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.
Hi,
This is not related with a specific homework question. I was studying this topic and have noticed that I didn't understand some bits.The car is negotiating a bend with a speed of V.
The slope of the banket is θ
The coefficient of friction is η
Weight of the car if mg
Radius of the bend is R...
Here and there I come across the following formula for the Lagrangian density of a real scalar field, but not a deriviation.
\mathcal{L} = \frac {1}{2} [ \dot \phi ^2 - ( \nabla \phi ) ^2 - (m \phi )^2 ]
Could someone show me where this comes from? The m squared term in particular...
Homework Statement
Derive the formula for rod's moment of inertia: I = ml2/12
Homework Equations
I = ml2/12
The Attempt at a Solution
The only one derivation I know of is dividing the rod into two parts and then integrating from 0 to l/2. However' I'd love to know if there's some...
Homework Statement
Derive the following relation, where z1 and z2 are arbitrary complex numbers
|z1z2*+z1*z2| ≤ 2|z1z2|
The Attempt at a Solution
I found the expression |z1z2*+z1*z2| = |2(a1a2+b1b2)| = √(4[a12a22 + 2a1a2b1b2 +b12b22])
But that is where I get stuck. How does the...
Homework Statement
On page 251 of Griffiths's quantum book, when deriving a result in first-order perturbation theory, the author makes the claim that <\psi^0|H^0\psi^1> = <H^0\psi^0|\psi^1> where H^0 is the unperturbed Hamiltonian and \psi^0 and \psi^1 are the unperturbed wavefunction and its...
I kindly ask for assistance in derivation of the equation for instantaneous power in an electric circuit, P(t) = V(t) I(t). I want to derive it as rigorously as possible. Here's what I got:
We start with P = {\bf F} \cdot {\bf v}, where {\bf v} = \frac{d\bf r}{dt}
We know that the force...
"use geometry"--Redshift derivation?
1. Use geometry to derive z=v/c where c is the speed of light and z = [v(obs)-v(em)]/v(em).
Homework Equations
None given... Though I am assuming that I am constant.
The Attempt at a Solution
I believe it has to do with the Doppler effect which...
The title says it all--I'm working through The Feynman Lectures, and came across the assertion that a magnetic field can be thought of as a relativistic-transformation of an electric field (and vice-versa). This makes sense to me, since the magnetic field of a moving point-charge can easily be...
In working out the derivation of the probability current density, I see (based on the definition of j(x,t)) that the limits of integration are changed from
d/dt∫(b to a) P(x.t) dx = iħ/2m[ψ*(x.t)∂/∂xψ(x.t) - ψ(x.t)∂/∂xψ*(x.t)](b to a)
to
d/dt∫(b to a) P(x.t) dx =...
Homework Statement
Derive the ripple voltage of a full-wave rectifier with a capacitor-input filter.
Homework Equations
Where V_{r(pp)} is the peak-to-peak ripple voltage and V_{DC} is the dc (average) value of the filter's output voltage.
And V_{p(rect)} is the unfiltered peak rectified...
This is not a home work, it is part of the textbook on elliptical polarization. Attached is a page in Kraus Antenna book, I cannot verify the equation on the last line. Here is my work
E_y=E_2(\sin{\omega} t \cos \delta \;+\; \cos \omega {t} \sin \delta) , \sin\omega {t} =\frac {E_x}{E_1}\;,\...
I'm in a high school pre-calculus class and a statistics class. For the latter, we are given z-tables for some of our tests. I don't like these z-tables.
Thus, I decided that a more direct approach (fundamental theorem of calculus) would be more accurate and, more importantly, more fun. My...
Can someone explain to me how one gets the values of n, l, and ml (principle quantum number, azimuthal quantum number, magnetic quantum number, respectively) from the Schrodinger equation for use in chemistry involving distribution of electrons in a hydrogen atom?
In Griffiths, for deriving the bound charges for a given polarization P , the formula used is the general formula for dipoles .i.e ( equation 4.9)
{Here the potential at r is calculated due to the dipole at r' )
V(r) = ∫\frac{x.P(r')}{X^2}d\tau'
Here X = r - r' , and x = unit vector in...
Hello guys, I'm studying Thermodynamics and I don't totally see how you introduce the potencials using Legendre transformations.
I have seen a non formal explanation showing how you can interpret them, but not a rigorous demonstration of how you get them via the Legendre transformations...
Hello Everybody,
Carroll introduces in page 106 of his book "Spacetime and Geometry" the variational method to derive the geodesic equation.
I have a couple of questions regarding his derivation.
First, he writes:" it makes things easier to specify the parameter to be the proper time τ...
Homework Statement
I've searched everywhere, and I cannot find an example of calculation of Lie derivation of a metric.
If I have some vector field \alpha, and a metric g, a lie derivative is (by definition, if I understood it):
\mathcal{L}_\alpha g=\nabla_\mu \alpha_\nu+\nabla_\nu...
Homework Statement
Problem 1:
Derive the Euler-Lagrange equation for the function ##z=z(x,y)## that minimizes the functional
$$J(z)=\int \int _\Omega F(x,y,z,z_x,z_y)dxdy$$
Problem 2:
Derive the Euler-Lagrange equation for the function ##y=y(x)## that minimizes the functional...
I have seen the derivation of the kinetic energy equation using
F=M*v'
and
E=F*x
And I can see how this works, however if you try to do this without thinking about velocity, and only thinking about the rate of change of distance, and the rate of change of rate of change of distance, then the...
U = energy
In the book:
\frac{dU}{dt} = \frac{d}{dt} (\frac{1}{2} mv^2 + \frac{1}{2} kx^2)
then we have m \frac{d^{2}x}{dt^2} + kx = 0 because v = \frac{dx}{dt}
however they get rid of \frac{dx}{dt} .
They are ignoring the case where v = 0, because then m \frac{d^{2}x}{dt^2} + kx...
This is actually the problem in the textbook.
I'm trying to derive the harmonic oscillator differential equation for this system, but It seems like it's very very challenging.
could anyone help me out?
Following is the question and figure from the textbook.
Homework...
I've been working my way through Intro to Electrodynamics (Griffiths), and in Chapter 3, one of the derivations comes out to
∫sin(n\piy/a) sin(n'\piy/a) dy ={ 0 if n'\neqn
a/2 if n'=n
where the function is...
Introduction
This is not a homework or coursework question (if it were it would be of the project type), and I am looking for hints not spoilers.
Hi,
I recently passed by kepler's laws again in a science class (this time Earth science), and am concurrently taking calculus in my math class...
Find the instantaneous velocity where r is the position vector as a function of time:
r(t)=(3.0m/s^2)t\hat{x}+(4.0m/s)t\hat{y}
I attempted to find the derivative of this to find instantaneous velocity, but the book's solution was different. I think the author of the book may have made a...
Homework Statement
Consider the following equality:
(\frac{∂S}{∂V})T = (\frac{∂P}{∂T})V
If I rearrange the equality so that I write:
(\frac{∂S}{∂P})? = (\frac{∂V}{∂T})?
What variables will be constant in each side?
I'm having some trouble in a few thermodynamics problems because...
http://imgur.com/SnHyP
What are the mathematical steps and assumptions to reach the conclusion that length(ab) ≈ dx + ∂u/∂x*dx ?
If you consider the the squares of the gradients to be negligible, you still have a square root and multiplication by the constant "2". What other assumptions do...
http://imgur.com/SnHyP
What are the mathematical steps and assumptions to reach the conclusion that length(ab) ≈ dx + ∂u/∂x*dx ?
If you consider the the squares of the gradients to be negligible, you still have a square root and multiplication by the constant "2". What other assumptions do...
I'm a little confused, in my fluid mechanics course we've covered many equations and they are all derived using an x-direction fluid flow. If I was to use these in a system in which fluid flowed in the y-direction would I have to re-derive them? Or would it be more of a case of using a...
Can someone tell me how I can derive Wien's law, i.e.,
\lambda_{max} T = constant
where \lambda_{max} is the peak wavelength and T is the absolute temperature of the black body, using the equation,
P=\frac{U^{*}}{3}
where U^{*} is the energy density.
Note: I'm not looking for...
i was reading about derivation of Euler's equations for rotational dynamics (john taylor, classical mechanics, chapter 10) when i got stuck on one of the reasonings
essentially it refers to the moment of inertia tensor, since the tensor itself about a point is dependent on the position of the...
Homework Statement
I am seeking a derivation of the formula for greatest detail or maximum resolution of an astronomical telescope, which is:
Homework Equations
M = fo/foe where:
M: magnification
fo: focal length of objective lens
foe: distance of primary image from the eyepiece...
Hey guys,
I was trying to reverse engineer Einstein's formula for energy, E=γmc^2 by re-engineering Newton's Law of motion, F=ma. I was talking with my physics prof about deriving energy from this because I got two different answers but it gets weird because the incorrectly derived formula...
Homework Statement
http://postimage.org/image/j2ccrtjp1/
Here is a scan of my work. The problem is on the scan. Just trying to derive the velocity of the target in an elastic collision, as sketched in the image...
Can't seem to find the problem for the life of me.
Equation attached.
For those who can't see the image here it is in text form, k=(Gd^4)/(8D^3 n )
It is the equation for the stiffness of a spring in terms of its dimensions:
G - shear constant
d - wire diameter
D - coil average diameter
n - number of active coils (total coils -2 as...
I'm just getting started on relativity. I watched this a couple of day ago -
But I didn't like the way Lorentz Transformation was derived (the assumption about the nature of the final transformations, to be more specific). I tried reading Einstein's original paper for a better derivation but...
I just have a question of "why/how?" I know that for instance \mathbf v=\omega \hat k \times \mathbf r where \mathbf v is my vector for velocity, \omega is my angular velocity and \mathbf r is my position vector from a point on the axis of rotation of a wheel to a point on the outer edge of the...
Homework Statement
I'm taking a fluid mechanics class and I'm having an issue with acceleration and background knowledge. I know this is ridiculous, but I was hoping someone might be able to explain it for me.
Homework Equations
I definitely understand:
##a=\frac{d\vec{V}}{dt}##
And I...
So I know about the lorentz factor and how it describes time dialition, mass increasing etc.. but I was wondering how it was derived in the first place?
Homework Statement
Consider a cylindrical vessel with cross-sectional area 1m^2
Derive the particle flux (1/4n\bar{v})Homework Equations
I have the solid angle:
\Omega = 2π(1-cosθ)
The Attempt at a Solution
I'm assuming that the solid angle represents the full area that the particles can...
Homework Statement
I was reading up on the Wave Function used in the Schrodinger Wave Equation. However one source said that
ψ(x,t)=e^(-i/hbar*(px-Et))
Another source had this
ψ(x,t)=e^(i/hbar*(px-Et))
Which one of these is true and could someone give a derivation for the correct...
Homework Statement
I tried to reach the Bernoulli principle this way:
Two pipes are connected, one has a cross-sectional area of S_{1} and speed of v_{1}; S_{2} and v_{2} for the other. The pipes are horizontal, the connecting wall between them at the crossing from one pipe to the other is...
Hi!
I've got a problem with question 5 on this paper:
http://www.freeexampapers.com/past_papers.php?l=Past_Papers%2FAEA%2FPhysics%2F2006/
Download AEA-PHYS-PP-MayJune-2006-AEA-Paper-1342.pdf.
Starting from b) i), we got that:
ε=Δ∅/Δt → W=εe
Where W is denotes work, ε is...
Homework Statement
Given the function f(x) defined as:
(x^3-y^3)/(x^2+y^2) if (x,y)≠(0,0)
0 if (x,y)=(0,0)
Find the parcial derivatives of the function at the point (0,0).
Is the function f differentiable?
Homework Equations
The Attempt at a Solution
d/dx [...
In thermodynamics one of the maxwell relations is:
\left( \frac{\partial S}{\partial V} \right)_T = \left( \frac{\partial P}{\partial T} \right)_V
When I try to derive it from dU = TdS - PdV i get:
T = \left( \frac{\partial U}{\partial S} \right)_V
P = -\left( \frac{\partial...
Homework Statement
As the title suggests, I need help finding resources that clearly shows the step by step process of the derivation of the rest or invariant mass using the Lorentz transformation.
Homework Equations
Energy-momentum relation
The Attempt at a Solution
Not looking...
Meaning of ct in Lorentz transformation -
In Lorentz transformation matrix, the first column is defined as - ct, not t itself. Is it because ct satisfies the units of x, y, z? Or, simpler Lorentz transformation matrix will be derived? The idea of 'ct', instead of t, is quite abstract for me...
Homework Statement
S=1+(a/r)-(b/r^3)
Homework Equations
need to find r=sqrt(3b/a) and S=1+ sqrt((4a^3)/(27b))) from a derivation of the above formula in #1.
The Attempt at a Solution
0=(3b/r^4) - (a/r^2)