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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

    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...
  4. Q

    Christoffel symbols

    http://en.wikipedia.org/wiki/Christoffel_symbols#Definition 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...
  5. 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...
  6. 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...
  7. 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.
  8. 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...
  9. 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...
  10. 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...
  11. 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...
  12. 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...
  13. 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...
  14. 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!
  15. Q

    Change to polar help

    http://img187.imageshack.us/my.php?image=polargy3.jpg The Attempt at a Solution http://img484.imageshack.us/my.php?image=picture155jy1.jpg 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...
  16. 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...
  17. 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...
  18. 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...
  19. 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...
  20. Q

    Dielectric sphere - Find the electric field

    Consider a dielectric sphere of radius R and dielectric constant e_r. The sphere contains free charges that have been uniformly distributed with density rho. (a) Show that electric field inside the sphere is given by E = [rho*r /(3*e_0*e_r)]* r hat where r hat is the unit vector pointing...
  21. Q

    Diffraction Grating Grooves

    A reflection grating is required that can resolve wavelengths as close as 0.02A (angstroms) in second order for the spectral region around 350 nm. The grating is to be installed in an instrument where light from the entrance slit is incident normally on the grating. If the manufacturer provides...
  22. Q

    Limit superior/inferior

    Hello, i just started in real analysis not too long ago. In my lecture notes There are 2 properties lim sup (x+y) < & = lim sup x + lim sup y lim sup (xy) < & = lim sup x * lim sup y however there are no proofs for them in my notes. so i was wondering if anyone knew where a proof of these...
  23. Q

    Fraunhofer intensity pattern

    Homework Statement Derive the equation describing the Fraunhofer intensity pattern from a single slit of width b centered at the origin. Then show that the same intensity pattern is obtained for a slit that is not centred at the origin (i.e assume the slit edges are at x = a - b/2 and x = a +...
  24. Q

    Optics hw

    Some homework q's i don't quite understand. Any help is appreciated. A double slit arrangement produces fringes on a distant screen. Using the light from a sodium spectral lamp (lamda = 589 nm) the fringes have an angular separation of 0.015 degrees. a) What is the separation of the slits...
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