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 .