Hello.
I have this function ## v(x) = -\sum_{i=1} x^i \sqrt{2}^{i-2} \int_{-\infty}^{\infty} m^{i-1} \cosh(m)^{-4} dm## which I can not seem to figure out how to simplify.I tried looking at some partial integration but repeated integration of ## \cosh ## gives polylogarithms which seemed to...
I can not see why this changes a whole lot. I just assumed some distribution of when a sensor will fail.
What sort of distribution will they follow since it is not Gaussian( ignoring the fact that it extends to ##-\infty##)? You obviously know a lot more about it than me, so please enlighten...
Sorry for the late reply. I have been traveling.
Ahh of cause I get it now. Thanks for the help!
What they give is a number of how long they say the sensor should at least work( for example 2000 hours.). If the sensor company does not want to many RMA's this number will be some low quantile...
Thank you both for your answers. A few comments.
Yes t is the same for all sensors. It is time since installation. I do not understand why the distribution of failed sensors will be binomial and do you mean the distribution of the amount of sensors failed at a given time? Can you elaborate?
It...
(Sorry for the terrible title. If anybody have a better idea, post and I will edit. Also I have no idea of the level so now I just put undergraduate since the problem is fairly easy to state.)
Suppose I buy ## N## sensors which the manufacturer tells me will fail at some point and the failure...
If your equation is given by ( please please please learn to tex )
$$ \frac{r^2}{f(r)} \frac{d^2 f(r)}{dr^2} + \frac{2mr^2}{h^2}\left(E + \frac{zt^2}{kr}\right) -a^2 = 0 $$
Then you can rewrite to
$$ \left( \frac{d^2}{dr^2} + \frac{2mE}{h^2} + \frac{2mzt^2}{h^2 kr} - \frac{a^2}{r^2} \right)...
It is in order to fulfill the boundary conditions. Using this trick the slope "out" of the lattice becomes zero.
Other methods of solution could be using Chebyshev polynomials.
Is p_{i,j} the fourier transform? You should take care that the method does not produce some unwanted complex phase which might ruin the solution.
The kx=0 entry is the mean value for that "row" so you can not just set it equal to zero. I would imagine it depends a bit on your RHS how to best...
Why would you think there is a problem with non-linear terms? I really can not see how this should pose a problem as long as he uses some explicit time integration scheme ( and even if he used an implicit I can not see why the difficulties would even be related to the finite difference method ).
I used a simple 5 or 9 point finite difference stensil.
You result in #28 is to be expected since you are differentiating a function given by ## f(x,y) = e^{-(x^2 + y^2)} + 1 ##, in the interior and ## f(x,u) = 0 ## on the boundary. That will generate problems. This however, is not the...