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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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    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

    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

    Accidental double post
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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

    [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

    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...