wonghang
Reputation
559
Top tag
Next privilege 1,000 Rep.
Create new tags
 Nov 14 awarded Popular Question Oct 30 comment How to find $\int_0^1f(x)dx$ if $f(f(x))=1-x$? @G-man yes. agree Oct 30 awarded Enlightened Oct 30 answered $\epsilon - \delta$ definition of a limit? Oct 30 awarded Nice Answer Oct 30 awarded Yearling Oct 30 answered How to find $\int_0^1f(x)dx$ if $f(f(x))=1-x$? Jun 22 comment Decomposing Toeplitz matrix can you try iterative method? I knew there is a book on this topic (but I never read it) epubs.siam.org/doi/book/10.1137/1.9780898718850 Feb 10 answered Markov Chain with heterogeneous transitions Jan 24 comment Building a proper homomorphism between groups. I think you can just simply write $f(x) = f(g^m) = m$ Dec 16 awarded Caucus Dec 9 asked Continued fraction approximation to a function and its derivative Jul 2 awarded Curious May 25 awarded Enthusiast Apr 15 comment Reliability of linear regression to predict future I think popovitsj may want to discuss the concept of consistent estimator and also Gauss-Markov theorem? Apr 8 comment How to show this: $\sum_{k=2}^{n}\frac{\ln{k}}{k^2}\approx \ln{n}\cdot\left(\zeta_{n}{(2)}-\frac{\pi^2}{6}\right)+C$ To relate $\zeta'(x)$ and $\zeta(x)$ and something like $f(b)-f(a)=f'(c)(b-a)$ for some $c \in (a,b)$. Imagine $\ln(n)$ is $f'(c)$, $\zeta_n(2) - \zeta(2)$ is $b-a$. Apr 8 comment How to show this: $\sum_{k=2}^{n}\frac{\ln{k}}{k^2}\approx \ln{n}\cdot\left(\zeta_{n}{(2)}-\frac{\pi^2}{6}\right)+C$ I don't have an answer. Did you try any method related to mean value theorem? The resulting formula looks like it Apr 3 comment Powers of permutation matrices. sorry I misread your question Apr 3 comment Powers of permutation matrices. because all possible permutation is finite, prove it by contradiction. Mar 26 comment Why are we interested in irreducible representation but not faithful representation? Thank you very much for your answer. I have spent many times on finding out in particle physics (self-study and google around, I am not in an university) to try to figure out your example. Basically, the symmetry of nature (in standard model) is $SU(3) \times SU(2) \times U(1)$ somehow describe the nuclear strong force, weak force and electromagnetic force. Then, the irreps of an element of $SU(3) \times SU(2) \times U(1)$ would describe a particle. Why trivial representation is important is that it is used to describe an elementary particle. Did I get it right?