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I hereby authorize whoever it may concern to post my comments as answers if they wish, whether as community wiki or otherwise if you like imaginary internet points.


Sep
25
comment Is it true to say that “it's not logically possible to prove something can't be done”?
Asok may be a graduate from IIT and a brilliant character, but he is written by Scott Adams, who is (arguably) neither.
Sep
24
comment what does full- dimensional means when speaking about covex cones
"Full-dimensional" means something whose dimension is the same as that of the space it is embedded in. This applies not only to cones but to arbitrary regions. For example, in $\mathbb R^3$, a ball is full-dimensional, but a disk lying in the $xy$-plane is not full-dimensional. Do you want a proof that for cones the two definitions in the question are equivalent to this notion?
Sep
24
comment Is there a difference between $a \cdot a^T$ and $a^2$?
I've never seen $a^2$ mean anything when $a$ is a vector... nor $1/y$ for that matter. Where did you encounter this formula?
Sep
19
comment When is 2d sparse numerical integration by Voronoi regions better than using triangular mesh elements
It's not reasonable to assume that. If you ignore the terms that make a difference then of course everything looks the same, but try integrating $f(x)=x^2$ with both methods and see which one gets you closer to the right answer. Given that so far every single one of your comments to me has been incorrect, I wish you would not be so quick to give me the "bad news".
Sep
19
comment When is 2d sparse numerical integration by Voronoi regions better than using triangular mesh elements
I've added a couple of pictures to the answer. I hope they clarify things.
Sep
19
revised When is 2d sparse numerical integration by Voronoi regions better than using triangular mesh elements
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Sep
18
comment Why is a Constant added to front?
You had a constant in $\ln|q|=-t/50+C$. Where did that go?
Sep
18
comment When is 2d sparse numerical integration by Voronoi regions better than using triangular mesh elements
(2) Add another point in the middle of the thin rectangle, with value say $f_0$. Then you get $(f_1+f_2+f_0)/3$ instead of $(f_1+f_2+2f_0)/4$. (1) The weights are continuous for a given topology. When the topology changes, all bets are off. Consider points at $(0,0),(1,0),(0,1),(1+\epsilon,1+\epsilon)$, then move the last one to $(1-\epsilon,1-\epsilon)$.
Sep
18
comment Proving that there always exists two opposite points on a circle where the temperature difference is less than 1
You're almost there. You still have to argue that you can't get from $D>1$ to $D<1$ without passing through a point where $|D|\le1$, which is where you'll use the fact that $D$ changes by at most $2$ at a time.
Sep
18
comment Proving that there always exists two opposite points on a circle where the temperature difference is less than 1
Hint 1: Suppose $D > 1$ at some point $i$. What is $D$ at the opposite point $j=i+n/2\bmod n$? Hint 2: How much can $D$ change between adjacent points $i$ and $i+1$?
Sep
17
comment Imaginary Numbers
Previously: What are imaginary numbers?
Sep
17
revised Traveling salesman problem: a worst case scenario
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Sep
17
comment Traveling salesman problem: a worst case scenario
Sorry, no idea.
Sep
17
answered Traveling salesman problem: a worst case scenario
Sep
17
comment When is 2d sparse numerical integration by Voronoi regions better than using triangular mesh elements
+1 Can you find the slope of the lines in log-log space? That would indicate the order of convergence.
Sep
17
answered How to conceptualize unintuitive topology?
Sep
17
comment Exist a function composed by simple continuous functions that $f:\Bbb R \rightarrow \Bbb N$?
Hey look: $\lfloor x\rfloor = x - \frac12 + \frac1\pi \tan^{-1}(\cot(\pi x))$. Can you find the catch?
Sep
16
revised When is 2d sparse numerical integration by Voronoi regions better than using triangular mesh elements
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Sep
16
answered When is 2d sparse numerical integration by Voronoi regions better than using triangular mesh elements
Sep
16
comment When is 2d sparse numerical integration by Voronoi regions better than using triangular mesh elements
If you put "@Rahul" somewhere in your comment I get notified of your reply. It doesn't matter whether the auxiliary function you've constructed is continuous or not. The final integral you compute is ultimately a linear combination of (a) the areas of the Voronoi regions, or (b) the total area of the adjacent triangles of each sample point. With Voronoi, the areas of the Voronoi regions always change continuously if you move the sample points. But with Delaunay, the mesh topology can change, and in that case the result of the integral will change discontinuously upon moving a point.