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12156
bio website math.uvic.ca/faculty/aquas
location University of Victoria
age 47
visits member for 4 years, 8 months
seen 1 hour ago
The pic is the phase portrait of a simple "piecewise isometry". Define a map by sliding the two halves of the plane: the top half to the right; the lower half to the left and then rotate. Around each periodic point of the map there's a "periodic island". These are what are in the image...

2d
comment Bound on $g(n+1)/g(n)$ for Landau's function
What I had in mind is that $g(n)$ is the largest value of $p_1^{\alpha_1}\times\dots \times p_j^{\alpha_j}$ such that $p_1^{\alpha_1}+\ldots+p_j^{\alpha_j}\le n$. For all values of $n$ that are at least 4, this is obtained with one of the $p_j$'s being equal to 2. Now if $g(n+1)=2^{\alpha_1}\times\dots \times p_j^{\alpha_j}$ with $2^{\alpha_1}+\ldots+p_j^{\alpha_j}\le n+1$, then $2^{\alpha_1-1}+p_2^{\alpha_2}+\ldots+p_j^{\alpha_j}\le n$ and $g(n)\ge 2^{\alpha_1-1}\times p_2^{\alpha_2}\times\dots\times p_j^{\alpha_j}=g(n+1)/2$.
2d
comment Bound on $g(n+1)/g(n)$ for Landau's function
How about $g(n+1)\le 2g(n)$ for all $n$.
Jun
30
comment What conditions imply that a function over $\mathbb{Z}$ is a polynomial?
If you differentiate it finitely many times and get 0 everywhere, maybe?
Jun
30
comment Generate Bernoulli vector with given covariance matrix
Does specifying the covariance matrix of Bernoulli random vectors fully specify the distribution?
Jun
29
awarded  Nice Answer
Jun
28
answered How to write an abstract for a math paper?
Jun
27
comment A Paradox by a Variant of Von Neumann's coin toss
Ummm... what if you never stop? <i>Gambler's Ruin</i>
Jun
26
revised continuity of the Boltzmann entropy in the Wasserstein metric
fix intervals so they are not adjacent
Jun
26
answered continuity of the Boltzmann entropy in the Wasserstein metric
Jun
25
comment Messages on rotating wheels
This question is definitely not appropriate for this site. I don't know if you cross-posted it (that is a no-no), but this site is for research level mathematics questions (which your question is not).
Jun
25
comment How to prove that this equation has only one solution?
Georges Rhin has a paper where he computes an explicit irrationality measure for $\log 2/\log 3$. He shows that $|a\log 2+b\log 3+c|\le \max(|a|,|b|,|c|)^{-13.3}$. That should make a very small search indeed.
Jun
24
comment A probability distribution in n dimensional space which its projection on any line is a uniform distribution?
If your initial distribution is a uniform distribution along a line $L_0$, then the projection on any line which is not orthogonal to $L_0$ is uniform on a subinterval of that line.
Jun
18
comment Book on the tetrahedron
all you want to know about the tetrahedron <i>but were afraid to ask</i>?
Jun
17
comment Embedding of planar graphs
intensive purposes $\to$ intents and purposes
Jun
17
comment Monte-Carlo computation of the Smith normal form
Does anyone know whether the limit in the question has been established? This sounds quite approachable.
Jun
16
comment Style of mathematical writing vs. too many lemmas
One thing that I like to do is have lemmas that can be described by a short phrase ("measurability of complementary spaces" etc). I think this helps the reader grasp the structure of the paper. Probably this is more utilitarian than artistic, but still...
Jun
16
comment How often does a one-dimensional lazy random walk end at the origin?
This doesn't really seem like a suitable question here to me.
Jun
4
comment Suprema of lower density of sums and products of sets with lower density 0
The first one is certainly 1. For a trivial construction, let $n_1\ll n_2\ll n_3\ll\ldots$. Then if $A=[n_1,n_2]\cup [n_3,n_4]\cup [n_5,n_6]$ while $B=\{0\}\cup [n_2,n_3]\cup [n_4,n_5]\cup\ldots$, their union is everything, but both have lower density 0.
Jun
2
comment Where can I find a proof of this result on optimal tessellation of a unit square?
That's the way I read it too... Presumably the hexagonal tiling is the unique limit of optimal tilings, but this would likely be considerably harder to prove.
May
31
comment Rate of convergence of an algebraic irrational rotation
You can reduce the case of different $\xi$ to the case $\xi=1$. If $\alpha^{n_i}$ converges exponentially to $\xi$, then $\alpha^{n_i-n_{i-1}}$ converges exponentially to 1.