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...
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...
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...
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...
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...
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...
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...
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...
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.
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...
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...
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 .
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...
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...
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...
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...
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!
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...
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...
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...
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...
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...
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.