Pietro Majer
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27,768
92/100 score
 7h awarded Popular Question Apr 23 comment Two similar integrals yes, thanks, corrected Apr 23 revised Two similar integrals added 58 characters in body Apr 21 comment Two similar integrals (I assumed that $i$ in front of $y_j$ denotes the imaginary unit) Apr 21 answered Two similar integrals Apr 16 comment Is there a closed form for $\sum_{k=0}^n \frac{x^k}{k!}$? It's a Taylor polynomial of $e^x$, so you can use the integral form of the remainder (this way you just get the answers below) Apr 7 comment Conjecture on matrix with reciprocal principal minors Yes, clear now, thank you Mar 25 comment Two minimization problems using singular value decomposition Note that the matrix $Q$ produced by $q_0$ and $q_1$ can be any square matrix. If det(Q)≤0, then, I think $\max_{A\in SO(n)} tr(A^TQ)$ is equal to $\sigma_1+\sigma_2+⋯+\sigma_{n−1}−\sigma_n$, where $\sigma_1\ge\sigma_2\ge,\dots,\sigma_{n−1}\ge\sigma_n$ are the singular values of $Q$ in decreasing order. Mar 24 revised Two minimization problems using singular value decomposition added 135 characters in body Mar 24 revised Two minimization problems using singular value decomposition added 8 characters in body Mar 24 answered Two minimization problems using singular value decomposition Mar 20 comment Hausdorff dimension and Hausdorff measure Since you only make the requirements for balls centered at the origin, doesn't any smooth spiral of infinite length around the origin answer affirmatively the question? Mar 20 revised Hausdorff dimension and Hausdorff measure typo Mar 15 awarded Nice Answer Mar 5 comment Shape whose translated and scaled copies are closed under intersection (Note that since ∂C is convex, all points but at most countably many are smooth. Also note, the analogous statement and proof hold true in any dimension ) Mar 4 answered Shape whose translated and scaled copies are closed under intersection Feb 28 comment Covering the sphere with sectors (I think all d but the last one should be rotated of 180 degrees to get p ) Feb 22 answered Generalized Jordan theorem and winding number Feb 22 comment Uninteresting questions with interesting answers It's a rather popular quotation. Here it is: I confess that Fermat's Theorem as an isolated proposition has very little interest for me, because I could easily lay down a multitude of such propositions, which one could neither prove nor dispose of. [A reply to Olbers' attempt in 1816 to entice him to work on Fermat's Theorem.] Quoted in J. R. Newman, The World of Mathematics (New York 1956). Feb 21 comment Add a multiple of $I$ to a matrix to minimize its operator norm in the case of A normal, I guess one gets s = the center of the minimum disk containing spec(A), right?