Stephen Montgomery-Smith
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 Apr19 awarded Informed Apr14 comment Is there a relationship between trigonometric functions and their “co” functions? Follow up question? How do they decide which is the original function and which is the co-function? My theory is that the original function (sin, tan, sec) is increasing on $[0,\pi/2)$. Otherwise, why is secant the reciprocal of cosine? Apr9 comment Prove or disprove a claim related to $L^p$ space I am really busy for the next few days, so I won't be adding much detail for a while. I do want to provide more details for why $f$ is in the Morrey space. I also got caught on the fussy details several times when I tried to make this work. I think sleeping on it was what helped the most. I find my mind does a lot of unconscious thinking while I sleep or daydream. Apr9 comment Prove or disprove a claim related to $L^p$ space The proof that $\int_a^b f(x) \, dx \le \sqrt{b-a}$ has quite a few details which I omitted, because I am rushed for time right now. Also thinking about it, I might have to change it to $\int_a^b f(x) \, dx \le 3\sqrt{b-a}$. Apr9 revised Prove or disprove a claim related to $L^p$ space Corrected upper bound for E_N Apr9 answered Prove or disprove a claim related to $L^p$ space Apr8 comment Prove or disprove a claim related to $L^p$ space This is a really fascinating problem. I am sure the conjecture is false, but I am struggling to find the counterexample. Mar16 comment $X = ABA^T$, $X$ is PSD and $B$ is Symmetric. Does $B$ have to be PSD to satisfy this equation? Take $B$ to be any symmetric matrix, some of whose eigenvalues are positive, and some of whose eigenvalues are negative. Let $A$ be the orthogonal projection onto the space spanned by eigenvectors corresponding to eigenvalues that are positive. So, for example, start with $B = \begin{bmatrix} 1 & 2 \\ 2 & 1 \end{bmatrix}$. Then $A = 2^{-1/2} \begin{bmatrix} 1 & -1\\-1 & 1\end{bmatrix}$ will work (and you don't need the $2^{-1/2}$ - that's just to make it a projection). Mar16 comment $X = ABA^T$, $X$ is PSD and $B$ is Symmetric. Does $B$ have to be PSD to satisfy this equation? So suppose $B = \begin{bmatrix} 1 & 0 \\ 0 & -1\end{bmatrix}$ and $A = \begin{bmatrix} 1 & 0 \\ 0 & 0\end{bmatrix}$? Mar15 comment $X = ABA^T$, $X$ is PSD and $B$ is Symmetric. Does $B$ have to be PSD to satisfy this equation? Does PSD mean positive semi-definite? If so, consider the case when $A = 0$. Mar15 comment Covariance and correlation of summations of independent random variables Looks OK to me. Or you could say that Y and W are independent. Mar14 comment Is monotony preserved under expectation? Yes, except you got the inequality the wrong way around. Mar14 comment Is the Gamma Function multivalued?? If you look at, for example, en.wikipedia.org/wiki/Gamma_function, you will see that the Gamma function can be extended to the complex plane without any branch cuts. The only difficulty will be with poles which are at the non-positive integers. Mar14 revised Bound on Kirchoff's formula for wave equation Added some absolute values. Mar14 comment vorticity flux conservation for NS equation in 2D I think that should work. Except if $w$ only decays like $|x|^{-2}$, I don't see how you can be sure that $\int_{\mathbb R^2} w(x,t) \, dx$ is well defined. Mar14 comment vorticity flux conservation for NS equation in 2D Something like that. I didn't think you were trying to be rigorous. It could be made rigorous, but then you need to state more hypotheses, and you need to quote (or prove) results about how solutions to the 2D N-S behaves. Mar14 comment Error in script for estimating $\pi$ Write a simple program to compute $\sum_{k=1}^3 k$. Then go step by step through the program to predict what the computer will do. Then it should become clear to you. Mar14 comment Error in script for estimating $\pi$ This is your error: initialize with sum = 0. Mar13 comment Bound on Kirchoff's formula for wave equation math.stackexchange.com/questions/291877/… Mar13 comment chain rule for derivations Have you considered a special case, like $a(x) = x^n$? Leibnitz' rule should give something.