Much appreciated. I believe this solves my question.
Don't worry about revealing the "proof", I would say that this problem is just a redefinition of a small mechanism in a larger problem, which has nothing to do with linear algebra, actually, so letting me in on the mechanism is of no great...
I suppose it was late, and this meant I had to improperly state the question!
Really, the question is does the set of RD vectors have nonzero measure over R^k, not whether they are dense or not. Of course the rationals are rationally dependent and dense, but they are a set of measure zero in R...
Hi guys:
I've got a problem I've been working on for some weeks and this might be the key to unlocking it.
The question is:
Given a vector in R^k, what is the measure of the set of vectors whose components are rationally dependent?
Rationally dependent means for a given vector, you may...
Hey, I'm doing some examples in QFT and I don't want to go too far with this one:
Doing gauge symmetries, we first introduce the Unitary spacetime-dependent gauge transformation that gives us a gauge potential. With the new gauge added Lagrangian, I want to take its variation to confirm the...
Homework Statement
The idea is to prove that the average of a harmonic function over a square is the same as the average over its diagonals.
Homework Equations
Really, none, other than the mean value theorem, that is the value of the function at a point is the same as the average of...
Right: I just meant the ratio, not the relative error.
I just did \frac{yours}{actual}
I don't understand that third statement: the largest error in [m,n] is at m + sqrt(m)? This isn't always in the interval. I'm also not sure what you mean by 2) your largest error is at two points? The error...
I think the easiest way to explain it is by what Wikipedia has:
A Killing field is one where when you move points along the field, distances are preserved.
So http://en.wikipedia.org/wiki/Killing_vector_field" [Broken] when you'e got a Killing field.
This is like a weight combo of up and down Bahkshali, right?
Here's your relative error:
It has an exponential approach curve
I think its a smart idea but computationally its as efficient as Bahkshali... and there are more efficient methods than Bahkshali. Mathematica isn't cooperating...
Hi notist,
If you are able to write down the perturbed Hamiltonian, you should be able to run through these computations quite easily :).
The idea is that to first order perturbation, the energy shifts are essentially the same as the expectation value of the perturbing Hamiltonian. It...
So here's the problem:
I'm asked to find the solutions to the 1-D Wave equation
u_{tt} = u_{xx}
subject to
u(x,0) = g(x), u_t(x,0) = h(x)
but also
u_t(0,t) = A*u_x(0,t)
and discuss why A = -1 does not allow valid solutions. I can't figure it out at all. The solutions to...
right... the problem is this solution isn't as easy as all that... there is a more trivial example solved with
\frac{dx}{x^2} = \frac{dy}{y^2} = \frac{dz}{z(x+y)}
Which can be solved by doing some proper addition and subtraction: so I know the idea. Its a matter of getting a form \frac{g*dx...
Hey guys, I'm having a little difficulty with a pde I'm trying to solve. It boils down to solving for a first integral. I don't want the answer, but I'd be glad to get a little help. We have the system:
\frac{dx}{x^2} = \frac{dy}{y^2} = \frac{dz}{xy(z^2 + 1)}
We can use the first two and find...
Homework Statement
I need to solve the Eikonal Equation c^2(u_x^2 + u_y^2) = 1
Initial condition u(x,0) = 0 C(x,y) = |x|, but x>0 to essentially C = x
Oh. And the solution is given as \ln{\frac{\sqrt{x^2 + y^2} + y}{x}}
Homework Equations
None other than the usual method of...
Its a quote I want to use it on a proof, I just don't want to screw it up and attribute it to Feynman (though its a good chance its his). I also don't remember the precise wording.
It goes something like this
Thanks guys! I know one of you knows this, its pretty damn famous, about every...
Thanks for the help: your idea is basically the point I used to solve the problem (the only one in the class, mind you :)
The best way to do this (at least mine) is to use a combination of the aforementioned idea, Taylor expansions, and thermodynamic principles, along with a statement of the...
So I've gotten a little ways on this, at least in some poor way, I think. Anybody out there with help?
Basically I have two ideas. The first involves the identification that we can regard the energy of a single particle as a continuous random variable with some distribution resulting from the...
Homework Statement
So this question has been bugging me because I can't begin to start it. The question is, prove that \Omega, the number of microstates of the combination of two physical states in thermal contact is a Gaussian of the energy of one of the states. \Omega is given here as...
Hi all,
I was recently accepted to the Math in Moscow program at the independent university of Moscow for the fall term. I have been recently informed my scholarship is not applicable, as the IUM is an "of course" independent institution. I was wondering if you all had any opinions on the...
Homework Statement
Show that as calculated in the rest frame comoving with the twin on the outgoing trip, the ratio of the two ages of the twins is the same: i.e. the twin on earth has age gamme times the other twin
Homework Equations
Lorentz Transforms
The Attempt at a Solution
We...
This is not a homework problem, it is something that is stumping a group of us right now.
Show that
z*exp(z) = a
Has infinitely many roots in the complex plane.
I would caution against a series approach as we can't guarantee roots of the polynomial
z*exp(z) - a.
Any ideas?
[SOLVED] ODE problem
Homework Statement
A situation in which the air resistance is proportional to the velocity of an object squared.
Object dropped off of a building with height 100m.
F = -mg + Fr Fr=.5*cw*p*A*v^2
cw=.5 p = air density = 1?
Homework Equations
I need to...
I retried the problem, and was able to do some integration by treating it as a differentials and deriving a seperable ODE. However, my answers seem very odd. Here's what I did.
m*dv/dt = -\alpha*e^\beta*v
dv/e^\beta*v = -\alpha*dt/m
letting u = e^-Bv
du = -B*e^-Bv
\int1/-B * du =...
Homework Statement
A boat with initial speed v[o] is launched, and experiences a retarding force of F = -ae^Bv, where a=alpha=constant and b=beta=constant
Find v(t)
Find Time and Distance for the boat to stop
Homework Equations
F=ma
The Attempt at a Solution
the second part for...