Hello all! I'm studying for my final, and I'm trying to figure out my teacher's method for the following problem. Could you help me out?
A plane wave is propagating in free space with a frequency of 10 GHz. The amplitude of the electric field in the x-direction is Ex = 2 V m-1.
(ii) Find...
Hello All!
I am currently in an Applied Analysis class, and I'm trying to do a little research outside of the classroom to try and understand what my teacher is trying to say.
So, I'm supposed to understand how to solve Fredholm Integral Equations (inhomogeneous and of the second kind)...
I swear that I used to know this.
If you have an independent sample of size n, from the uniform distribution (interval [0,\theta]), how do you find the Expected Value of the largest observation(X(n))?
Okay. I think I understand that now.
(i.e. x^3-9 is irreducible over integers mod 31 cause no x makes x^3=9mod31 true. But It is reducible over integers mod 11... (x-4)(x^2+4x+5).)
But how do I prove part c? (Sorry I'm asking so many questions. I appreciate the help!)
I don't know. I don't know how to prove that they're irreducible, really. I'm just following what somebody said about it being sufficient to show that it has no zeros...
Homework Statement
a. Prove that x^2+1 is irreducible over the field F of integers mod 11.
b. Prove that x^2+x+4 is irreducible over the field F of integers mod 11.
c. Prove that F[x]/(x^2+1) and F[x]/(x^2+x+4) are isomorphic.
Homework Equations
A polynomial p(x) in F[x] is said to...
Homework Statement
http://img206.imageshack.us/img206/7900/physicsml8.jpg
Note: Acceleration=1e18 m/s^2
The Attempt at a Solution
I've tried to do the ones marked with a red x, but I'm really not sure how... any hints would be greatly appreciated!
Good Morning, Morphism!
I'm looking at this last post, and I'm still a bit confused (forgive me). How did you decide that for Z_3 x Z_3 we were using lcm{2,3}?
Thank you so much for your time and patience. :-D
Thanks for the luck! I'm probably going to need it.
Is there a simple way to test whether or not something has an element of a certain order (i.e. Z_3 x Z_3 not having an element of order 9)? I want to make sure I understand this fully before morning.
Thanks again!
Okay. Thanks so much! I was trying to make it more complicated than it needed to be, I think. :-D
This is a side question that kind of pertains to this. Why is Z_3 x Z_3 not isomorphic to Z_9?
Thanks again for your help, Morphism! You're a lifesaver! (I have a test in less than 10...
The fundamental theorem of finite abelian groups states that every finite abelian group can be expressed as the direct sum of cyclic subgroups of prime-power order.
Z_2 x Z_2 x Z_2 x Z_3 x Z_3
Z_2 x Z_2 x Z_2 x Z_9
Z_2 x Z_4 x Z_3 x Z_3
Z_2 x Z_4 x Z_9
Z_8 x Z_3 x Z_3
Z_8 x Z_9
Yes?
Homework Statement
Determine the number of non-isomorphic abelian groups of order
72, and list one group from each isomorphism class.
The Attempt at a Solution
72 = 2^3*3^2
3= 1+1+1= 2+1= 3 (3)
2= 1+1= 2 (2)
3*2 = 6
And then I get lost on the...