goes away and the N exponent comes down but where does the +1 come from?
  10. ajayguhan

    Derivation of mazwell boltzman statistics.

    Let number of energy levels be e(subscribe 0), e(subscribe 1)...e(subscribe r) N be the total number of particles and n(subscribe i) be the number of particle in with energy level where i =0,1,2,...r Let Ω be the number of ways attaining a given microstate Ω=N!/[ n(subscribe 0)!*n(subscribe...
  11. L

    Michelson interferometer average power derivation

    Homework Statement Using the trig product identity, cosαcosβ=\frac{1}{2}[cos(α+β)+cos(α-β)], show that the time-average power at the detector can be written as Pavg = 1+cos(δ) That = is supposed to be a proportional symbol. Homework Equations Other than the ones given in the problem...
  12. ajayguhan

    Derivation of rayleigh jeans law

    How is the number of oscillations per unit volume in the frequency range of v and dv is (8v^2*dv)c^3 where c is the velocity of light
  13. P

    Simple Derivation (1D) Lorentz Transformation

    Appendix 1 - simple Lorentz transformation derivation found at - http://www.bartleby.com/173/a1.html Given in equation (3) (x'-ct') = Y(x-ct) [Y = const.] by rearrangement, it yields, (x'-ct')/(x-ct) = Y. But it is stated that both (x-ct) and (x'-ct') are zero, so...
  14. K

    Help with Derivation: u^-1(\partial_\mu u)u^-1 = \partial_\mu(u^-1)

    Hello there! I'm trying to read a set of notes on the standard model and the author states the following equality without any explanation: -u^{-1}(\partial_\mu u)u^{-1} = \partial_\mu(u^{-1}), u is here a NxN representation of some continuous gauge group and is a function over spacetime...
  15. H

    Continuity equation derivation in Griffiths - why partial derivative?

    Greetings, In Griffiths E&M, 3rd. Ed., on page 214, the following is part of the derivation of the continuity equation (the same derivation is shown on the Wikipedia article for the current density, under the continuity equation section: http://en.wikipedia.org/wiki/Current_density)...
  16. PsychonautQQ

    Trouble understanding derivation of current density

    Current Density = (I/A) I = (Q/t) = (nVq)/t where n is the number of charges, V is the volume, q is the average charge and t is time. nVq/t = n(Ax)q/t = nAvq where v is velocity. Current Density = (I/A) (nAvq)/A = nvq My question is on the step where it goes Q/t = nVq/t Why does...
  17. C

    Group Velocity Derivation: Understanding the Role of Ignored Terms

    I was reading the derivation on Wikipedia: http://en.wikipedia.org/wiki/Group_velocity#Derivation Why is the first part before the integral sign ignored when calculating the velocity? Surely it would also cause a phase shift in some time interval and make the waves move forward (or backward)?
  18. M

    Mathematica Mathematica derivation Question

    I'm trying to work through a derivation and am getting some funny results. For example, when trying to compare some expressions, Mathematica was telling me they weren't equal, and when I worked them out by hand, I new they were equal. I then tried something like this: ExpandAll[x] ===...
  19. I

    Thermodynamics(math) derivation step

    hi, i just need help with a step in a derivation in my thermodynamics book (indicated by the red arrow) http://i.imgur.com/C8k3xzT.jpg firstly, what's the point of a -(q+N) term if they're just going to cancel it out with a +q and +N? basically i want to know how the terms inside...
  20. R

    Derivation problems for dilation

    Homework Statement Show that, if there are no body forces, the dilation e ( e=e_{xx} + e_{yy} + e_{zz} = div \;\vec{u}) must satisfy the condition \nabla^2 e = 0 Homework Equations (1) (\lambda + \mu)\frac{\partial e}{\partial x} + \mu \nabla^2U_x = 0 (2) (\lambda + \mu)\frac{\partial...
  21. R

    Questions about derivation of equation

    I'm studying linear elasticity and I came across an equation that I having problems figuring out the derivation. I want to understand this in case I may need to know it later in the course. The equation is as follows: \frac{\partial^2e_{zz}}{\partial x \partial y} = \frac{\partial}{\partial...
  22. J

    HEY YOU Double Doppler/Radar Guns/Equation Derivation

    Alright. Physics Internal. I am investigating a physics principle applied into a practical way. Radar Guns and the Doppler Effect. Now the issue is, firstly, that I have encountered two equations to give me the perceived frequency of a wave with a moving observer and stationary source. I am not...
  23. mnb96

    Doubt on derivation of complex functions

    Hello, I have a doubt on how to differentiate a complex function f:ℂ→ℂ defined as follows: f(z)=zz^* where the * stands for complex conjugation. According to this source (at the very end of the Section, where it says: "...As this is a complex value, G*(f) acts as a constant...") the result...
  24. P

    Derivation by first principles: cos(x^0.5)

    Homework Statement Find the derivative of the function f(x)=cos(√x) by first principles Homework Equations f'(x)= lim as h tends to zero of [f(x+h)-f(x)]/h The Attempt at a Solution Problems arise immediately, since I have no idea what to do with the expression cos(√(x+h)), I've...
  25. Y

    Derivation of Green's Function

    The normal form of Green's function is ##\oint_c\vec F\cdot \hat n dl'=\oint_{s}\left(\frac{\partial M}{\partial x}-\frac{\partial N}{\partial y}\right)dxdy## I want to get to \oint _cMdy-Ndx=\oint_{s}\left(\frac{\partial M}{\partial x}-\frac{\partial N}{\partial y}\right)dxdy Let ##\vec...
  26. W

    Derivation of Newton's Law of Universal Gravitation

    ##F = G \frac{ m_{1} m_{2}}{ r^{2} } ## Where does the formula come from? And why does it work that way? How would it relate to Newton's Second Law? ##F = ma## Using Newton's Second Law, is it possible to get the Law of Universal Gravitation?
  27. P

    Why Do These Riemann Tensor Terms Cancel Each Other Out?

    I was working on the derivation of the riemann tensor and got this (1) ##\Gamma^{\lambda}_{\ \alpha\mu} \partial_\beta A_\lambda## and this (2) ##\Gamma^{\lambda}_{\ \beta\mu} \partial_\alpha A_\lambda## How do I see that they cancel (1 - 2)? ##\Gamma^{\lambda}_{\ \alpha\mu}...
  28. P

    Using linear algebra to tell when your derivation is impossible?

    Sorry if this is the wrong place to ask this, but I think linear algebra is the best place to ask my question. Feel free to move this thread elsewhere if I am wrong. I would like to know how I can use linear algebra to help me figure out when I am deriving an equation if the derivation I...
  29. E

    How Is the Formula PEcos(θ) Derived for Dipoles in a Constant Electric Field?

    I know that the potential energy of a dipole in a constant electric field is P(dot)E=PEcos(θ), but I can't seem to find how they got here; its not in my textbook. If anyone knows why please tell me.
  30. M

    Is this a correct derivation of Moment of Inertia?

    Hello everybody! This is the derivation (for a single particle). \tau = F_{\perp }r \ = ma_{\perp}r \ = \alpha mr^2 \\ \text{if }\ \tau = I\alpha \text{ where } I \text{ is resistance to accleration then } \\ I = mr^2 I'm curious what the problem with this is because I haven't...
  31. I

    Help with derivation of torque equation T = p x E

    \vec{\tau}=\vec{F}x\vec{r} \vec{F}=\vec{E}q \vec{p}=q\vec{d} \vec{\tau}=(\vec{E}q)xr=\vec{E}x\vec{p} so then how do we end up with \vec{\tau}=\vec{p}x\vec{E}?
  32. R

    Total energy derivation: energy as a time component of a four-vector

    I'm kind of new to special relativity, I mean beyond what they tell you in survey courses. In any case, I've heard there was a relationship between energy and time in special relativity (I've actually heard someone say the "time component" of energy), and I've always been fascinated with E = mc2...
  33. M

    Relativistic Energy Derivation math problem

    Hey, In a derivation of relativistic energy (in Physics for Scientists and Engineers, 5th edition, Serway and Beichner) they use a method of integration by substitution: Given that F=\frac{dp}{dt} and relativistic momentum is given by p=\frac{mv}{\sqrt(1-(v^2/c^2))} W=∫F...
  34. J

    Derivation of trigonometric identities form rotation on the plane

    Homework Statement I want to derive the trig identities starting with rotation on the plane. Homework Equations One rotation through a given angle is given by $$x' = xcosθ - ysinθ $$ $$y' = xsinθ + ycosθ$$ The Attempt at a Solution What if I wanted to rotated through any...
  35. Y

    Double check the derivation integral representation of Bessel Function

    I am reading the article Mirela Vinerean: http://www.math.kau.se/mirevine/mf2bess.pdf On page 6, I have a question about e^{\frac{x}{2}t} e^{-\frac{x}{2}\frac{1}{t}}=\sum^{\infty}_{n=-\infty}J_n(x)e^{jn\theta}=\sum_{n=0}^{\infty}J_n(x)[e^{jn\theta}+(-1)^ne^{-jn\theta}] I think there is a...
  36. O

    (Simple) Derivation of Yang-Mills Equations

    Hello all, my teacher assigned a problem related to the yang-mills equation in my general relativity class and I just wanted to ask a couple of questions about this problem. I believe it is a simplified version of the Yang-Mills you encounter in particle physics. Basicly assuming that...
  37. R

    Cooling Tower's equation of humidity derivation

    Humidity is known as mass of water vapor/mass of dry air Hs (saturation) = (Mw/Ma){Ps/(P-Ps)} P is total pressure Ps is saturation pressure what is the derivation for this equation?
  38. B

    Variational Derivation of Schrodinger Equation

    In reading Weinstock's Calculus of Variations, on pages 261 - 262 he explains how Schrodinger apparently first derived the Schrodinger equation from variational principles. Unfortunately I don't think page 262 is showing so I'll explain the gist of it: "In his initial paper" he considers...
  39. Y

    Question on derivation of potential of a small current loop

    The vector magnetic potential is given \vec A=\frac{\mu I}{4\pi}\oint\frac{e^{-j\beta R_1}}{R_1}dl' After a few steps, the equation becomes: \vec A=\frac{\mu I}{4\pi}e^{-j \beta R}\left[ (1+j\betaR)\oint\frac{dl'}{R_1}-j\beta\oint dl'\right] The Book claim the second integral obviously...
  40. K

    Blackbody radiation - Radiative flux derivation of the Stefan-Boltz.

    I am trying to resolve some long standing problems I have encountered with blackbody radiation. Namely, the derivation of the radiation energy flux equation $$J=\sigma_{B} T^4$$. I understand the derivation of the energy density of photons in "a box". $$U/V=const. T^4$$ I do not understand the...
  41. A

    Validity of Directional Derivatives for Unit Vectors

    For directional derivatives: Let \hat{u}=<a,b,c> be the direction. Thus, \frac{∂\hat{u}}{∂x}=\frac{\sqrt{a^2+b^2+c^2}}{a} and so on. So, \frac{∂x}{∂\hat{u}}=\frac{a}{\sqrt{a^2+b^2+c^2}}=a Thus, \frac{∂F}{∂\hat{u}}=\frac{∂F}{∂x}a+\frac{∂F}{∂y}b+\frac{∂F}{∂z}c=∇F \bullet \hat{u}.
  42. A

    Derivation of Potential Energy for Multi-Particle Systems

    I am reading 'Classical Dynamics: A Contemporary Approach' by J. Jose, and I am confused about a step in the author's development of potential energy for a system of many particles. He begins by writing down a term equivalent to the total change in kinetic energy of the system: \sum_i...
  43. genxium

    Derivation of ElectroMagnetics Boundary Conditions

    As learning laser fundumentals, I've just reviewed the boundary conditions for electromagnetic waves. However, I came back to a point that confused me in the past and want to get it clear now :) One of the boundary conditions, regarding the magnetic fields parallel to the medium-interface...
  44. E

    Lorentz transformation derivation. What exactly is wrong?

    This is probably a stupid mistake I am making, but I can't figure it out. My apologies in advance... I am familiar with the text-book derivation of the Lorentz transformation (I don't have any problem with it). It starts out stating: x2+y2+z2-c2t2 = x'2 + y'2+z'2-c2t'2 meaning that a...
  45. G

    Why Do We Derive Energy Functions to Find Force Components?

    A potential energy function for a two-dimensional force is of the form U = 3.21x3 y - 5.79x. Calculate the force that acts at the point (1.47m,1.42m). Enter the x-component first and then the y-component. -2.38×101 N -1.02×101 N I know in order to find the force components of this energy...
  46. H

    Derivation of ideal gas law by Hamiltonian mechanics

    Hi! I am trying to understand the statistical mechanics derivation of the ideal gas law shown at: http://en.wikipedia.org/wiki/Ideal_gas_law inder "Derivations". First of all, the statement "Then the time average momentum of the particle is: \langle \mathbf{q} \cdot \mathbf{F} \rangle=...
  47. D

    Temperature CONFUSION in derivation for Helmholtz Free Energy

    Dear all, I have been spending 12 hours on this and cannot seem to come up with a solution. We derive Helmholtz Free Energy (A) from the second law of thermodynamics. dS(Total) = dS(system) + dS(surrounds) we try to express dS(surrounds) with properties of the system. Assuming...
  48. O

    Time independant perturbation - Difficulty understanding derivation

    Hamiltonian is in the form ##H = H_0 + \lambda W##, where ##\lambda \ll 1## and ##W## is the perturbation. Assume the eigenstates ##\mid \psi(\lambda) \rangle## and engenenergies ##E(\lambda)## can be expanded in a power series of ##\lambda##. $$\mid \phi(\lambda) \rangle = \mid 0 \rangle +...
  49. V

    Calculating Induced Voltage in a Single-Turn Circular Coil: How Can It Be Done?

    Can any ine tell from where i can get this information If a single turn circular coil generates a magnetic field around it how can we calculate the induced voltage in a single turn circular coil located at a distance of d
  50. S

    Drift velocity formula derivation confusion

    In the derivation of drift velocity i have seen two variations and want to know which one's correct. s=ut +\frac{1}{2}at^{2} Assume that the drift velocity of any electron in any conductor is : v_{d}=l/t Due to the electric field the acceleration of electrons in any conductor...
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