Homework Statement
Let p be a prime number. Which of the following series converge p-adically? Justify your answers: (all sums are from n = 0 to infinity)
(i) Ʃp^n
(ii) Ʃp^-n
(iii) Ʃn!
(iv) Ʃ (2n)! / n!
(v) Ʃ (2n)! / (n!)^2
Homework Equations
The definition given for p-adic...
This is my biggest problem, trying to figure out what the hell my lecturer means :S I mean I assume he wants us to find it in cylindrical coords by the diagram & reference to r^2 = x^2 + y^2...
How would I go about working out the Electric Field E(X) in cylindrical coordinates? The question is,
Suppose pho = pho(r) find E^pho. Suggestion to use Greens & Gauss theorem
Think I got it,
c=? q=0.7 s=2 therefore
g/c <=1
0.35c/g <= 1
therefore
g <= c <= g/0.35
we know c = g +10 so g= 10-c & sub in
c-10 <= c <= (c-10)/0.35
so assuming c is positive then
c >= 200/13 so take greatest lower bound = 200/13
however I'm still not sure that c = g+10 rather than...
[PLAIN]http://img96.imageshack.us/img96/7816/12530747.jpg
Hopefully this will post successfully...
Erm its the first part I'm not sure on, after that it's easy. I'm just not understanding the wording.
I need to work out the effective green time during the cycle
F: C(Omega) -> D'(Omega); F(f) = F_f
--
O = Omega
Introduce the notion of convergence on C(Omega) by
f_p -> f as p -> inf in C(O) if f_p(x) -> f(x) for any xEO
Show that then F is a continuous map from C(O) to D'(O)
Hint: Use that if a sequence of continuous functions converges to a...
[PLAIN]http://img820.imageshack.us/img820/5817/img8968h.jpg
Any hints please, just starting question. Haven't really done any questions like this before
Ha ha, yes I see what you mean. Hm that was silly.
As an aside if you were to set phi(x) = phi(0) + xphi'(0) + O(x^2)
What would you do with the phi(0), obviously xphi'(0) gives you your result and all O(x^2) terms (and higher) just = 0 as n-> infinity
Uh for the second one I'm getting -1/2 Phi'(0) not -Phi'(0)
Have they made a mistake? I can't see a problem with my method. It's essentially the same as the first question except you use the fact that
int between 1/n and -1/n of \frac{-3n^3}{2}xPhi(x).dx is equal to
int between 1/n and -1/n...
f(nx) = 3/4(1-(n^2)(x^2)) for -1/n <= x <= 1/n and
f(nx) = 0 for |x| > 1/n
Hence we have the integral between -1/n and 1/n of nf(nx)Phi(x).dx
but the integral between -1/n and 1/n of nf(nx) = 1 so we just have
the integral between -1/n and 1/n of Phi(x).dx
This is where I am so far...