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  1. Q

    Finding this distribution

    Homework Statement Let X1, X2, ..., Xn be iid random variables with continuous CDF FX and suppose the common mean is E(Xi) = μ. Define random variables Y1, Y2, ..., Yn by Yi = 1 if Xi > μ; 0 if Xi ≤ μ. Find the distribution of ∑ni=1Yi. I'm having a hard time figuring out how to begin to find...
  2. Q

    Parallelised ODE solver

    I wish to solve the following DE numerically on the interval t:[0,a] using parallel processors. Given y'(t)=f(t,y) and y(0)=y0. One way to parallelise the DE is to split the interval [0,a] into n subintervals [ak/n, a(k+1)/n] where k = {0,1,...,n-1}. Problem: I need to know the initial...
  3. Q

    4 coupled ode

    thanks, problem solved
  4. Q

    4 coupled ode

    Hi guys, i have 4-coupled ode's that are giving trouble (1) \frac{dy_1}{dt}=y_2y_3-\mu y_1, \hspace{1cm} \\(2) \frac{dy_2}{dt}=y_1y_4-\mu y_2, \hspace{1cm} \\(3) \frac{dy_3}{dt}=1-y_1y_2, \hspace{1cm} \\(4) \frac{dy_4}{dt}=1-y_1y_2 I need to show that the steady state solutions are y_1=\pm...
  5. Q

    Christoffel symbols

    Thanks, I just did not know it was possible to raise or lower indices for the christoffel symbol. I've figured it out now though
  6. Q

    Christoffel symbols

    I do not understand this "well g_{mk} \Gamma^m_{il}=\Gamma_{kil}" specifically, how you can have a christoffel symbol with 3 lower indices, how does that work? should the 2nd equation not be 0=\frac{\partial{g_il}}{\partial{x^k}}-\Gamma_{lik}-\Gamma_{ilk} instead of...
  7. Q

    Christoffel symbols start with 0=\frac{\partial g_{ik}}{\partial x^l}-g_{mk}\Gamma^m_{il}-g_{im}\Gamma^m_{kl} in wiki it said "By permuting the indices, and resumming, one can solve explicitly for the Christoffel symbols as a function of the metric...
  8. Q

    Divergence of vector/tensor

    Hi guys, trying to solve a problem in MHD, i realised i need to be able to take the divergence of this following integral, but I don't know how to do it. M is a symmetric rank 2 tensor, r is a vector. The integral is as follows \int_{\partial V} (\textbf{r} d \textbf{S} \cdot...
  9. Q

    Christoffel Symbols problem in GR

    Thank you very much Cristo
  10. Q

    Christoffel Symbols problem in GR

    Why is it that when I try to solve it using the Lagrangian, my answer is off by a factor of 2 for the c-symbol \Gamma^0_{10} Lagrange's equation for x^0 time component is -\frac{d}{d\sigma}(\frac{\partial L}{\partial(\frac{\partial x^0}{\partial\sigma})})+\frac{\partial L}{\partial x^0}=0...
  11. Q

    Mathematica help

    Hi, not sure where to put this, so i'll just put it here. i was wondering if there is a way to define functions of this sort in mathematica. For example. f(x)=x if x>0 and f(x)=2x if x<=0. I know you can break it up into 2 functions and go something like g[x_]:=x; h[x_]:=2x; but those...
  12. Q

    Question about laplace

    i'm a little bit confused. if the velocity potential Φ = Φ(x,y,t). and it says Φ satifies laplace's equation. does that mean ∂²Φ/∂x² + ∂²Φ/∂y² = 0 or ∂²Φ/∂x² + ∂²Φ/∂y² + ∂²Φ/∂t² = 0. does the time variable get included?? i'm thinking it isn't but i'm not exactly sure.
  13. Q

    Differential eq (implicit sol)

    Homework Statement i have a differential equation. ∂h/∂t + [g sin a h²/v]∂h/∂x = 0. where h = h(x,t). i need to show by substitution that the (implicit) general solution for h is h = f(x - (g sin a h²t/v)) where f is an arbitrary differential function of a single variable. The Attempt...
  14. Q

    If it takes me 60 seconds to make a cup of tea, and my manager wants

    if it takes me 60 seconds to make a cup of tea, and my manager wants me to make it 25% faster, does that mean i make it in a) 60/1.25 = 48 seconds b) 60*0.75 = 45 seconds some people say a, some people say b. What do you guys think? I think personally think it's a. If someone told you...
  15. Q

    Astro, p-p process

    part c i've got, directly using E = mc² gives 4.3*10^9 kg but i still have trouble with part b :( Luminosity of sun is 3.826*10^26 W which is 3.826*10^26 J/s 6.55 MeV = 1.049 * 10^-12 protons/J .
  16. Q

    Astro, p-p process

    H1 means hydrogen with mass 1, H2 means hydrogen with mass 2 (has a neutron), etc 1) H1 + H1 -> H2 + positron + neutrino + 1.18 Mev (+0.26MeV) 2) H1 + H2 -> He3 + photon + 5.49MeV 3) He3 + He3 -> He4 + 2*H1 + 12.86 MeV (The neutrino produced in 1 for all practical purposes do not...
  17. Q

    E&M toroidal magnets

    help? anybody? please?
  18. Q

    E&M toroidal magnets

    The magnetic field inm the gap of the toroidal permanent magnet is 0.50 T. The length of the magnetic circuit is 20 cm and that of the gap is 1.0 cm. what are the magnitudes of i) B in the material ii) H in the gap iii) H in the material iv) M in the material The Attempt at a Solution...
  19. Q

    E&M capacitors

    thank you for help. i managed to figure it out now with your tip :)
  20. Q

    E&M capacitors

    Two identical, oppositely-charged, conducting plates of area 2.50cm² are separated by a dielectric 1.80 mm thick, with a dielectric constant of 3.60. The resultant electric field in the dielectric is 1.2*10^6 V/m. a)Compute the charge per unit area on the conducting plate. b)Compute the...
  21. Q

    Astro, flux & energy

    oh!! Thank you (yeh i think i typed something wrong in the calculator before).
  22. Q

    Astro, flux & energy

    The neutrino flux from supernova 1987A was estimated to be 1.3e14 m^-2 at the Earth. SN 1987A occured in the Large Magellanic cloud, which is located at a distance of 50 kpc. If the average energy per neutrino was 4.2 MeV, estimate the amount of energy released in the form of neutrinos during...
  23. Q

    E&M - flux encircled by orbit of particles is conserved

    Prove that in a magnetic mirror the flux encircled by the orbit of the particles is conserved when the magnetic field varies. How do you do this? i have no idea how to approach/start this!
  24. Q

    Change to polar help

    oops, i meant to write dw1 = cos thi dw. nevermind, i got it. I have to use Jacobian matrix instead of what i did.
  25. Q

    Change to polar help The Attempt at a Solution i get an extra cos² thi term!! WHY!! am i doing the substitution completely wrong?? or i forgot/left something out which i can not seem to see...
  26. Q

    Laplace equation separation of variables

    u(r, θ) satisfies Laplace's equation inside a 90º sector of a circular annulus with a < r < b ; 0 < θ < π/2 . Use separation of variables to find the solution that satisfies the boundary conditions u(r, 0) = 0 u(r, π/2) = f(r) ; a < r < b u(a, θ) = 0 u(b, θ) = 0 ; 0 < θ < π/2 Consider all...
  27. Q

    Pde involving airy function

    pde involving airy function!! If u(x,t) satisfies ∂u/∂t + ∂³u/∂x³ = 0, with u(x,0) = f(x), and u, ∂u/∂x, ∂²u/∂x² -> 0 as |x| -> ∞, use Fourier transform methods to show that u(x,t) = (3t)^(-1/3) ∫f(y) Ai[(x-y)/((3t)^(-1/3))] dy (integral from -∞ to ∞), where Ai(x) is the Airy function, for...
  28. Q

    Special Relativity-Lorentz Transformation

    Can you guys please verify/help me with some questions. Consider 2 events, A & B. In frame S they are seperated by Δx and Δt. It is reasonable to say that the events are causally connected if it is possible for a signal (such as a light pulse) to travel between them. We mean that one might...
  29. Q

    Special relativity and rest mass

    What is the rest mass m of a particle traveling with the speed of light in the laboratory frame? i believe m = (E² - (pc)²)^.5 / c² is the correct equation to use? as velocity goes up, so does energy and momentum? so when velocity is at speed of light, E = infinity and momentum = infinity...
  30. Q

    Dielectric sphere - Find the electric field

    well gauss' law is just integral of E.dA = Q/e_0 since we have a sphere the SA is just 4*pi*r^2 so it gives E = Q/[4*pi*e_0*R^2]. How does the density rho and dielectric constant e_r affect/influence this? Thanks everyone for helping.