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. SebastianRM

    I What is the 'formal' definition for Total Derivative?

    A total derivative dU = (dU/dx)dx + (dU/dy)dy + (dU/dz)dz. I am unsure of how to use latex in the text boxes; so the terms in parenthesis should describe partial differentiations. My question is, where does this equation comes from?
  2. Max Loo Pin Mok

    Black body radiation, Planck's law, derivation

    The following are 3 equations of Planck's law or Planck's distribution function. Are they all correct? How do they derive from each other? Equation One: From page 512 of http://metronu.ulb.ac.be/npauly/art_2014_2015/shockley_1961.pdf We denote by Qs the number of quanta of frequency greater...
  3. K

    A Steps in an electron's magnetic moment derivation

    Hello! I am reading Schwarz's book on QFT and in chapter 17 he introduces the anomalous magnetic moment. I am not sure I understand a step in the derivation (from a mathematical point of view), when going from 17.23 to 17.24 (I attached a SS of it). I was able to get certain terms, but I am not...
  4. J

    B Learning Lorentz Derivation: Solving x=vt+γx' vs. x=vt+x'/γ

    From a previous thread, Nugatory: "If the answers already supplied are not enough for the original poster to work out for themself why x=vt+x'/γ, and not x=vt+γx′, is the correct expression, we can have another thread devoted to only that question." Here it is. Either Wiki is wrong or I am. In...
  5. J

    B Basic Lorentz transformation derivation

    The Lorentz transformations are mathematically simple. I had always imagined they could be easily derived. I however just found out from another PF thread that this is not so. Their originators Lorentz and Poincaré simply stated them without derivation. And the "proofs" I have seen to date have...
  6. N

    Isospin Doublet Derivation Using Clebsch-Gordan Coefficients

    Homework Statement I am trying to improve my understanding of the Clebsch-Gordan coefficients. I am looking at page 5 of the following document https://courses.physics.illinois.edu/phys570/fa2013/chapter3.pdf Homework Equations I have derived the result for the I = 3/2 quadruplet but am...
  7. S

    Simple Harmonic Motion derivation

    Homework Statement Hookes Law gives: F = -kx. This is SHM. But I cannot see how to get to the sinusoidal expression from this. (In all the explanations, they cheat, and just introduce de novo Omega or Omega^2.) But how do you get to m. d2x/dt^2 = -x.(omega) ^2 Homework Equations F = -kx. m...
  8. Dorian

    Solid Disk Pulley + 2 Mass system, v derivation using 2 methods

    Homework Statement [please see attached photo] Homework Equations [please see attached photo] The Attempt at a Solution [please see attached photo] The issue for me starts with (but probably doesn't end with) replicating the velocity equation using the Conservation of Energy equations. Is...
  9. K

    I Gravitational time dilation derivation

    If a beam of light is shot from a fast space ship, it travels a distance c*t1 according to their reference frame. The same beam of light seen from an outside observer goes at an angle and travels a distance c*t2. The distance the spaceship travels is equal to v*t2. Using the triangle made from...
  10. T

    I Question on the Derivation of Temperature/Scale Factor Relation

    In 'Introduction to Cosmology' by Barbara Ryden, there is an argument made using the first law of thermodynamics to derive the relation T(t) ∝ a(t)-1 on pages 29 and 30. MENTOR NOTE: removed copyrighted material. I've been able to work out all the omitted details up to 2.37, which gives the...
  11. Math Amateur

    MHB Exploring Remmert's Derivation of Cauchy-Schwartz Inequality

    I am reading Reinhold Remmert's book "Theory of Complex Functions" ... I am focused on Chapter 0: Complex Numbers and Continuous Functions ... and in particular on Section 1.3: Scalar Product and Absolute Value ... ... I need help in order to fully understand Remmert's derivation of the...
  12. prodo123

    I Trying to understand my prof's derivation of Planck's Law

    Not many people understood his proof in class, and the textbook's proof wasn't very clear so we went by with other derivations online. Then he filled half the midterm with his method, so I'm trying to understand how he did things. Looking back it seems very similar to the proofs we found online...
  13. M

    Delay and Sum Beamforming Equation Derivation

    Homework Statement I have to simplify this beam form (equation 1) which simplifies to equation 2 and then finally to equation 3. Homework Equations equation 1: e^-ix((1-e^y)/(1-e^z)) where x = Beta*M_(1/2), y = beta*M, z= Beta equation 2: sin(M*Beta/2)/(sin(Beta/2)) equation 3...
  14. Arman777

    Derivation of Relativisitic Doppler effect with angle

    Homework Statement Derive the formula for the Doppler effect for a receiver traveling at an angle theta away from a planar source Homework EquationsThe Attempt at a Solution [/B] I thought that we can assume that the wavelength has two components ##λ_x## and ##λ_y## where ##λ_x = ct+vtcosθ##...
  15. J

    I Is this derivation of the Born rule circular in any way?

    https://arxiv.org/abs/1411.6992 They derive the born rule from the MWI. Is this circular?
  16. cookiemnstr510510

    Derivation of electric potential charged disk from ring

    Homework Statement a)recall that electric potential is a scalar quantity. For a circular ring of radius, R', carrying charge, Q, what is the electric potential at a height,y, above the center of the ring? b)Use your above answer to determine the electric potential at a height,y, above the...
  17. T

    Confusion in the derivation of the force on a magnetic dipole

    Homework Statement ok this is not a homework but i am confused by the derivation of ## f = \nabla (m . B)## both start out with ##\vec B(r) \approx \vec B_0 + (\vec r' . \nabla)\vec B|_0 ... \\ f = \iiint_{v'} \vec J( r') \times (\vec r' . \nabla)\vec B|_0 ## where prime is body coordinates and...
  18. M

    Derivation of the expression for exergy

    I am using the book 'Fundamentals of thermodynamics' by Moran et al., In the exergy chapter, while deriving the expression for exergy ,a term representing the entropy generation in the combined system is neglected.Then the resulting expression is said to be the expression for exergy.But that...
  19. F

    Derivation of D'Alembert equation (for pressure waves)

    In my textbook there is an explanation of a derivation of D'Alembert equation for pressure waves. (##\frac{\partial^2 y}{\partial x^2}=\frac{\rho}{\beta}\frac{\partial^2 y}{\partial t^2}##) I put the picture (the only one I found on internet) but I'll call ##y_1 ,y_2## as ##\psi_1,\psi_2## and...
  20. L

    Derivation of the Potential Energy of an Electric Charge System

    Hi, I learned about how PE = U=kq1q2/r is the electrical potential energy for the system. It is found by taking the integral of electrical force and dr from infinity to the point of location we are interested in. So that is the intregral(F*dr) from r=inf to r=ro. My question is that do I...
  21. AwesomeTrains

    Trying to understand a derivation in a paper

    Hello PF, first of all I don't know where to put this post as it's not exactly a homework question but a clarification question for a project. I'm going through the derivation of the effective permeability of two stacked medias, given the polarization of an incoming EM wave but I'm stuck at the...
  22. Sanchayan Ghosh

    I Canonical form derivation of (L1'AL1)

    Hello everyone, I actually had a problem with understanding the part where they have defined L'AL = Λ. There, they have taken γΛγ1 = Σy2λ = 1. Why have they taken that? Is it arbitary or does it come as a result of a derivation? Thank you
  23. K

    Charge-Dipole Derivation - Assumption That x >> a

    In this derivation: https://cpb-us-e1.wpmucdn.com/sites.northwestern.edu/dist/8/1599/files/2017/06/taylor_series-14rhgdo.pdf they assume in equation (8) that x >> a in order to use the Taylor Expansion because a/x has difficult behavior. Why does that assumption work? Meaning, why can we...
  24. C

    I Derivation of Rindler Metric and How It Resolves the Twin Paradox

    From what I have read the twin paradox can be resolved with the Rindler metric and without the need to bring in general relativity. Special relativity will suffice. But how does the Rindler metric get derived in the context of a constant accelerating reference frame. I haven't seen anything in...
  25. K

    Derivation, absolute value problem

    Homework Statement Find k so that y - 36x = k is a normal to the curve y = 1 / abs(x-2). Homework EquationsThe Attempt at a Solution My problem is regarding the absolute value. I know that the tangent to the curve must be (-1/36). In the solutions manual, it is said that by knowing the sign...
  26. DatLemonDoe

    B Deriving Lorentz Factor: An Analysis of Jimmy360's Method

    Hello! This is my first post on this forum, so make sure to tell me if I am doing something wrong :) I was trying to derive the Lorentz factor today, and I used the following page as a guide. The top answer by Jimmy360 is what I followed...
  27. P

    Projectile Motion: Initial Velocity Derivation

    Hey guys, I am working on a school project and have fired some water rockets at different angles. I am now trying to compare theoretical results vs experimental results. But I am struggling to produce an accurate mathematical model. I have attached my attempt to this post. It is quite long and...
  28. redtree

    I Derivation of the Euler-Lagrangian

    I have a question about a very specific step in the derivation of Euler-Lagrangian. Sorry if it seems simple and trivial. I present the question in the course of the derivation. Given: \begin{equation} \begin{split} F &=\int_{x_a}^{x_b} g(f,f_x,x) dx \end{split} \end{equation} Thus...
  29. F

    I Derivation of Lax-Wendroff finite volume scheme

    I'm trying to figure out how the finite volume version of Lax-Wendroff scheme is derived. Here is the PDE and Lax-Wendfroff scheme, assume initial conditions are given: $$u=\text{function of x,t}\\\hat{u}=\frac{1}{\Delta x}\int_{x_{i-1/2}}^{x_{i+1/2}}u\thinspace dx \text{ (the average flux...
  30. E

    A Derivation of Einstein Field Equations w/o Poisson or Least Action

    I would be grateful if some one would consider my following thought and indicate to me the likely mistakes, which I cannot do. Following the paper “Why the Riemann Curvature Tensor needs twenty independent components” by David Meldgin UC Davis 2011, I understand that with a coordinates...
  31. A

    I Zeno effect - standard derivation?

    Hi, I'm trying to grasp the standard derivation of the quantum Zeno effect. But my calculus is limited. I would love some assistance! Schroedinger evolution tells us that the state at time t, given the initial state at time t=0, is: |\psi_t\rangle = e^{-i H t} |\psi_0 \rangle We can then...
  32. D

    Vpr statics derivation of beam hinging

    For a beam above between two columns and bars are yield and hinging.. the formula to get the probable shear or vpr (from statics) is V= M(+) + M(-) /ln I guess it is derived from V * ln = M(+) + M(-) First of all. Why is the shear only present when it is hinging and not before (I'm talking...
  33. Mentz114

    I Derivation of the partition function

    Starting from the definition of energy levels ##e_n## and occupations ##a_n## and the conditions ##\sum_n a_n = N## (2.2) and ##\sum_n a_n e_n = E## (2.3) where ##N## and ##E## are fixed I'm trying to find the distribution which extremizes the Shannon entropy. Using the frequency ##f_n=a_n/N##...
  34. N

    What is the derivation of the ABC magnetic field components?

    Can somebody please post the derivation of the ABC magnetic field components whose magnetic field components in the three cartesian directions(B1, B2, B3) are given by the following: B1=A*sin(z)+C*cos(y) B2=B*sin(x)+A*cos(z) B3=C*sin(y)+B*cos(x)
  35. redtree

    I Redshift and the Friedmann metric

    My discussion of the Friedmann metric comes from the derivation presented in section 4.2.1 of the reference: https://www1.maths.leeds.ac.uk/~serguei/teaching/cosmology.pdf I have a couple of simple questions on the derivation. The are placed at points during the derivation.I note the...
  36. R

    Derivation of EoM for two interconnected rigid bodies

    I set a small project for myself to design a controller for a rocket, which moves a mass around to shift the center of mass, in order to steer a rocket. The picture shows a simplified model of a rocket plus a movable mass. , shown is a rod for the rocket, and a mass for the controller. there...
  37. S

    Can dx/dy always be used for integration and derivation on a circle?

    Homework Statement is dx/dy= x/y if yes can i use it always Homework Equations for example in a circle dA/dtheta=A/360The Attempt at a Solution if its right sometimes what are the conditions of using it
  38. Decimal

    I Deriving Einstein Equations: Questions on Linearity & Symmetry

    Hello, I am currently taking a course on general relativity with the book "General Relativity: An introduction for physicists" by M.P. Hobson. I am a having a hard time understanding the derivation presented for the Einstein equations. The book states that Einstein proposed the following...
  39. Kaguro

    I Doubt regarding derivation of Lorentz Transformations.

    I have just started learning the Special Theory of Relativity. While deriving, I am facing some problems. I obviously have made some kind of mistake while using the equations... What is wrong if I don't use the time transformation equation in Event #2?
  40. S

    A Derivation of a complex integral with real part

    Hey, I tried to construct the derivation of the integral C with respect to Y: $$ \frac{\partial C}{\partial Y} = ? $$ $$ C = \frac{2}{\pi} \int_0^{\infty} Re(d(\alpha) \frac{exp(-i \cdot ln(f))}{i \alpha}) d \alpha $$ with $$d(\alpha) = exp(i \alpha (b + ln(Y)) - u) \cdot exp(v(\alpha) + z...
  41. T

    Kinematics derivation: what's "ds/dv" ?

    Hello, here's a derivation for one of the equations for Uniform Accelerated Motion (UAM). I like it because it's far more concise than the algebra version. Question though: is there any kind of meaningful interpretation of ds/dv (which starts everything off in step 1)? Thank you!
  42. GiovanniNunziante

    A Derivation of the Heisenberg equation for electron density

    I'm studying plasmons from "Haken-Quantum Field Theory of Solids", and i need some help in the calculation of the equation of motion of eletrons' density \begin{equation} \hat{\rho}_{\overrightarrow{q}} = \frac{1}{\sqrt{V}} \sum_{\overrightarrow{k}}...
  43. S

    I Uncertainty relation derivation

    Hey guys , my lecturer introduced a new concept with reference to the commutation of two operators.He claimed that if two commutators commute then they can be simultaneously measured.I can clearly see how this works.He then went on and state if they don't commute they can't simultaneously be...
  44. Vicol

    A Canonical transformation - derviation problem

    Let me show you part of a book "Mechanics From Newton’s Laws to Deterministic Chaos" by Florian Scheck. I do not understand why these integrands can differ by more than time derivative of some function M. Why doesn't it change the value of integrals? It seems this point is crucial for me to...
  45. Z

    Derivation of the energy principle from Gregory Classical Mechanics textbook

    I'm working through Gregory's Classical Mechanics and came across his derivation of energy conservation for a system of N particles that is unconstrained. We get to assume all the external forces are conservative, so we can write them as the gradient of a potential energy. There's a step he...
  46. R

    Calculus derivatives word problem

    Homework Statement Is it possible to accurately approximate the speed of a passing car while standing in the protected front hall of the school? Task: Determine how fast cars are passing the front of the school. You may only go outside to measure the distance from where you are standing to the...
  47. I

    I Data Model of Kepler's Second Law of Planetary Motion

    Hello, I am completing a research project for differential equations class. I am to derive Kepler's three laws and then compare the results of the derivation with real-world data. For Kepler's second law (a planet sweeps out an equal area in an equal time), I was hoping to find orbital data for...
  48. B

    Derivation of resonant frequency for SHM systems

    Homework Statement My question here isn't a specific question that has been given for homework, but a more general one. For an assignment I have to 'derive an expression for the resonant frequency, ω0' for two different systems, the first for 'a mass M connected to rigid walls via two springs'...
  49. EastWindBreaks

    Derivation process? (Heatsink Fin Heat Conduction Equations)

    Homework Statement I don't understand the derivation of the right side of the last equation. Homework EquationsThe Attempt at a Solution I got to this point, I also don't understand why it did not include C_2 for the variation of temp. along the fin. I am guessing the right side is the...
  50. C

    I Riemann curvature tensor derivation

    Riemann tensor is defined mathematically like this: ##∇_k∇_jv_i-∇_j∇_kv_i={R^l}_{ijk}v_l## Using covariant derivative formula for covariant tensors and covariant vectors. which are ##∇_av_b=∂_av_b-{Γ^c}_{ab}v_c## ##∇_aT_{bc}=∂_av_{bc}-{Γ^d}_{ac}v_{db}-{Γ^d}_{ab}v_{dc} ##, I got these...
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