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bio website math.uvic.ca/faculty/aquas
location University of Victoria
age 46
visits member for 3 years, 9 months
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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...

7h
comment Aperiodic set of corner Wang Tile
If you believe the answer to your previous question mathoverflow.net/questions/164400/… which you accepted, then an aperiodic edge-type Wang tile translates directly to an aperiodic corner-type Wang tile.
23h
comment Digits <---> Numbers
If you decide to ask on MSE, make sure to explain what you've managed to do already. People there don't like being asked to do your homework unless you explain that you've done something yourself.
2d
comment boundary density of the Von Koch flake
Right. Presumably the $\infty$ is a typo. All points have the same limit in the $\infty$ direction.
Aug
18
comment Integer valued polynomial through some points with rational coordinates
If you're looking for an integer-valued polynomial such that $y_i=P(x_i)$ for each $i$, you should certainly assume the $x_i$ are distinct(!)
Aug
17
comment Linear dependency of real numbers with integer coefficients adding up to zero
Your question is precisely whether the reals $x_2-x_1$,...,$x_n-x_1$ are linearly independent over the rationals.
Aug
12
answered Bounded martingales of infinite path length
Aug
12
awarded  Popular Question
Aug
5
comment Name of a generalized version of semi-continuity
The empty set is open. Do you mean $f^{-1}U$ contains a non-empty open set whenever $U$ is a non-empty open set?
Jul
31
comment Is any particular algebraic number known to have unbounded continued fraction coefficients?
Nice revision @StevenStadnicki! I didn't understand at all what the original question was asking.
Jul
30
comment Prove that …, f(x-2), f(x-1), f(x), f(x+1), f(x+2),… is algebraically linearly independent without the Fourier transform
Instead of changing the norm, I think it's probably nicer to say you know the space of translates is finite-dimensional, so pick a (finite) orthogonal basis. By the condition in this answer, the inner product with any basis element goes to 0. Hence the strong norm (of $f(x-k)$) goes to 0 as $k\to\infty$.
Jul
28
comment Double Markovity
Do you mean that you have three random variables $X$,$Y$ and $W$ all defined on the same probability space, such that $\mathbb P(Y=y|X=x,W=w)=\mathbb P(Y=y|W=w)$ and $\mathbb P(W=w|X=x,Y=y)=\mathbb P(W=w|Y=y)$?
Jul
26
comment Pairwise dependent random walk recurrent
Your summands have the property of 1-dependence: if $|i-j|>1$, then $X_i$ and $X_j$ are independent. There are CLT for 1-dependent random variables. The events that $\limsup S_n=\infty$ and $\liminf S_n=-\infty$ are tail events, and therefore have probability 0 or 1 by Kolmogorov's 0-1 law. It's not hard to see the probability is not 0.
Jul
25
comment The lonely molecule
If they're randomly placed, then they will almost surely cluster somewhere sooner or later. It's easiest to work on the torus, but completely equivalent because you can unfold $2^d$ copies of the cube to make 1 copy of the torus.
Jul
19
comment A non-standard ergodic limit
I don't think it's right that the answer is yes for an irrational rotation and the function $f$ is taken to be $L^1$. There is a theorem called the transference principle (I think of it as a photocopying machine) allowing you to transfer a counterexample that diverges for one measure-preserving transformation to any other aperiodic measure-preserving transformation.
Jul
17
comment Lebesgue measure of a set of irrational numbers
I don't think @EmilJeřábek is right here. The fact that the geometric mean of the $a_i$'s is something doesn't tell you how big the largest one is.
Jul
8
comment Volume of normal cone of a simplex (at a vertex)
Right. The cones $C_j=\{y\colon y_j=max_{i=1}^n y_i\}$ have the same volume: the orthogonal transformation that simply rotates the string of coordinates by one place: $(y_1,\ldots,y_n)\mapsto (y_n,y_1,\ldots,y_{n-1})$ maps $C_j$ to $C_{j+1}$.
Jul
8
comment Is the universal constant in Caccioppoli's inequality one?
Why is $|\nabla(u\chi)|\le |u||\nabla\chi|$?
Jul
7
awarded  Nice Answer
Jul
7
revised Volume of normal cone of a simplex (at a vertex)
added 4 characters in body
Jul
7
comment Base change for $\sqrt{2}.$
Algebraic irrationality "is independent of" base expansions; there are countably many algebraic irrationals; Therefore "with probability 1", all algebraic irrationals are normal to all bases.