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    Rational Dependence

    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...
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    Rational Dependence

    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...
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    Rational Dependence

    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...
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    Variation of simple Lagrangian

    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...
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    Mean value of a harmonic function on a square

    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...
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    Valid Estimation of Square Roots?

    right, just approximating x by floors and ceilings
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    Valid Estimation of Square Roots?

    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...
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    An intuitive explanation to the Killing equation?

    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.
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    Valid Estimation of Square Roots?

    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...
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    Perturbation theory / harmonic oscillator

    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...
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    Boundary Value Problem for the 1-D Wave

    should be moved to homework... sorry!
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    Boundary Value Problem for the 1-D Wave

    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...
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    Help with first integral of PDE

    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...
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    Help with first integral of PDE

    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...
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    PDE: The Eikonal Equation method of characterstics, etc.

    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...
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    Looking for the author of this quote

    Wheeler! Thanks!
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    Looking for the author of this quote

    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...
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    Looking for the author of this quote

    Accidental double post
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    The # of Microstates of a given Macrostate

    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...
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    The # of Microstates of a given Macrostate

    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...
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    The # of Microstates of a given Macrostate

    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...
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    Math in Moscow

    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...
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    Twin Paradox in outgoing frame

    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...
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    Complex Roots

    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?
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    ODE problem

    you are a lifesaver. Thanks a ton.
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    ODE problem

    ahh... thank you very much. Didn't think about the change of base.
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    ODE problem

    [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...
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    Transcendental Retarding Force

    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 =...
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    Transcendental Retarding Force

    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...
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