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. Decimal

    A Question about the derivation of the tangent vector on a manifold

    I am trying to understand the following derivation in my lecture notes. Given an n-dimensional manifold ##M## and a parametrized curve ##\gamma : (-\epsilon, \epsilon) \rightarrow M : t \mapsto \gamma(t)##, with ##\gamma(0) = \mathbf{P} \in M##. Also define an arbitrary (dummy) scalar field...
  2. bagasme

    B Derivation of Wheel Relationship Formulas

    Hello, Here in this thread I will derive formulas for relation between two wheels, either teethed (e.g. gears) or non-teethed. In wheel relationship, we have three cases: Two wheels at the same axle Two wheels intersected in parallel (meshed) Two wheels connected by a belt We will examine...
  3. bagasme

    B Derivation of Cosine and Sine Method of Vector Sum

    Hello all, In high school physics, the magnitude sum of vector addition can be found by cosine rule: $$\vec {R^2} = \vec {F^2_1} + \vec {F^2_2} + 2 \cdot \vec F_1 \cdot \vec F_2 \cdot cos ~ \alpha$$ and its angle are calculated by sine rule: $$\frac {\vec R} {sin ~ \alpha} = \frac {\vec F_1}...
  4. jk22

    A Lorentz Transformation Derivation Question

    I wanted to make a derivation of the Lorentz transformation : $$x'=Ax+Bt\\t'=Dx+Et$$ The conservation of the quadratic form ##c^2t'^2-x'^2## yields the equations: $$A^2-B^2/c^2=1\\D^2-E^2/c^2=-1/c^2\\AD=BE/c^2$$ Hence ##B=c\sqrt{E^2-1}##,##D=\sqrt{E^2-1}/c##,##A=\pm E##. The speed of the...
  5. MathematicalPhysicist

    A A derivation in Peskin and Schroeder in chapter 18.

    They write on page 618: where for those who don't have the book at hand, I'll write the related equations: $$(18.94) \ \ \ \sigma(e^+ e^- \to \text{hadrons})=\frac{4\pi \alpha^2}{s} [ I am c^1(q^2)+Im c^{\bar{q}q}(q^2) \langle 0| m\bar{q}q|0\rangle+ $$ $$+Im c^{F^2}(q^2)\langle 0 |...
  6. patric44

    A derivation of the Vdc in a fullwave rectifier with smoothing?

    i was trying to derive the Vdc in a fullwave rectifier with smoothing capacitor , i guess i had it right as my final equation matches the book equation : Vdc~(1-(1/2fRC))Vp , but i am not really sure that my attempt was completely right as i assumed that Vdc is the average value of the...
  7. bagasme

    I Derivation of a Higher Order Derivative Test

    Hello, In second-order derivative test, the test is inconclusive when ##f''(c)=0##, so we had to generalize to higher-order derivative test. I was wondering how such tests can be generalized and derived? For example, how can I prove that ##f(x)=x^4## have minimum at 0? Bagas
  8. Andrew3

    A question about the derivation of Fermion Quantization in QFT

  9. bagasme

    Wheatstone Bridge: Substitution Resistance Formula Derivation?

    Hello, In high school, I had been taught about finding substitution resistance from Wheatstone bridge. The formula: a. If the cross product of ##R1## and ##R3## is same as ##R2## and ##R4##, the galvanometer in the middle (##R_5##) can be omitted and use series-parallel principle to solve for...
  10. M

    Derivation of the Equations of Motion for a System

    Summary:: This is a system and we want to find the equations of motion. After some force-based attempts, I think that it would be easier to use some energy methods. Hi, I wanted to ask about deriving equations of motion by using the Lagrangian. The question is in the picture below. We are...
  11. M

    Question about the Derivation of the Stream-function for a Doublet

    Hi, I just wanted to ask a question about the derivation of the stream function \psi for a doublet. In the pictures below is a derivation (in this one the source is on the left and the sink is on the right). I understand everything in the left photo, however my questions are: 1) Why do we...
  12. B

    Radial acceleration derivation with minimal knowledge

    Just started learning about uniform circular motion. I really don't understand how we get aΔt2/2 on the side. I also searched on the internet for a similar derivation, but there are none so simple. Thanks for your help! P.S There is a mistake in calculation in second line (textbook error).
  13. B

    Confusing Derivation of torque acting on disk question

    Not sure how they obtained an answer of (2meukenetic *Mg/R^2)*r^2 dr = dt When they say disk I am assuming it's not ring shaped. So since F * Dr= DT where I guess F acting on a small point on the disc is constant from the table top. And Dr is the variable distance from a random small point from...
  14. Adesh

    Derivation of [itex] p = \frac{E}{c} [/itex] using Maxwell's light

    Imagine that we have an electromagnetic wave or light propagating in x direction, and \mathbf{E} is oscillating in z direction and \mathbf{B} in y direction. The picture looks something like this Now, if there exists a charged particle q on the xx axis at rest, then our B field can't do...
  15. B

    A The derivation of the volume form in Ricci tensor

    In this derivation,i am not sure why the second derivative of the vector ## S_j '' ## is equal to ## R^{u_j}{}_{xyz} s^y_j v^z y^x## could anyone explain this bit to me thank you it seems ## S_j '' ## is just the "ordinary derivative" part but it is not actually equal to ## R^{u_j}{}_{xyz}...
  16. T

    Adiabatic approximation in the derivation of the speed of sound

    The speed of sound in a gas at temperature T is given to be ## v=\sqrt{\frac{\gamma RT}{M}}##, where ##\gamma## is the adiabatic exponent, R is the gas constant and M is the molar mass of the gas. In deriving this expression, we assumed that the compression and expansion processes were so fast...
  17. n3pix

    I How does my book get ##\frac{1}{2}## by this derivation?

    The integral is called the line integral of ##F## from ##A## to ##B##. The work done in the displacement by the force is defined as, ##W(A\rightarrow B)=\int_A^B \vec{F}.dr## where the limits ##A## and ##B## stand for the positions ##r_A## and ##r_B##. We now return to the free particle...
  18. U

    Derivation of the oscillation period for a vertical mass-spring system

    I understand the derivation of T= 2π√m/k is a= -kx/m, in a mass spring system horizonatally on a smooth plane, as this equated to the general equation of acceleration of simple harmonic motion , a= - 4π^2 (1/T^2) x but surely when in a vertical system , taking downwards as -ve, ma = kx - mg...
  19. R

    A Missing step in the derivation of the Robertson-Walker metric

    To arrive at the Robertson-Walker metric for a spatially homogeneous and isotropic cosmology, one first writes down the the metric for spatial sections i.e. constant t surfaces, dσ2 = d2 +f2(r) (dθ2 + sin2θ dφ2), where f(r) can take only 3 special forms, and then one promptly writes the...
  20. K

    I Palmgren-Miner equation derivation

    Summary: This equation is used in ISO standard ISO 6336-6. I want to understand how it is derived. This equation helps to consolidate damage caused by multiple torque, cycle bins. A bin means a torque applied for a given number of cycle. As an outcome of the equation, a single equivalent...
  21. E

    I I'm searching for a specific book with the derivation of ##E\propto v^2##?

    Twice I found the following derivation of ##E\propto v^2## in a little distinct forms. https://www.physicsforums.com/threads/the-final-explanation-to-why-kinetic-energy-is-proportional-to-velocity-squared.78484/#post-609992 The derivation is in post #9, if it is not shown properly. This...
  22. T

    A Help understanding a term in the derivation of #\Pi(\vec(x),t)# for KG eq.

    When deriving ##\Pi(\vec{x},t)## for the Klein-Gordon equation (i.e. plugging ##\Pi(\vec{x},t)## into the Heisenberg equation of motion for the scalar field Hamiltonian), we come across a term that is the following ##\int_{-\infty}^{\infty}d^{3}y...
  23. D

    Black body radiation and the derivation of Stefan Boltzman

  24. A

    I Question about the Derivation of the Equations of Vibration

    For undamped free vibrations, we have the following differential equation. mu'' + ku = 0 where m is the mass of the object hanging on the end of a spring, and u is the distance from the equilibrium position as a function of time. This yields u = Acosωt + Bsinωt where ω is √(k/m)...
  25. lohboys

    Engineering Derivation of Thermodynamic Relations

    dG= -SdT + VdP ... now dividing by dV holding temperature constant (dG/dV)T = -S (dT/dV)T + V (dP/dV)T ... now dT and constant temperature cancel out final answer: (dG/dV)T = V (dP/dV)T
  26. Luke Tan

    B Landau's Derivation of Lorentz Transformations: Questions Answered

    In his book, Landau derives the Lorentz transformations using the invariance of the interval, and I have some questions about it that I would like to clarify 1. What is a parallel displacement of a coordinate system? Does it refer to moving along any axis? I don't see how any arbitrary...
  27. arcTomato

    Fourier transform and derivation

    Homework Statement: I don't know how can I derivation Eq.(2.2) Homework Equations: Fourier coefficients Homework Statement: I don't know how can I derivation Eq.(2.2) Homework Equations: Fourier coefficients Dear all. I don't know how can I derivation Eq.(2.2). Where Σk is come from??
  28. J

    Derivation of the equation for HV Gaseous Breakdown?

    Hello, I am solving a dielectric materials assignment to derive the equation for the growth of current in a gap stressed with the high electric field. The equation is as follows: The equation combines the anode, cathode and attachment process as shown below: I have derived the two equations...
  29. MathematicalPhysicist

    Derivation of equation (9.117) on Schutz's textbook

    On page 238 of his second edition of Schutz's he writes the following: Where Eq. (9.107) is: $$\bar{h}^{TT}_{xx}=A\cos (\Omega (z-t)) , \bar{h}_{yy}^{TT}=-\bar{h}^{TT}_{xx}$$ and ##\delta \bar{h}^{TT}_{xx}=2\pi \sigma m \Omega \ell_0 R \sin [\Omega (z-t)-\phi]##. Here's what I tried: $$A\tan...
  30. MathematicalPhysicist

    I Derivation of the conservation of total energy and momentum

    I want to derive from ##T^{\mu \nu}_{,\nu}=0## the equation: ##\int T_{0\mu}d^3 y=constant##, I don't see how exactly. From the derivative I know that ##T^{0\mu}_{,\mu}=0##, but I don't see how to integrate this equation, it's ##T^{00}_0+T^{0i}_i=0##. But how to proceed from here? Thanks in...
  31. MathematicalPhysicist

    I Derivation of an identity for ##\partial^2_t \int T^{00}(x^i x_i)^2d^3

    I'll write down my calculations, and I would like if someone can point me to my mistakes. $$\partial_t \int T^{00}(x^i x_i)^2 d^3 x = -\int T^{0k}_{,k}(x^i x_i)^2 d^3 x = \Dcancelto[0]{-\int (T^{0k}(x_ix^i)^2)_{,k}d^3 x} +\int (T^{0k}(x_i x^i)^2_{,k})d^3 x$$ After that: $$\partial_t \int...
  32. E

    Derivation of pV = 1/3 Nmc^2

    This is such a small point but I just wondered if anyone could clarify. It is easy to work out the time between successive collisions with one wall of the box, namely $$\Delta t = 2L/v_{x}$$However, if this time interval is for instance 1 second, then we could have either 1 or 2 collisions in...
  33. n3pix

    Converting Velocity Formula: Polar to Cartesian

    I have a little question about converting Velocity formula that is derived as, ##\vec{V}=\frac{d\vec{r}}{dt}=\frac{dx}{dt}\hat{x}+\frac{dy}{dt}\hat{y}+\frac{dz}{dt}\hat{z}## in Cartesian Coordinate Systems ##(x, y, z)##. I want to convert this into Polar Coordinate System ##(r, \theta)##...
  34. takunitoche

    A Derivation of the Yang-Mills 3 gauge boson vertex

    Hello everyone, I am stuck in the derivation of the three gauge-boson-vertex in Yang-Mills theories. The relevant interaction term in the Lagrangian is$$\mathcal{L}_{YM} \supset g \,f^{ijk}A_{\mu}{}^{(j)} A_{\nu}{}^{(k)} \partial^{\mu} A^{\nu}{}^{(i)} $$ I have rewritten this term using...
  35. D

    Unusual escape velocity derivation

    Is it possible to derive escape velocity say using momentum and force balance considerations? or using angular momentum consideration? Namely, any other approach then energy consideration that utilizes gravitation potential energy and kinetic energy?
  36. MathematicalPhysicist

    I Derivation of Riemann tensor's first order-equation

    According to Schutz's second edition book, the equation for Riemann tensor to first order in ##h_{\mu\nu}## is: $$R_{\alpha\beta\mu\nu}= \frac{1}{2}(h_{\alpha \nu,\beta \mu}+h_{\beta\mu,\alpha\nu}-h_{\alpha\mu,\beta \nu}-h_{\beta \nu , \alpha \mu})$$ which (as stated in the book) can be derived...
  37. KF33

    B How do I differentiate vectors with derivatives and properties?

    Homework Statement: The homework problem is included below, but I am looking at the derivatives of vectors. Homework Equations: I have the properties of derivatives below, but not sure they help me here...
  38. Adesh

    Derivation of the change of air pressure with height

    If we take a slab of air with cross-sectional area of A and height dz in our atmosphere. Now, what we do is make an argument like this :- Pressure from below must balance both the weight and Pressure from above to keep the slab at rest. ( I have added an attachment for clarification) And...
  39. abby11

    A Derive Radial Momentum Eq. in Kerr Geometry

    I am trying to derive the radial momentum equation in the equatorial Kerr geometry obtained from the equation $$ (P+\rho)u^\nu u^r_{;\nu}+(g^{r\nu}+u^ru^\nu)P_{,r}=0 \qquad $$. Expressing the first term in the equation as $$ (P+\rho)u^\nu u^r_{;\nu}=(P+\rho)u^r u^r_{;r} $$ I obtained the...
  40. christang_1023

    Derivation about the wave interference

    Starting from the simple case, there is a single wave ##e=a\cos(2\pi ft+\frac{2\pi}{\lambda}x+\phi_0)##, and integrate in such a way, where ##T_{eye}## stands for the response time of human eyes' response time towards energy change: $$I=\int_{0}^{T_{eye}}e^2dt$$ The calculation includes...
  41. J

    Derivation of Lagrangian in the calculus of variations

    Hello. In a chapter of a book I just read it is given that ##\frac {d} {d\epsilon}\left. L(q+\epsilon \psi) \right|_{\epsilon = 0} = \frac {\partial L} {\partial q} \psi ## While trying to get to this conclusion myself I've stumbled over some problem. First I apply the chain rule...
  42. J

    Sinking Object Motion Equations

    Hi guys! I am currently learning about fluid dynamics, and I am stuck on a certain equation derivation. It's about sinking motion which considers only gravity force, buoyant force, and viscous resistance. The link attached has the details...
  43. tjholi

    Derivation of the Emptying Time for a buoyant box to drain

    Problem Statement: I am having trouble deriving the expression from the initial equations. (Calculate the emptying time considering Volume conservation) Relevant Equations: Q=A*sqrt(b(H-h(t)) And we have dh/dt =Q/S (conservation equation) and we have to obtain h/H = 1-(1-t/te)^2 with te=...
  44. R

    Derivation of ideal magnetic dipole field strength

    For reference, this is from Griffiths, introduction to quantum mechanics electrodynamics, p253-255 When deriving the ideal magnetic dipole field strength, if we put the moment m at origin and make it parallel to the z-axis, the book went from the vector potential A $$ A=...
  45. jk22

    B Deriving Lorentz Transformation: Wave Eq Invariance & General Relativity

    I read the Lorentz transformation can be obtained by solving the requirement of invariance of the wave equation. If one considers linear transformations this the same as the spacetime interval squared to be invariant. What are the other nonlinear transformations keeping the wave equation...
  46. B

    Question about the derivation of linear magnification

    I tried assumed ##\theta \approx sin \theta \approx tan \theta##. By Snell's law(after approximation), $$n_1 \tan( i_1)= n_2 \tan( i_2)$$ If ##\tan (i_1)=\frac {h_o}{ u}## and ##\tan (i_2)=\frac {h_i}{ v}##,then $$m=\frac {h_i}{h_o}=\mod{\frac {v n_1}{un_2}}$$ Which is the expected...
  47. berlinspeed

    A Derive 4-Velocity Components: Anyone Know How?

    Anyone know how to derive ##u^0=\frac {dt} {d\tau}=\frac {1} {\sqrt {1-\mathbf {v}^2}}## and ##u^j=\frac {dx^j} {d\tau}=\frac {v^j} {\sqrt {1-\mathbf{v}^2}}##?
  48. K

    I Derivation of the Lorentz transformations

    It seems that there is a considerable number of ways of deriving the Lorentz transformations. Does anyone know how many ways are there?
  49. W

    Bernoulli's Principle -- correct derivation

    In this scenario I'm assuming that there is a shared velocity of water within the pipes, as well as a shared pressure and that water is non-compressible. If I understand correctly when someone says that pressure at a point is P at some point, it is the same as saying that if I put a small cube...
  50. I

    I Where did the extra 8 come from in the derivation for density of states?

    I was looking for a derivation for the density of states and I came across this page: https://ecee.colorado.edu/~bart/book/book/chapter2/ch2_4.htm I followed the derivation and came up with: g(E) = (1/L3)dN/dE = (1/L3)L3/∏2*k2 * dk/dE =K2/∏2 * dk/dE =K2/∏2 * g(E) =...
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