john mangual
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 Feb23 answered Show that $\sum_{n=1}^\infty nx^{n-1}$ converges uniformly on $[0,\frac{9}{10}]$ Feb23 comment duality theory question In your first equation, $x^T x = ||x||^2$ the norm of the vector. So you ask for the point of minimum norm across a certain affine subspace. Then you can generalize the point-to-line distance formula. Feb23 answered Proving $\frac{n^n}{e^{n-1}} 2$. Feb21 comment Why is the Derangement Probability so Close to $\frac{1}{e}$? doesn't it seem odd the error is less than $\frac{1}{(n+1)!}$ but $S_n$ has only $n!$ elements? Feb21 answered Why is the Derangement Probability so Close to $\frac{1}{e}$? Feb16 answered Derivation of the Boltzmann factor in statistical mechanics Feb15 revised Finding a value from 5 systems of equations of 5 variables(CHMMC 2014) fixed +/- errors and fixed variable names Feb15 answered Finding a value from 5 systems of equations of 5 variables(CHMMC 2014) Feb12 comment For what values of $x$ will $ax^2+b$ be perfect squares? solve in integers: $ax^2 - y^2 = b$ math.stackexchange.com/questions/8684/… Feb11 comment Variants of the change-of-variables formula amazon.com/Geometric-Integration-Theory-Dover-Mathematics/dp/… Feb8 comment Minimal circle containing set of points @brick it's unique because otherwise you can build a circle containing all the points, smaller than your original two "minimum" circles. Feb8 revised Minimal circle containing set of points added 501 characters in body Feb8 revised Minimal circle containing set of points found an important graphic Feb8 comment Minimal circle containing set of points @brick the convex hull is a more delicate object than a circle, which is why I tried to do without it. My original two-line proof still works. The rest of the discussion is trying to construct the new minimizing circle $C_1$. Feb8 revised Minimal circle containing set of points discussion of convex hulls Feb8 comment Minimal circle containing set of points @brick You are correct, e.g. take $\{ 0, 1 \} \subset \mathbb{C}$ and adjoin the point $p = i$ in the complex plane. The minimal circles cut each other. We can still do induction where $C_1$ must surround $p$ and the convex hull of $x_1, \dots, x_n$. Feb8 revised Minimal circle containing set of points relate to the problem of appolonius Feb8 answered Minimal circle containing set of points Feb6 comment Proving that $\int_{\mathbb{R}} f \ d\mu = \frac{1}{N}\sum_{i=1}^N f(\lambda_i)$ @Integral this seems like making a simple question really complicated. can't you define direc measure this way? $$\int_{\mathbb{R}} f \ d\mu = \frac{1}{N}\sum_{i=1}^N f(\lambda_i)$$ Feb5 revised Are there any differences between tensors and multidimensional arrays? added 741 characters in body