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. J

    Deriving gravitational potential energy -- mistake

    Homework Statement Hi I'm attempting to derive the gravitational potential energy of a point mass (##m##) that's moving from infinity to a point r' inside a gravitational field produced by a another mass ##M##. For simplicity I treated it as a one dimensional case. The problem I get is that the...
  2. bhobba

    I Interesting Derivation of Maxwell's Equations

    I really love seeing derivations of the EFE's, Maxwell's equations, Schrodinger equation etc. I have seen a number of derivations of Maxwell's Equations but this is the shortest, most illuminating and best I have come across - it basically just uses covarience - and as it says - a little bit...
  3. Conductivity

    Derivation of magnetic field of a Solenoid: Biot savart law

    Hello, I have seen that biot savart's law works for infinitely narrow wires: "The formulations given above work well when the current can be approximated as running through an infinitely-narrow wire." When I wanted to derive the magnetic field of a solenoid, I had to do this substitution...
  4. A

    MHB Derivation of an inequality from the paper “A CLT For A Band Matrix Model” by Anderson's and Zeitoun

    I am trying to see how to derive the following inequality on page 36 in the proof of Lemma 11.3: https://arxiv.org/pdf/math/0412040.pdf I.e, of: $$\| fg \|_{Lip} \le \bigg(1+\ell \sup_{t\in T} |g'(t)|\bigg)\sup_{t\in T}|f'(t)| , \ \ supp \ f(1-g)\subset S^c$$ My thoughts about how to show...
  5. binbagsss

    A Schwarzschild Derivation: Sean Carroll Notes - Theorem Name?

    Hi, Page 166, theorem expressed as 7.2, does anybody know it's name? Many thanks
  6. binbagsss

    I FRW metric derivation: constraints from isotropic and homoge

    I don't understand the reasoning for any of the three constraints imposed. why would ##dtdx^i## terms indicate a preferred direction? what if there was identical terms for each ##x^i## would there still be a specified or preferred direction? (or is it that in this case we could rename ##t## to...
  7. A

    I Density of States -- alternative derivation

    I am trying to understand the derivation for the DOS, I get stuck when they introduce k-space. Why is it necessary to introduce k-space? Why is the DOS related to k-space? Perhaps if someone could come up to a slightly different derivation (any dimensions will do) that would help. My doubt ELI5...
  8. E

    I Derivation notation with capital D?

    Hi, I came across a derivation notation I didn't recognize: Let ##s## be some four-vector and ##\tau## the proper time. What is the significance of $$\frac{Ds}{\mathrm{d}\tau}?$$ I know ##Ds## can be used to mean the Jacobian, but I've never come across the notation above. Does someone...
  9. T

    I Why do we need to use causality arguments in the Landau damping problem?

    Related to Figure 8.4 the author mentions this when stating (8.25): "Note that the semi-circle deviates below the real -axis, rather than above, because the integral is calculated by letting the pole approach the axis from the upper half-plane in -space." Why is the pole calculated in this way...
  10. QuantumRose

    About the derivation of Lorentz gauge condition

    The question: Show that the Lorentz condition ∂µAµ =0 is expressed as d∗ A =0. Where A is the four-potential and * is the Hodge star, d is the exterior differentiation. In four-dimensional space, we know that the Hodge star of one-forms are the followings. 3. My attempt Since the four...
  11. Amaterasu21

    B Archimedes' Principle for gases - derivation?

    Hi all, I understand where Archimedes' Principle comes from in liquids: If we imagine a cylinder immersed in a liquid of density ρ whose cross-sectional area is A and whose top is at depth h1 and whose bottom is at depth h2: Force(top of cylinder) FT = ρgh1A Force(bottom of cylinder) FB =...
  12. Clara Chung

    I I can’t understand the derivation of the formula Cp=Cv+nR

    I think that dU = Cv dT can only be used when the volume of the gas is constant. Similarly, Cp = dQ/dT can only be used when the pressure is constant. Such as We have Cv=dQ/dT and ΔU=Q+W dU=Q+pdV Therefore, dU/dT = dQ/dT only when dV is zero Why am I wrong? Thank you so much for your help. The...
  13. MathematicalPhysicist

    A Derivation in Ashcroft and Mermin (The Pseudopotential)

    On page 208 of Ashcroft and Mermin they write: I tried to derive equation (11.30) but got stuck on something, I hope someone can help me with it. I'll write below my attempt at deriving equation (11.30). First, notice the following few equations on pages 206-207: $$(11.24) \ \ \ \ \...
  14. V

    Equivalence of Derivations in the Wave Equation from Maxwell's Equations

    Homework Statement I am actually following the derivation of the wave equation from Maxwell equations. And I do not understand one step, because in the task for the derivation I get a slightly different result (maybe they are equivalent, but I am not sure). Homework Equations In the attached...
  15. Z

    I Derivation of E=mc2 from Four-Vector Definitions in Special Relativity

    In SR, fundamental concepts velocity, acceleration, force, momentum were defined as four-vectors. https://en.wikipedia.org/wiki/Four-vector Does someone show me a derivation of the equation E = mc2 from those definition?
  16. Clara Chung

    I I don't understand the derivation of the wave equation

    If there is a net force along the y-axis, i.e. T sin(θ2) - T sin(θ1) Why is it equals to ma, where a is the acceleration of the piece of string along the y-axis? Shouldn't there be a torque so the piece of string rotates? Sorry for sounding stupid.
  17. J

    Buck Converter (Step Down Chopper Derivation)

    Hi, I'm studying Choppers and I'm struggling with derivation of Buck Converter. As per equation 13.3 if I solve it ahead I get Vs D T - Vo D T = - Vo T + Vo D T Solving this ahead I get Vs (D T ) = Vo (-T + DT + DT) Vs (DT) = Vo(2DT - T) Vs D = Vo (2D - 1) Vo / Vs = D/(2D - 1) Not sure how to...
  18. Y

    Please check my derivation of the gain of single ended diff amp

    I am having a very difficult time verifying the equations for full differential amplifier. I literally read all the articles I can find from Google. Here is one of the question I think the paper by Jim Karki is wrong. The equation is equation (9). I verified the rest of the equation already...
  19. R

    Derivation of the Eqation of Motion from Fermi Lagrangian density

    Homework Statement Hello, I am trying to find the equations of motion that come from the fermi lagrangian density of the covariant formalism of Electeomagnetism.Homework Equations The form of the L. density is: $$L=-\frac{1}{2} (\partial_n A_m)(\partial^n A^m) - \frac{1}{c} J_m A^m$$ where J...
  20. J

    I Understanding Equation (2.34) in Heald and Marion: A Step-by-Step Derivation

    Would someone explain the last step in eq.(2.34) in Heald and Marion? Much thanks ahead.
  21. Pushoam

    Derivation of Bernoulli Binomial distribution

    Homework Statement Derive the bernoulli binomial distribution.Homework EquationsThe Attempt at a Solution Each bernoulii trial could have only two possible outcomes . Let’s name one outcome as success and another outcome as failure. Let’s denote the probability of getting success and failure in...
  22. D

    How to prove vector identities WITHOUT using levi civita ?

    Mentor note: Thread moved from homework sections as being a better fit in the math technical section. Multiplying components of both sides are also off limits. I am trying to derive vector identities on introduction chapters in various EMT books. For example : (AXB).(CXD) = (A.C)(B.D) -...
  23. G

    Derivation: Maxwell's equation only from the Lorenz gauge

    Hi. Here, somebody apparently derives Maxwell's equations using only symmetry of second derivatives and the Lorenz gauge condition. Unfortunately it's in German, but I think the basic ideas are clear from the maths only. In this derivation, the magnetic field turns out to be divergence-free...
  24. jamalkoiyess

    I Delta x in the derivation of Lagrange equation

    Hello PF, I was doing the derivation of the Lagrange equation of motion and had to do some calculus of variations. The first step in the derivation is to multiply the integral of ƒ(y(x),y'(x);x)dx from x1 to x2 by δ. and then by the chain rule we proceed. But I cannot understand why we are...
  25. J

    Source free RL Circuit derivation

    Hi, I'm struggling with source-free RL Circuit derivation. In the books in the right side diagram they've reversed polarity of inductor to get equation: V(r) = - V(L) But why? I checked google and everywhere they had put inductor with positive sign upwards. Here is what I think-- In left...
  26. Jenna

    Using Energy and momentum conservation to derive the equation

    Homework Statement I need to find the intial velocity of a ball, given the angle the pendulum bob swings through. I need to derive this equation. [/B] V0=4.43mtotalL1/2{1-cosΔθ}1/2/mball Homework EquationsThe Attempt at a Solution I have barely any attempts since I can't even think where to...
  27. I

    B Regular derivation on The Universal Law of Gravitation?

    Hello Everybody, I am Meaningless and I had this doubt on Newtons laws of gravitation while deriving it. My textbook stated the following derivation 9 for any two masses m1, m2, and radius 'r' It stated that according to the law of product of masses...
  28. H

    A Derivation of the Casimir energy in flat space

    I am trying to understand the derivation of the Casimir energy from https://en.wikipedia.org/wiki/Casimir_effect#Derivation_of_Casimir_effect_assuming_zeta-regularization. At one point, the derivation writes the following: The vacuum energy is then the sum over all possible excitation modes...
  29. G

    Derivation of the Fourier series of a real signal

    Homework Statement Consider the Fourier series of a signal given by $$x(t)=\sum_{k=-\infty}^{\infty} a_ke^{jk\omega_0t}$$ Let's consider an approaches to this series given by the truncated series. $$x_N(t)=\sum_{k=-N}^{N} a_ke^{jk\omega_0t}$$ a- Show that if $x(t)$ is real then the series...
  30. MathematicalPhysicist

    Derivation of the energy of an alloy

    Homework Statement Homework EquationsThe Attempt at a Solution My question is how to derive ##(4.13)## from the above preceding paragraphs?, I am not sure how achieve these terms.
  31. S

    Derivation of an expression for centripetal acceleration

    Homework Statement I have derived the expression for the velocity of the satellite v= root of GM/r however I'm struggling to derive an expression for the centripetal acceleration of a satellite orbiting Earth. Homework EquationsThe Attempt at a Solution I'm not entirely sure which equations to...
  32. T

    Deriving motion equations for two blocks on a rough table

    Two small blocks, each of mass m, are connected by a string of constant length 4h and negligible mass. Block A is placed on a very rough tabletop as shown below, and block B hangs over the edge of the table. The tabletop is a distance 2h above the floor. Block A is then released from rest at a...
  33. MathematicalPhysicist

    Derivation of the expansion of the potential in rectangular coordinates

    Homework Statement I want to derive the expansion of ##\Phi(x)## in rectangular coordinates: $$ \Phi(\vec{x}) = \frac{1}{4\pi \epsilon_0} \bigg[ \frac{q}{r}+\frac{\vec{p}\cdot \vec{x}}{r^3}+\frac{1}{2}\sum_{i,j} Q_{ij} \frac{x_ix_j}{r^5}+\ldots\bigg]$$ Homework Equations $$\vec{p}= \int...
  34. M

    Derivation of Equation (1.6) in Schutz: A First Course in GR

    Homework Statement From pages 10--11 in "A First Course in General Relativity" (Second Edition) by Bernard Schutz: Given $$\Delta\overline{s}^2 = \phi\left(\textbf{v}\right)\Delta s^2,$$ where ##\Delta \overline{s}^2## is the interval measured between two events in frame ##O'##, which is...
  35. R

    I Understanding the Paradox of the Cantor Set: A Closer Look at Its Derivation

    I am puzzled by the derivation of the Cantor set. If the iteration of removing the middle-thirds leaves an uncountable set of points, it seems the iteration had to be performed an uncountably infinite number of times. Is this the case? If so, that seems paradoxical to me.
  36. OcaliptusP

    I Derivation of pi using calculus

    I tried to derivate pi using calculus but i just found a quite different result. Can you spot my wrong please?First i started with equlation of a circle which is: $$x^2+y^2=r^2$$ I am assuming circle's center stands on the center of origin. To reach pi we shoud consider the situation that...
  37. B

    What is the relationship between a force field and a potential field?

    Homework Statement [/B] I have been given an equation for the magnetic potential of a buried magnetic object which is as follows Pm=α/x2 Where α is some constant and x is the distance from the magnetic body. I need to derive an expression for the magnetic field strength at some distance x...
  38. G

    Help with this differential calculus

    <Moderator's note: Moved from a technical forum and therefore no template.> Hi everybody I've been trying to solve this problem all the afternoon but I haven't been able to do it, I've written what I think the answers are even though I don't know if they're correct, so I've come here in order...
  39. binbagsss

    I Derivation of geodesic equation from the action - quick question

    Hi, I am following this : https://en.wikipedia.org/wiki/Geodesics_in_general_relativity and all is good except how do we get ## \delta g_{uv}=\partial_{\alpha}g_{uv}\delta x^{\alpha}## Many thanks
  40. PrathameshR

    I Derivation of Euler Lagrange's equations from D'alemberts principle

    In the derivation given in Goldstein's book it is given I can't understand from where it comes. It's not at all trivial for me but it's presented as if it's trivial.
  41. D

    Trying to find this double integral using polar coordinates

    Homework Statement question : find the value of \iint_D \frac{x}{(x^2 + y^2)}dxdy domain : 0≤x≤1,x2≤y≤x Homework Equations The Attempt at a Solution so here, i tried to draw it first and i got that the domain is region in first quadrant bounded by y=x2 and y=x and i decided to convert...
  42. bdolle

    B How can I derive the hydraulic equation using conservation of energy and work?

    Hey All, Question about hydraulics. Can't seem to find anyone videos or material to walk me through how to get the formula deltaF = rho*g*(A1+A2)d2 Any takers? My book states: The conclusion is conservation of evergy. Work is done on the liquid by a small force pushing the liquid through a...
  43. C

    A Derivation of Euler Lagrange, variations

    What is wrong with the simple localised geometric derivation of the Euler Lagrange equation. As opposed to the standard derivation that Lagrange provided. Sorry I haven't mastered writing mathematically using latex. I will have a look at this over the next few days. More clarification. I...
  44. C

    I Klein-Gordon propagator derivation

    I was reading about the classical Klein-Gordon propagator here: https://en.wikipedia.org/wiki/Propagator#Relativistic_propagators Basically they are looking for ##G##, that solves the equation $$(\square _{x}+m^{2})G(x,y)=-\delta (x-y).$$ So they take the Fourier transform to get...
  45. B

    I Derivation of the atomic nucleus formula

    Does anyone know the heuristic derivation of this formula? $$R=r_{0} \cdot A^{\frac{1}{3}}$$ with ##R## the atomic nucleus, ##r_0## the radius of a nucleon (proton or neutron) and ##A## the number of nucleons. I know that there is a sperimental derivation, but I would find a theoretic/heuristic...
  46. S

    A Plasma physics - relativistic derivation

    Hello, I am trying to work through attached paper, deriving from equation 2.2 to 2.4. I am not familiar with the notation. If I try and get the integral of inside the <> brackets, I end up with a different eqn 2.4. I need some maths help here :) Any help would be greatly appreciated...
  47. davidge

    I Derivation of the radial equation

    When considering bound states of potential energy that tends to zero at large ##r##, my book arrives in $$\frac{d^2}{dr^2} u_{E} = \kappa^2 u \ \ \ \ \kappa^2 \equiv -2mE/ \hbar^2 > 0 \ \ \ \ r \rightarrow \infty$$ from the differential equation satisfied by ##u_{E} \equiv R_{El} (r) / r##...
  48. F

    I Angular dependance of NEXAFS spectroscopy - derivation

    Hi all, this is my first time posting so I hope it's in the right place, if not I apologise. I'm trying to understand the angular dependence in NEXAFS spectroscopy for linearly polarised light. So from what I understand, the quantum mechanical description of the excitation process for a single...
  49. W

    Reynolds Transport Theorem Derivation Sign Enquiry

    Hi, Our lecturer explained us the Reynold Transport theorem, its derivation , but I don't get where the - sign in control surface 1 comes from? He said that the Area goes in opposite direction compared with this system. I can't visualise this on our picture. Can you please help me understand...
  50. K

    B Derivation of exact differential

    Exact differential of a scalar function f takes the form of ∇f⋅dr=Σ∂ifdxi (where dr is a vector) f:R->Rnand I am not sure why this equation is valid in the sense that if we integrate the equation, ∫∇f⋅dr=∫{Σ∂ifdxi} ∫df=∫{Σ∂ifdxi} the above equation is true because integration is a linear...
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