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15h
revised Finding functional equations that a given function satisfies
added 649 characters in body
1d
comment Rational power Napier number
The six exponentials theorem implies that there are at most two primes $p$ such that $p^e$ is algebraic.
1d
comment Style guide for referring to past work
@D.R. Of course past tense, unless you're psychic ("Roe will prove this in 2018").
1d
comment Average minimum number of random k-sparse vectors in GF(2) to span the whole space?
You might look at this related MO question of mine and its answer by Kevin Costello.
1d
answered Finding functional equations that a given function satisfies
2d
answered Logarithms of matrices in the disk-algebra
Apr
28
comment Banach-Mazur distance between the cube and the octahedron
$n=5$ also seems difficult for the Global Optimization Toolbox.
Apr
28
revised Banach-Mazur distance between the cube and the octahedron
added 22 characters in body
Apr
28
revised Banach-Mazur distance between the cube and the octahedron
added 22 characters in body
Apr
28
answered Banach-Mazur distance between the cube and the octahedron
Apr
28
comment Extremal Lipschitz convex functions
You mean Lipschitz-$1$, i.e. $|f(x) - f(y)| \le \|x-y\|$?
Apr
27
comment Can the matrix exponential be equal to the elementwise exponential
$\pmatrix{\ln(-4/3) & \ln(-2) & \ln(-2)\cr \ln(-2) & \ln(-4/3) & \ln(-2)\cr \ln(-2) & \ln(-2) & \ln(-4/3)}$
Apr
27
comment convergence of ODE
Phase plane analysis.
Apr
25
comment Mathematicians with Aphantasia (Inability to Visualize Things in One's Mind)
I don't think I have aphantasia, but I don't generally produce very detailed and vivid mental images. I think this can be an advantage when dealing with mathematical objects: their geometrical relationships, when they have them, tend to be rather simple, and you don't want to get distracted by unnecessary details. Also, most of mathematics is dealing with objects, e.g. those of more than three dimensions or with nontrivial topology, which nobody can really visualize. It helps to be used to not panicking when something resists visualization.
Apr
25
comment Adapting arguments and plagiarism
Of course it would be better if you could come up with a brilliant new method that blows all these problems away. In the absence of that: most research makes incremental progress by adapting existing tools to a slightly different situation.
Apr
22
answered On number of perfect matchings
Apr
22
comment How to estimate a specific infinite matrix sum
Note that $x^T M x = \|x\|^2$ if $e \cdot x = 0$. Let's say $n$ is even. For any $y \in \mathbb Z^{n/2}$, the vector $x = (y_1,-y_1,y_2,-y_2,\ldots,y_{n/2},-y_{n/2})$ has $x^T M x = \|x\|^2 = 2 \|y\|^2$. Thus for any $k$, $$S_{M,k} \ge \sum_{y \in \mathbb Z^{n/2}} e^{-2 \|y\|^2} = \left(\sum_{y \in \mathbb Z} e^{-2 y^2}\right)^{n/2}$$ which does grow exponentially in $n$.
Apr
21
comment Matrix diagonalization after a completely positive transformation
Of course: from $U$ and $D$ you compute $A$, with that and the $L_j$ you get $\widetilde{A}$, and from that you get (non-uniquely, of course) $\widetilde{D}$ and $\widetilde{U}$. But if you want a much simpler way than that, it's rather unlikely.
Apr
20
revised Spectral radius's relation with row sum
edited body
Apr
20
answered Spectral radius's relation with row sum