bio  website  math.uvic.ca/faculty/aquas 

location  University of Victoria  
age  47  
visits  member for  4 years, 9 months 
seen  9 mins ago  
stats  profile views  4,141 
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...
1h

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A Linear Order from AP Calculus
A side comment: The class $\Theta$ is a very small subclass of the logarithmicoexponential functions studied by Hardy (see also Boshernitzan's work). These have very nice properties including no oscillation: for any two distinct functions in a Hardy Field, eventually $f$ is bigger than $g$ or vice versa. 
4h

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“Edge Density” of Infinite Planar Graphs
My reading was that the vertices of $G$ were not labelled, but that the vertices of the subgraphs were labelled (so that if $G$ is an infinite path, for example, then there are $n!/2$ subgraphs of size $n$). 
12h

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convex hull of the set of permutations with one cycle
I don't think so. For example if the permutation is a transposition, then there are 2 columns and rows with weight 1/2 and the rest with weight 0. 
13h

revised 
convex hull of the set of permutations with one cycle
added 9 characters in body 
13h

answered  convex hull of the set of permutations with one cycle 
14h

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convex hull of the set of permutations with one cycle
another comment: the $i$th row and the $i$th column have the same sum for each $i$. 
14h

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convex hull of the set of permutations with one cycle
So the matrix with a single 1 somewhere is not in the convex hull. Also the convex hull gives weight 0 to the diagonal, so the convex hull is certainly more complicated than you think. 
21h

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Coupling Marginals of Distributions on the Sphere
You shouldn't expect to be able to do this for atomic distributions. If you had a distribution supported on values whose squares never sum to $n$, you would have a counterexample. The same would be true if the distribution is `almost atomic' (e.g. 99.99% of the mass is within $10^{100}$ of a collection of values with the above property. 
1d

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Permutations of given length
You're asking to express $n$ as $m_1+\ldots+m_k$ with $m_i\le M_i$ 
1d

answered  $\langle X\rangle_t = t$ 
1d

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2dimensional sublattices with all vectors having very big square (in absolute value)
Presumably you want your lattice not to be a multiple of any other lattice? 
2d

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A finite field $0$free restrictive sumset problem
You need $d$ large enough that $(\log m)^d\ge m$. Otherwise any set will contain a set of at most $m$ linearly dependent elements. The form of the dependence (since the base field is $\mathbb F_2$) is exactly $\sum_{v\in S}v=0$. 
Aug
24 
answered  Rajchman measures via strong mixing systems 
Aug
22 
answered  Is there a version of the Titchmarsh Convolution theorem to find singular support? 
Aug
21 
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Counting the size of the largest sets of independent strings
Here's an idea for dealing with strings that are not outrageously sparse: take a string, split it up into blocks of length $n/10$, say. For each block, store $\lfloor 10\log_2$(weight)$\rfloor$. If two strings have the same weight vector (and are not ridiculously sparse), then they match. Since there are only $(\log n)^{20}$ weight vectors, this should give a good bound on nonsparse independent sets... 
Aug
20 
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A regular variation in infinite ergodic theory
Then taking $A=B=E$ would make this not make sense. 
Aug
20 
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Identities and inequalities in analysis and probability
I think this concern is probably too broad to be useful. Maybe I'll wait a while before voting in case people come up with really inspiring answers proving me wrong. At the very least, this should be community wiki. 
Aug
20 
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A regular variation in infinite ergodic theory
Probably not very interesting as this would say that if $A$ and $B$ don't intersect initially, they never will. (The identity transformation has this property, but not much else). 
Aug
20 
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Algebraically independent matrix invariants
If you've edited the question and made a substantial change, you should indicate in the question what the edits are so that the comments still make sense. 
Aug
20 
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Inequality for a gradient of a function in Holder space
Surely this is dimensionaly hopeless: if you halve X, the left side doubles, whereas the right side decreases by a factor of $2^{2N1}$. 