Recent content by russel

I tried to prove that P(X(n+1) | X(1),...,X(n))=P(X(n+1) | X(n)) but I can't. Must I use the P(A|B)=P(A,B)/P(B) ? Is it easier to prove that has independent increments and, therefore, it's markovian? The funny part is I found the transition matrix... Could I just say that the probability X(n)...

Hello there, I'm stuck at a problem on markov chains... Could anyone help? Here it is: There are two machines that operate or don't during a day. Let $$X(n)$$ be the number of machines operating during the n-th day. Every machine is independently operating during the n-th day with probability...

What I had in mind was about computation related subjects, like the one you mention about enumerating all proofs. So, it has to do with the "power" of the theory too? Has it to do with noncompleteness too? For example, if you give a theorem to a not finitely axiomatizable theory it may be not...

Hello to everyone, I would like to ask what does it mean that a theory is NOT finitely axiomatizable? What are the pleasant and unpleasant consequences of that?

Hello there, I'd like to ask if the Φ space (the one where each element is a sequence of finite non-zero terms) with norm 1 is isomorphic to Φ space with norm 2. Is it or not? And why? Has this to do with the fact that Φ is never Banach?

The exercise does not refer to a particular space. It is just a normed space X with an uncountable Hamel basis. A solution I came up with was to make a finite dimension closed subspace and show using baire that it is X, leading to a contadiction. If the problem gave us a space for this example...

Hello everyone, I have a problem and cannot solve it. Could you help? Here it is We have a normed space and an uncountable Hamel basis of it. Prove that it is not a Banach space. Should I use Baire theorem? Any suggestions?

referring to the initial problem, could someone thoroughly explain how to prove that this Lie algebra is a semi-simple one?

Oh, I see. So, I'll choose every element and see if this condition is satisfied.

I'll haven't had enough time, so I didn't really managed to solve it. As far as I know, a lie algebra is a semi-simple one if it is a direct sum of simple lie algebras. I will follow this path? Or should I think of a different way to prove it?

I think I got it! Thanks a lot! What about the last equation? How do I prove it?

ok! I fixed it! I didn't know the exact code, sorry!

Hello there! Above is a problem that has to do with Lie Theory. Here it is: The operators P_{i},J,T (i,j=1,2) satisfy the following permutation relations: [J,P_{i}]= \epsilon_{ij}P_{ij},[P_{i},P_{j}]= \epsilon_{ij}T, [J,T]=[P_{i},T]=0 Show that these operators generate a Lie algebra. Is that...