bio  website  math.uvic.ca/faculty/aquas 

location  University of Victoria  
age  47  
visits  member for  4 years, 8 months 
seen  1 hour ago  
stats  profile views  4,033 
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

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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 $2^{\alpha_11}+p_2^{\alpha_2}+\ldots+p_j^{\alpha_j}\le n$ and $g(n)\ge 2^{\alpha_11}\times p_2^{\alpha_2}\times\dots\times p_j^{\alpha_j}=g(n+1)/2$. 
2d

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Bound on $g(n+1)/g(n)$ for Landau's function
How about $g(n+1)\le 2g(n)$ for all $n$. 
Jun 30 
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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 
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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 
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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 
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Messages on rotating wheels
This question is definitely not appropriate for this site. I don't know if you crossposted it (that is a nono), but this site is for research level mathematics questions (which your question is not). 
Jun 25 
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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 
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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 
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Book on the tetrahedron
all you want to know about the tetrahedron <i>but were afraid to ask</i>? 
Jun 17 
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Embedding of planar graphs
intensive purposes $\to$ intents and purposes 
Jun 17 
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MonteCarlo computation of the Smith normal form
Does anyone know whether the limit in the question has been established? This sounds quite approachable. 
Jun 16 
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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 
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How often does a onedimensional lazy random walk end at the origin?
This doesn't really seem like a suitable question here to me. 
Jun 4 
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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 
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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 
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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 $\alpha^{n_in_{i1}}$ converges exponentially to 1. 