# theory

1. ### Computing complexity in graph theory

Let P denote the graph with V(P) = {2 sets of [5]} and vertices adjacent if and only if they are disjoint (as sets). The complexity of a labeled graph is the number of spanning trees contained in the graph. Let t(G) denote the complexity of graph G. 1. Please compute t(P), the complexity of...
2. ### Graph Theory Optimization Problem

Hi everyone, I'm currently working on an algorithm aiming to find the best route between two vertices (the best, not the shortest...(Nod)) My hypothesis : - G a graph - each vertex is graded (a grade out of 10 for example) - the edges are also weighted - we call "mean of a path" the...
3. ### Set Theory

Hello :) When solving some inequalities, I have come to the following results and I was wondering if there is anything else to be done. 1. A \cup (B \cap C^c) and \left( (A^c \cap B^c) \cup (B \cup C) \right) Working with the right hand side and applying De Morgan's law; \left( (A^c \cap...
4. ### Graph Theory: Asteroidal-Triple

Hello there! I'm currently working on Interval Graph Recognition Algorithms and I'm reading on Asteroidal-triple free graph recognition. I'd highly appreciate it if anyone could give me a graph example of an asteroidal triple. Thank you!
5. ### Group Theory Project

My research into String Theory has stalled. I'm stuck at Conformal Field Theory. The problem is that I have taught myself all the advanced Math that I know and I know there are gaps, omissions, and outright errors in my knowledge. What I need is a good tutor for several subjects and I'm not...
6. ### Need help with probability (theory and calculation)

Hi all Greetings. Need help to check & help with the questions below: Gender\Major Accounting Management Economics Total Male 80 120 30 230 Female 50 60 20 130 Total 130 180 50 360 (a) Give an example of a simple event. --- Need help (b) Give an example of a joint event. --- Need...
7. ### Can somebody check my solution: Control Theory with scrap values

Okay, so I have been working on this problem but want to know if I am correct or on the right lines. I set up the Hamiltonian Took the derivatives with respect to u and x but I am a little unsure about what I do after the boundary conditions and if I am correct with what I did with the scrap...
8. ### Automata Theory regular expressions

hello , hopefully i made this post in the right section lol. im trying to brush up on my automata for a test and i ran into something thats confusing me. this question asks Which of the following regular expressions denotes the set of all strings over the alphabet {0,1} that contains at least...
9. ### Group theory: direct products.

Hi: Let G be a p-group, p prime, G= A1 x ..., x Ak, Ai cyclic, H <= G, f: G --> G/H the natural homomorphism, Ai= <x_i>, |<x_i>| = p^{a_i}. If G/H= B1 x ... x Bm, with Bi= <y_i>, |<y_i>| = p^{b_i}, and a_m <= b_k. I say that for all i there exists j such that f(Ai) <= Bj. Is this true, because...
10. ### Help with control theory and general solutions to characteristic eq.

Can somebody explain very basically the general solution to the characteristic equation below. max_u \int (-x - (1/2)u^2)e^{-2t} dt x` = x+u x(0)=1 x(T) free u(t) in +/- infinity I am fine with setting up the Hamiltonian etc but I get lost with the general solutions for the following two...
11. ### Group theory: minimal generating sets.

I want to know: In an finiteAbelian group, is a minimal generating set necessarily an independent set? I have tried to prove it but I have failed. Perhaps if the group is primary (a p-group for some prime p)? More precisely, suppose I have a set that generates G. By removing elements from the...
12. ### Graph Theory

How do I prove that every circulant of girth at least 4 and with degree 4 is non-planar?
13. ### Theory Problem About Integration

I have been given a problem in a series that deals with the underlying ideas behind integration, Riemann sums, et cetera. It reads as follows: If the amount of mayhem is constant in an episode of the Muppet Show, there is a simple formula that gives the amount of mess created: Mess = Mayhem...
14. ### Group Theory

Hi, I'm studying Group Theory, and I've come across this problem. Say I have a subgroup K which is not normal, how do you determine other two subgroups of the general group say L to which the subgroup K is conjugate. Thanks for the help in advance. And i really appreciate this forum. caboampong
15. ### What are the elementary divisors of U(Z/nZ) (group theory)?

Hi: The problem: What are the elementary divisors of U(n), the multiplicative group of all congruence classes [a] mod n with (a,n)=1? Notation: a = b means a equal b or a isomorphic to b depending on context. I find that U(p^m q^n) = U(p^m) x U(q^n), where p,q primes, using the Chinese...
16. ### introduction to set theory

I have some trouble when proving the existence of set. In this particular case, I would like to have some help as to how to prove that Seq(A) exists. Where Seq(A) denotes the set of all finite sequences of elements of A. I am using as textbook "Introduction to set theory" from Hrbacek. I would...
17. ### General question in Fuzzy theory

Hello every body Please let me know , what is Ã , B~ ,.. (fuzzy fuctions)called ? These are called a-tiled , b-tiled ,... ? Thanks
18. ### Number Theory-- Sum of Cubes

Let k be a prime integer such that 100 < k < 225. How many distinct values of k exist such that k = a^{3} + b^{3} where a and b are both positive integers? The answer key says 0 and I suspect this has something to do with k being prime. What's the explanation behind this?
19. ### Mathematical anomaly (group theory).

Let f: G --> G/K, where K normal in G, f the natural homomorphism. Let H in G, K not in H. What is f(H)? Well, f(H)= {f(h): h in H}= {Kh: h in H}= H/K. What is this monster H/K?
20. ### couple questions beginning number theory

A professor at my school directed me to this http://wstein.org/ent/ent.pdf to learn number theory. But I've run into the problem that i haven't learned groups, rings, or fields. Although my teacher said that wasn't too much of a problem. But I just started reading and right now I'm stuck because...