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bio website math.uvic.ca/faculty/aquas
location University of Victoria
age 46
visits member for 4 years
seen 12 mins 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...

4h
comment A game of stones
So isn't it sufficient to prove that you can do this starting from a single stone?
Nov
21
comment Does anyone want to see the critical figure for n= 7?
This is not a site to get your proofs checked. I'd suggest trying to find a professional mathematician who is willing to discuss with you, and either help you present things so that they can be understood by the community; or help you identify possible issues with your claimed solution.
Nov
21
comment The upper and lower bound of the projection of a subshift of finite type
@Nikita: Yes I am sure. Write $f(a_1,\ldots,a_{n-1})$ for the maximum value of $\sum_{k\ge n}x_kq^{-k}$ over all sequences $(x_k)_{k=n}^\infty$ that are compatible with $a_1,\ldots,a_{n-1}$. The maximum occurs somewhere (maybe with ties). Define $G(a_1,\ldots,a_{n-1})$ to be the word $a_2\ldots a_{n-1}x_n$ where $x_n$ is the first letter of one of the infinite words achieving the maximum. The point is that $f(a_1,\ldots,a_{n-1})=x_nq^{-n}+(1/q)f(G(a_1,\ldots,a_{n-1}))$. This makes use of the specific form of the `projection'.
Nov
20
comment Infected square
@NoamD.Elkies: Good comment for the well-informed (or those with access to google like me)
Nov
19
answered The upper and lower bound of the projection of a subshift of finite type
Nov
14
comment Determinant of matrix from set {-1, 1}
@Noam: It seems yesterday's post was deleted. That post asked what's the probability that an 11x11 $\pm 1$ matrix has determinant above 4000. It had an answer from Robert Israel that is very close to the calculation that Neil Strickland re-did today since the previous post was deleted.
Nov
14
comment Infected square
The magic words are bootstrap percolation.
Nov
14
comment Determinant of matrix from set {-1, 1}
This question appears to be off-topic because it is essentially the same as your question from yesterday.
Nov
13
answered $P_{x}(T_{A}<\infty)<P_{x}(T_{B}<\infty)$ imply $Cap_{N}(A)<Cap_{N}(B)$, where $Cap_{N}$ is Newtonian capacity
Nov
9
comment Hausdorff densities
What makes you think the result is true?
Nov
9
comment Hausdorff densities
What if the map is constant?
Nov
8
awarded  Yearling
Nov
6
comment Earth mover/Wasserstein distance between a pdf and an empirical distribution
Looking at the paper you cite, it seems that that paper cites an earlier work for the $W_1$ distance, which I think is the "earth-mover distance": [11] V. Dobri and J. Yukich. Asymptotics for transportation cost in high dimensions. Journal of Theoretical Probability, 8:97-118, 1995.
Nov
5
comment How to solve a couple of ODEs
For english speakers EDP = PDE
Nov
5
revised Degree of polynomial approximating characeristic function of finte set
added 1 character in body
Nov
5
answered Degree of polynomial approximating characeristic function of finte set
Nov
5
comment Degree of polynomial approximating characeristic function of finte set
Why not do it one point at a time?
Nov
2
revised Lower regularity version of Moser's theorem on volume elements
added 3 characters in body
Nov
2
comment Lower regularity version of Moser's theorem on volume elements
Thanks again @alvarezpaiva: I have just had a brief look at the paper, but this seems as though it will answer my question (when I understand the paper). If you make this an answer, I can accept it.
Nov
1
comment Decomposition of non-singular matrix
Do you have a reason to think this is true? Have you tried some obvious seeming possible counterexamples such as the identity matrix? Also, are $n_1,n_2,k_1,k_2$ supposed to be given or free?