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Oct
22
comment A Problem on Improper Integrals
@ziangchen: No, it was flawed, and now it's corrected. My brain is a little unclear today and I mistakenly thought $h(0)=0$ before. Thank you!
Oct
22
revised A Problem on Improper Integrals
added 54 characters in body
Oct
22
comment A Problem on Improper Integrals
@ParamanandSingh: I wrote my answer in this way because I thought you would prefer a hint rather than a full answer. Is it better if I add all the details to my answer?
Oct
22
comment For a closed plane curve, showing some inequalities.
@JeongNam-ho: You are welcome.
Oct
22
revised A Problem on Improper Integrals
added 150 characters in body
Oct
22
comment For a closed plane curve, showing some inequalities.
@JeongNam-ho: You don't have to hear that. You can prove it by yourself, as I said in the first comment.
Oct
22
answered A Problem on Improper Integrals
Oct
22
comment For a closed plane curve, showing some inequalities.
@JeongNam-ho: Yes, $\langle,\rangle$ denotes inner product. I thought it was a conventional notation, so I didn't mention it. Sorry about the confusion. For the remark, I think it's not very hard to prove, but it need quite a few words to write down all the details.
Oct
22
comment For a closed plane curve, showing some inequalities.
@JeongNam-ho: It's just the linearity of integral. To see this more clearly, you may write write $v=(v_1,v_2)$, $\gamma'(t)=(x'(t),y'(t))$, and evaluate both sides of the equality.
Oct
22
revised For a closed plane curve, showing some inequalities.
added 1495 characters in body
Oct
22
answered For a closed plane curve, showing some inequalities.
Oct
21
comment Computing a limit almost surely using the strong law of large numbers
@Shanks: You are welcome! :)
Oct
21
revised Computing a limit almost surely using the strong law of large numbers
added 17 characters in body
Oct
21
answered Computing a limit almost surely using the strong law of large numbers
Oct
21
revised convergence of total variation measure
added 512 characters in body
Oct
21
answered convergence of total variation measure
Oct
20
comment Could someone explain chirality from a group theory point of view?
You are welcome and thank you for your understanding.
Oct
20
revised Order of Double Coset
deleted 175 characters in body
Oct
20
answered Order of Double Coset
Oct
20
comment Is $x_1^{\alpha_1} + \dotsb + x_n^{\alpha_n}\geq x_1^{h/n}\dotsb x_n^{h/n}$ an example of power means?
Compare $\lambda_1y_1+\cdots+\lambda_ny_n\ge \left(y_1^{\lambda_1}\cdots y_n^{\lambda_n}\right)^r$ with the inequality in my last comment. Then we can find the following correspondence: $\frac{h}{n\alpha_i}\leftrightarrow \lambda_i$ and $x_i^{\alpha_i}\leftrightarrow y_i$.