Derivation Definition and 1000 Threads

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. 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
  2. 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.
  3. 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...
  4. 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...
  5. 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...
  6. 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...
  7. 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...
  8. 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...
  9. 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##...
  10. 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...
  11. 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...
  12. 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...
  13. M

    I Fermi's golden rule derivation

    I'm reading Modern Particle Physics by Mark Thomson and watching Susskind's lecture on QM. In Thompson's book, equation (2.41) the wavefunction is expressed in terms of complete set of states of the unperturbed Hamiltonian as \Psi(\textbf{x}, t) = \sum_{k} c_k(t)\phi_k(\textbf{x})e^{-iE_kt}...
  14. G

    I Usage of partition function in derivation of Sackur-Tetrode

    Why do they introduce the partition function. I have seen it in the derivation of the Boltzmann distribution. But I don't know the physical significance of it here? And how do they get to (L.11) after that? I get everything until L.7. Including L.7. The rest of the proof is here just in case...
  15. Felix Gonzales

    I don't understand the derivation process here, help?

    Homework Statement I understand the derivation it showed that included the sin (15.7 in the image) I just don't understand the following (15.8 in the image). Does "t" get pulled out of the equation? If so what do we derive for then? Does it become 0? If so, it would remain 0 and sin(0) is just...
  16. D

    I Investigating a Possible Derivation Error in f(R) Gravity Field Equation

    In this paper (https://arxiv.org/abs/astro-ph/0603302) the authors derive the field equations for f(R) gravity considering a spherically symmetric and static metric. Now the Ricci scalar only depends on r so you could write f(R(r)) = g(r) for some g. However what it seems the authors have done...
  17. M

    What is Implicit Differentiation for a Circle?

    Homework Statement Hello I have this circle with the equation : [/B] (x-a)^2+(y-b)^2=r^2 I want to find dy/dx for it 2. Homework Equations (x-a)^2+(y-b)^2=r^2 The Attempt at a Solution I am looking on the internet and it appears that I should use what is called "Implicit differentiation"...
  18. R

    Permanent Dipole - Permanent Dipole Interaction Derivation

    Homework Statement I am trying to derive the dipole-dipole interaction derivation, which is: U=(-p1p2/4πϵ_0) (1/z^3) ((2cosθ_1cosθ_2)− (sinθ_1sinθ_2cosζ)) Where p1 and p21 are the two dipole moments, r is the distance between two dipoles on the y axis, θ_1 and θ_2 are the angles between the...
  19. DoobleD

    I Comoving distance and redshift relationship derivation

    Hello PhysicsForum, There is something I don't get at the end of this course notes PDF file. In the last section, titled "Comoving distance and redshift", which I have copied below, we have a short derivation of the comoving distance and redshift relation. Almost all is well, the only thing...
  20. B

    I Calculus in the derivation of Euler-Lagrange equation

    In the derivation of Euler-Lagrange equation, when differentiating S with respect to α, there is a step: $$\frac{\partial f(Y,Y',x)}{\partial\alpha}=\frac{\partial f}{\partial y}\frac{\partial y}{\partial\alpha}+\frac{\partial f}{\partial y'}\frac{\partial y'}{\partial\alpha}$$ Where $$ Y =...
  21. U

    I Derivation of non-dimensional Navier Stoke equation

    Take the first three terms of Navier Stoke equation: $$\rho \cdot \left ( v_{x}\cdot \frac{\partial \vec{v}}{\partial x} + v_{y}\cdot \frac{\partial \vec{v}}{\partial y} + v_{z}\cdot \frac{\partial \vec{v}}{\partial z}\right )$$ Define the length ##v## of the velocity vector field...
  22. Pushoam

    I Derivation of length contraction

    Problem : To measure length of a scale Rest frame : The frame w.r.t. which scale is at rest Moving frame : The frame w.r.t. which the scale is moving with speed v along +ve x-axis In rest frame ,the positions of the two ends of the scale are (measured simultaneously ) x1 and x2. So length L =...
  23. A

    I Help a novice with EL equation derivation

    Hello everyone, Reading Landau and Lifshitz Course of Theoretical Physics Volume 1: Mechanics (page 3) I got suck in the following step (and I cite in italics): The change in S when q is replaced by q+δq is \int_{t_1}^{t_2} L(q+δq, \dot q +δ\dot q, t)dt - \int_{t_1}^{t_2} L(q, \dot q, t)dt...
  24. LyleJr

    I Derivation of the Laplacian in Spherical Coordinates

    Hi all, Sorry if this is the wrong section to post this. For some time, I have wanted to derive the Laplacian in spherical coordinates for myself using what some people call the "brute force" method. I knew it would take several sheets of paper and could quickly become disorganized, so I...
  25. M

    I 1D Phonon density of state derivation

    I'm having some trouble finding consistent results for the derivation of the 1D phonon density of state. I'm applying periodic boundary conditions to a 1D monatomic chain. I can work through and find that D(K)=L/(2π). This is the same result as given by Myers (1990, p. 127). Myers uses only...
  26. E

    B Why Does ln(y) = ln(bεax) Cause Issues in Derivation?

    I know that deriving y = bεax gives dy/dx = abεax, I also know that the inverse of dx/dy equals dy/dx, so how come I don't get dy/dx = abεax when I do the following: ln(y) = ln(bεax) = ax ln(bε) -> x = ln(y)/(a ln(bε)) -> dx/dy = 1/(ay ln(bε)) -> dy/dx = ay ln(bε) = abεax ln(bε) ≠ abεax What...
  27. E

    B Derivation with logarithms and product

    I went through an example question that showed me how to solve the question but I'm not sure if I've misunderstood something or if they did a mistake. Question: Derivate y = (1/ax)ax ln(y) = ln( (1/ax)ax ) = ax( ln(1) - ln(ax) ) = -ax ln(ax) (1/y)(dy/dx) = -ax * ax ln(a) - a * ln(ax) dy/dx =...
  28. U

    Bernoulli equation derivation with added mechanical work

    I´m able to derive Bernoulli equation from the force bilance of the flowing element (particle): dm\cdot \left (\frac{D \vec{v}}{D \tau } \right )_{flowing particle}=\vec{dF}_{g}+\vec{dF}_{p} where dFg is the gravitational force acting on the particle, dFp is the pressure force acting on the...
  29. P

    A Evaluate this paper on the derivation of the Born rule

    I have encountered this paper "Curie Wiess model of the quantum measurement process". https://arxiv.org/abs/cond-mat/0203460 Another work by the same authors is "Understanding quantum measurement from the solution of dynamical models" https://arxiv.org/abs/1107.2138 I am still evaluating the...
  30. snate

    I Troubleshooting a Derivation: Why μ*ε=1/c^2?

    I've been following the derivations in the following video up until that point. I don't quite understand why does it imply that μ*ε=1/c^2. Thanks.
  31. S

    A Stress-Energy Tensor - derivation

    In page 64 of David Tong's notes (http://www.damtp.cam.ac.uk/user/tong/string/four.pdf) on conformal field theory, Tong mentions that 1. the stress-energy tensor is defined as the matrix of conserved currents which arise from translational invariance, $$\delta\sigma^{a} = \epsilon^{a},$$ where...
  32. M

    Derivation of motion equations for collision detection

    Dear all, I am working on a car-accident prediction model. I found the following equations here that worked in my model. However, I could not figure out how the equations were derived. Could anyone help me in understanding the derivation of the mintime and mindist equations (Steps 3 and 5...
  33. ThinkerCorny

    How Is Stoke's Drag Formula Derived Beyond Dimensional Analysis?

    I was looking for the derivation of stoke's drag F=6πηrv But I'm only getting the derivation by dimensional analysis. Can anyone please provide it's real derivation? I'll really appreciate it.
  34. Mr Real

    Understanding Work Done and Integration: Exploring Small Work and Electric Flux

    My question is:why is small work done,dW taken as F.dx instead of x.dF because integrating the latter should also give the same result(taking x out of the integral and integrating dF gives x (F) ).Visualising this integration graphically seems to suggest the same. Similar is the case with...
  35. E

    Maximum area for inscribed cylinder

    Homework Statement Inscribe in a given cone, the height h of which is equal to the radius r of the base, a cylinder (c) whose total area is a maximum. Radius of cylinder is rc and height of cylinder is hc. Homework Equations A = 2πrchc + 2πrc2 The Attempt at a Solution r = h ∴ hc = r - rc A =...
  36. U

    Reynolds transport theorem derivation - linear momentum

    I've managed to derive the form of Reynolds transport theorem as a bilance of linear momentum of the system: \left (\frac{\vec{\mathrm{d} p}}{\mathrm{d} \tau} \right )_{system}=\frac{\mathrm{d} }{\mathrm{d} x}(\int_{V}^{ }\vec{v}\cdot \rho dV)+\int_{A}^{ }\vec{a}dm+\int_{A}^{ }\vec{v}\cdot \rho...
  37. G

    I Derivation of second order Adams-Bashforth

    My notes state that the method is constructed based on the idea: yk+1=yk+∫f(x,y)dx where the integral is taken from xk to xk+1 We can estimate the integral by considering ∫f(x)dx (from xk to xk+1) =c0fk+c1fk-1 To simplify the equation, we move xk to the origin such that ∫f(x)dx (from 0 to h)...
  38. T

    I Derive Relativistic Beaming Equation: Learn Physics Easily

    While studying about some physics things, I came to know a term Relativistic beaming. I looked up in wiki and found a pretty decent article which gives you an equation where the real and apparent luminosity are related by a factor of (Doppler factor)^3-a where a is spectral index. But where's...
  39. needved

    A Help to understand the derivation of the solution of this equation

    Please, help here people. Im reading this article Wave Optics in Gravitational Lensing (T. T. Nakamura, 1999) . In the article start work with \begin{equation} (\nabla ^2 +\omega)\tilde\phi = 4\omega^2U\tilde\phi \end{equation} where $$\tilde\phi = F(\vec r)\tilde\phi_{0}(r)$$. Using...
  40. mertcan

    I Weibull distribution derivation

    hi, I am looking for a proof of weibull distribution, I have searched a lot but nothing is reasonable for the proof, so ıs there derivation of this distribution ? What is the origin of this distribution ?
  41. L

    I How to understand the derivation for this process in QFT?

    I'm reading the book "Quantum Field Theory and the Standard Model" by Matthew Schwartz and I'm finding it quite hard to understand one derivation he does. It is actually short - two pages - so I find it instructive to post the pages here: The point is that the author is doing this derivation...
  42. D

    Alternate derivation of output capacitor ripple voltage buck

    Homework Statement I'm trying to find the output voltage ripple of a buck converter by using just the waveforms and the inductor ripple. Homework Equations [/B] I know that the answer is supposed to be D(1-D)Vin/(16*L*C*f^2) but I keep getting D(1-D)Vin/(8*L*C*f^2)The equations I end up...
  43. N

    I Kleppner & Kolenkow derivation error in free precession?

    Hi all. I ended up to this section in K&K (2nd edition, but with 1st is the same) when they derive the wobbling motion of a simple body in torque-free precession. [see the attached file] Equations 8.23 and 8.24 are integrated into 8.25[a|b], but I think signs are wrong. Shouldn't be negative...
  44. S

    I Understanding Lorenz Gauge Derivation

    Can someone explain to me (or point me towards a source) how is the Lorenz Gauge derived? I am reading the Griffiths book and from what I understand we can do the transformation ##A' = A + \nabla \lambda## and at the same time ##V' = V - \frac{\partial \lambda}{\partial t}## and B and E remain...
  45. B

    MHB What is the Derivation of the Average Value of a Waveform Using Calculus?

    Hello. I was having a hard time determining how the formula for the average value of the waveform can be achieved. I've read that the ave since the waveform is symmetric is (Imin+Imax)/2. I want to know how to derive it using calculus. Thanks.
  46. Y

    Why Does My RL Circuit Analysis Yield a Positive Time Constant?

    Homework Statement After a long time, an inductor is disconnected quickly from the battery and then attatched to a resistor. Homework Equations V = Ldi/dt V = ir The Attempt at a Solution KVL: voltage across inductor - voltage across resistor = 0 Ldi/dt - ir = 0 di/i = rdt/L ln|i| from i(t)...
  47. K

    I Understanding the Derivation of the Metric Tensor

    Hello, I have a question regarding the first equation above. it says dui=ai*dr=ai*aj*duj but I wonder how. (sorry I omitted vector notation because I don't know how to put them on) if dui=ai*dr=ai*aj*duj is true, then dr=aj*duj |dr|*rhat=|aj|*duj*ajhat where lim |dr|,|duj|->0 which means...
  48. Z

    Work Done by Gravity and Derivation of G.P.E.

    I came across this website and I intend to find out more about work done by gravity and derivation of gravitational potential energy (Sorry, the thread name is too long, so I abbreviate it as G.P.E.) Ok, here is the problem. I am quite confused with the calculation of work done against gravity...
  49. T

    Derivation: Entropy of Vaporisation using Redlich-Kwong EoS

    Homework Statement For some reason it is not letting me add the image here, here is the link to the question: http://imgur.com/a/3DLWM The part I'm stuck on is the last part. Basically, the question is to obtain the following equation for the entropy of vaporisation using the Redlich-Kwong...
  50. I

    Derivation for number of periods finance formula

    Homework Statement Hi, I am reading this book called, Introduction to Corporate Finance, by Berk, Demarzo, Harford (second edition). In it they try to explain how to calculate the number of periods in a loan payment formula. Authors give the following equation. $$ 0 =PV + PMT \times...
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