bio  website  math.uvic.ca/faculty/aquas 

location  University of Victoria  
age  46  
visits  member for  3 years, 11 months 
seen  15 mins ago  
stats  profile views  3,587 
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...
3h

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Parity of primes
I've noticed that most primes seem to start with a 1 in their base 2 expansion. 
3h

answered  Parity of primes 
1d

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What should be considered a finite size of an infinite dimensional space?
@Michael: Even if you want linear maps, this just boils down to the cardinality of the basis of the vector space. The interesting question is if you ask about bounded maps with respect to a norm. Then this is really quite subtle. 
1d

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A calculus question
@Anand: I don't think this is right. There are quite easy upper bounds of $1/(c(\log(1/c))^q)$. On $[e,c^{1/4}]$, you can bound the integrand above by (a multiple of) $r$; on $[c^{1/4},c^{1/2}]$ you can bound above by a const. multiple of $r/(\log(1/c))^q$; on $[c^{1/2},\infty)$, you can bound above by a const multiple of $re^{cr^2}/(\log(1/c))^q$. Then you can integrate all of these. 
1d

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How to prove $\lim _{ \delta\rightarrow {0}^{+}}\int_{a}^{b} F_{\delta}(x)dx=0 ? $
Hello @nobody. Not getting an answer on MSE (in 17hrs) isn't sufficient qualification to put the question on this site. This is not a mathematical research question. Voting to close. 
1d

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The behavior of series involving special subsets of the prime numbers
So the crudest heuristics suggest that this should be finite for all $k$: if each number $n$ is `prime with probability $1/\log n$', then the probability $n$ belongs to $\mathbb P_k$ is around $2k/(\log n)^2$. Hence you should expect $\sum_{p\in\mathbb P_k}1/p\approx \sum_{n>1} 2k/(n(\log n)^2)<\infty$, and expect that this should grow like $k$. More refined heuristics take into account small factors of $n$ etc. I doubt this would change the expected outcome much. 
2d

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Is there effective algorithm for finding “minimal discovery time” for large graphs?
So you're asking about the cover time (or a variant). 
2d

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A proof from Lang's undergraduate analysis
So if $A=(1,1)\setminus\{0\}$, then it's a bounded subset of $\mathbb R^1$ and its boundary consists of $\{1,0,1\}$. On the other hand $\bar A=[1,1]$, so that its boundary consists of $\{\pm1\}$. Hence, as you suspected it's not true in general that $\partial A=\partial\bar A$. Also, as you suggest, I see no place where the supposed equality of these two sets is used. 
Oct 18 
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A calculus question
@Anand: No I mean your expression $c\log(1/c)^qf_q(c)$ converges to something positive as $c\to 0$. 
Oct 18 
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A calculus question
@Anand: I agree. I think I was integrating from 1 to $\infty$. I corrected the answer. 
Oct 18 
revised 
A calculus question
fix math error 
Oct 18 
answered  A calculus question 
Oct 18 
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Fermat's little theorem with smaller powers
This question does not belong on this site. 
Oct 18 
answered  About the regularity of the boundary of a set 
Oct 15 
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How to prove a relation holds almost surely?
Hello. Welcome to MO. Unfortunately this question is much too broad to be useful. Try having a look at the tour for suggestions for how to ask questions. 
Oct 15 
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1 dimensional flows and phase portraits
I flagged it for a moderator for possible transfer (I'm not sure if this the right course of action, but I have no doubt I'll be set right if this isn't the right thing...) 
Oct 15 
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1 dimensional flows and phase portraits
This isn't a suitable question for this site (which is for research mathematics). You might try math.stackexchange.com 
Oct 12 
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Why we mistaken coin toss to be an example of classical probability?
So there's a big difference between tossing a coin and dropping a coin (which is what the cited article is about). I have probably seen 1000 coins tossed in my lifetime, and never seen one land on its edge. If the frequency were anywhere close to that claimed in the posting, many of us would have seen coins land this way. 
Oct 12 
answered  A question regarding Kingman's theorem as described in “Ergodic Theorems” book written by Ulrich Krengel 
Oct 12 
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A question regarding Kingman's theorem as described in “Ergodic Theorems” book written by Ulrich Krengel
I possess a copy of that book, and have read a version of Kingman's theorem, but the manner in which you ask the question does not encourage me to dig them out. You are asking about a single inequality. How hard would it be to define the terms in the inequality? 