meta user
network profile
| bio | website | |
|---|---|---|
| location | Santa Cruz, CA | |
| age | 27 | |
| visits | member for | 1 year, 1 month |
| seen | May 17 at 22:33 | |
| stats | profile views | 6 |
Ph.D. Student of Computer Engineering at University of California, Santa Cruz.
M.Sc. in Computer Science from University of Calgary.
B.Sc. in Computer Engineering from Sharif University of Technology.
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Jul 18 |
asked | Notation for element-wise division of vectors |
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Jun 22 |
comment |
Segmented area between circles Thanks, @Victor. I do not believe if it is easy at all to formally prove that $A_{22}$ grows with distance to $t$. I think numerical evaluation of the regions (like what you did in your answer) is the best way to approach the problem. Unfortunately, I am not familiar with Mathematica; so, I am trying to implement some code in MATLAB. I will update the post if I come up with more interesting results. |
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Jun 21 |
revised |
Segmented area between circles added 190 characters in body |
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Jun 21 |
revised |
Segmented area between circles deleted 324 characters in body; edited title |
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Jun 21 |
comment |
Segmented area between circles @GerryMyerson: Thanks for your comment. I am not sure though, given that $A_{22} < A_{12}$ when $s_2 \to \infty$, can we claim that $A_{22} < A_{12}$ for any $s_2$ between $s_1$ and $\infty$? |
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Jun 21 |
comment |
Segmented area between circles @HenningMakholm: I think I am not getting you quite clearly. With that new point, say $s_0$, are we getting rid of $A_{01}$? Would that new circle centered at $s_0$ contain only $A_{02}$ with which we compare $A_{12}$ and $A_{22}$? |
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Jun 21 |
comment |
Segmented area between circles @HenningMakholm: I am not concerned with naming. My point is that by moving $s_1$ to the right, you also shrink radius $r$. Note that both circles centered at $s_1$ and $s_2$ have the same radius $r$. What you are trying to do by moving $s_1$ to the right is similar to down scaling the picture and does not change the problem. |
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Jun 21 |
comment |
Segmented area between circles Well, if you want to move $s_1$ anywhere, you are also changing the radius $r$. In other words, the circle centered at $s_1$ must always pass through $t$. This is, in fact, part of the problem definition. |
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Jun 20 |
comment |
Segmented area between circles Thanks for the comment, @HenningMakholm. The fact is that $s_1$ is a fixed point at distance $r$ from $t$ and $s_2$ is the only point that we arbitrarily choose. In other words, we are not allowed to move $s_1$. Regarding your question on the numerical evidence, I should say no. In fact, I do not know any way to numerically evaluate these regions. Whatever I said is just based on my intuition and of course I am not sure of its correctness. |
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Jun 20 |
asked | Segmented area between circles |
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May 18 |
awarded | Supporter |
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Mar 30 |
awarded | Editor |
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Mar 30 |
revised |
A contradiction when calculating the expected value of a discrete random variable deleted 12 characters in body |
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Mar 30 |
awarded | Student |
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Mar 30 |
asked | A contradiction when calculating the expected value of a discrete random variable |
