# Search results

1. ### Calculate Electric Field in Medium

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...
2. ### Electromagnetics Specifically depth problems.

Homework Statement A plane wave of 1 MHz frequency in free space is incident normally on a copper surface [\sigma=5.8*10^7, \mur=1, and \epsilonr=1]. If the magnetic field strength at the surface is 1 mA m-1, find the depth at which it is 2.5% of this value. Calculate the...
3. ### Fredholm Integral Equations

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)...
4. ### Expected Maximum

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))?
5. ### Irreducibility over Integers mod P

Okay. Thanks Dick. Your help is very much appreciated. To everyone else... help with part c?
6. ### Irreducibility over Integers mod P

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!)
7. ### Irreducibility over Integers mod P

Well... 2+3 = 5. So it's a partition of 5...?
8. ### Irreducibility over Integers mod P

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...
9. ### Irreducibility over Integers mod P

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...
10. ### Electric Field

Homework Statement http://img206.imageshack.us/img206/7900/physicsml8.jpg [Broken] 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!
11. ### Number of Non-Isomorphic Abelian Groups

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
12. ### Number of Non-Isomorphic Abelian Groups

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!
13. ### Number of Non-Isomorphic Abelian Groups

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...
14. ### Number of Non-Isomorphic Abelian Groups

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?
15. ### Number of Non-Isomorphic Abelian Groups

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...
16. ### If in Ring, evaluate (a+b)(c+d)

Okay, that makes sense, PingPong! So, technically, the order is different. (a+b)(c+d) => (a+b)c+(a+b)d => ac+bc+ad+bd
17. ### If in Ring, evaluate (a+b)(c+d)

Okay, so I'm going to guess that everyone agrees with me that this is right? It just seems too easy! Oh well, I'll accept it and move on. :-D
18. ### If in Ring, evaluate (a+b)(c+d)

I doubt it simply because I'm in a 4000 level Math course. It can't be this easy an answer.
19. ### If in Ring, evaluate (a+b)(c+d)

Homework Statement If a,b,c,d \in R, evaluate (a+b)(c+d). (R is a ring. Homework Equations The Attempt at a Solution I think that it's simple foiling, but I'm not sure. ac+ad+bc+bd
20. ### Non-Isomorphic Groups of Order 30

That either k is 0 or x is 1 or 0. Since k cannot equal 0 (because it is between 1 and 15 inclusive) that means that x has to be either 0 or 1. And because x^15=1, we know that the only choice is for x to equal 1. So there are 4 nonisomorphic groups of order 30... 1 is abelian, and the other...
21. ### Non-Isomorphic Groups of Order 30

Hey Guys, StatusX-- Thanks for telling me that theorem! I didn't know it (my professor is a teeny bit incompetent...) So, I can use that to prove that because 4*3=12 means C_4xC_3 is isomorphic to C_12? It makes sense. :-D Morphism-- I proved that a group G s.t. o(G)=30 has a normal...
22. ### Non-Isomorphic Groups of Order 30

It would be redudant because... 4=2^2?
23. ### Non-Isomorphic Groups of Order 30

I'm sorry, but I am intensely confused right now. How does nowing that it has normal subgroups of order 3 and 5 help? Thanks for using your time to help me. :-D
24. ### Non-Isomorphic Groups of Order 30

Alright, let's see if I can take a crack at this. :-D C_30 , C_2xC_15 , C_3xC_10, C_5xC_6 So, there are 4? Is that right?
25. ### Non-Isomorphic Groups of Order 30

Homework Statement How many different nonisomorphic groups of order 30 are there? Homework Equations The previous parts of the problem dealt with proving that 3-Sylow and 5-Sylow subgroups of G were normal in G when o(G)=30, though I'm not sure how that relates... The Attempt at a...
26. ### Permutation Representation

Okay, now that it's morning, this makes much more sense. Thanks for the clarification HallsofIvy. I guess now, my only question is, does a 4 element permutation have a 4 element permutation representation or a 4!=24 element permutation? Thank you so much!
27. ### Permutation Representation

Sorry, I think I'm really confused, after reading the post directly before my previous post. I swear I'm trying to understand. Thank you.
28. ### Permutation Representation

Okay, so I only missed one? And we get our 3-cycles through multiplying the 2-cycles? And as far as the cyclic group of order n... How is that specifically different from Sn? Thank you so much for all of your help!
29. ### Permutation Representation

Hmm... I think I kind of understand. Then again, I'm also really tired, so who knows? So, for S3, we'd have (1)(2)(3),(12)(3),(13)(2),(1)(23),(123) ? Or am I totally off?
30. ### Permutation Representation

Homework Statement a. Find the permutation representation of a cyclic group of order n. b. Let G be the group S3. Find the permutation representation of S3. Homework Equations n/a The Attempt at a Solution I unfortunately have not been able to come up with a solution. I really...
31. ### Expressing as Product of Disjoint Cycles

Sorry. I looked at it again. Here's my second attempt at a solution: a. (1,4,5,6,7,8,9,2,3) b. (1,3,2)
32. ### Expressing as Product of Disjoint Cycles

Homework Statement Express as the product of disjoint cycles: a. (1,2,3)(4,5)(1,6,7,8,9)(1,5) b. (1,2)(1,2,3)(1,2) The Attempt at a Solution a. (1, 2, 3) ( 4, 5, 6, 7, 8, 9) b. (1, 2, 3) These are the answers I got directly through the product. Would anybody be willing to check...
33. ### Compactness Proof w/o Heine-Borel

I think that that comment right there might have helped. :-D Because F \subseteq K, the open covers of K also cover F. Let's take a look at the covers of F that do not also cover K. One such cover is the complement of F within K, which can be written as K\F. This is open because it is the...
34. ### Compactness Proof w/o Heine-Borel

"However, remember that you need to find a subset of the O's alone that covers F, ie, you can't use any of the P's to cover part of F. One way to guarantee you won't need any P's to cover F is to pick each P to lie outside of F. Hint: you'll only need one P, and constructing it will use the fact...
35. ### Compactness Proof w/o Heine-Borel

So, you're saying that I need to pay attention to the open covers that are not open covers of K, even though they're open covers of F, because they are contained in K? That makes sense, I'm just not sure how to approach that case. Maybe... Because F is closed, for every open cover, there must...
36. ### Compactness Proof w/o Heine-Borel

Homework Statement Prove directly (i.e., without using the Heine-Borel theorem) that if K \subseteq Rd is compact and F \subseteqK is closed, then F is compact. Homework Equations Definition of a Compact Set: A set K is said to be compact if, whenever it is contained in the union of a...