Mathematics - 2011-12-07 (page 6 of 6)

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Jonas Teuwen

23:01

What?

t.b.

why on earth did that comment get 3 upvotes? am I missing something?

Srivatsan

Oh right. I forgot about there are direct formulae to compute the Fourier series. Now the hilbert-space and linear-algebra tags look quite silly.

Asaf Karagila

Is my comment justified?

J.M. should rejoin very soon, I'd think.

Srivatsan

23:17

@AsafKaragila cstheory is research level, and I am not sure if this question is a research level question. It might be.

t.b.

@Srivatsan I think it's fine. It's linear algebra and hilbert space techniques anyway.

Jonas Teuwen

I need to buy a heating.

Asaf Karagila

@Srivatsan I think you can phrase it in research level.

He's looking for a useful algorithm, one can ask it in a clever way.

Jonas Teuwen

@tb Not sure.

Asaf Karagila

Much like asking about a specific function can be cleverly and nicely asked about a general family of functions instead.

Srivatsan

23:19

@AsafKaragila I don't understand what graphs though. Could be the Hamming graph (connect two sets if their symmetric difference is a singleton set). But that doesn't fit too well either.

Asaf Karagila

@Srivatsan Yeah, and set theory... this question is all about forcing without choice in modal logic, under large cardinal assumptions.

Yes, it has the word "set", it must be [set-theory]. Not even elementary set theory.

t.b.

@JonasTeuwen I guess it's just a reiteration of your comment. But note that $f(x)$ is a common abus de notation for the function $x \mapsto f(x)$.

Jonas Teuwen

Yes, but it is very ugly.

Srivatsan

@AsafKaragila Why did MSE settle on set theory and elementary set theory, rather than advanced set theory and set theory?

Or advanced set theory and elementary set theory?

Asaf Karagila

@Srivatsan I don't know. It was brought on meta several times, though. I do agree with the current status, [set-theory] is what you do when you actually deal with the axioms; the other stuff... equivalence relations and whatnot is all elementary stuff.

Much like [elementary-number-theory] vs. [number-theory]

t.b.

23:26

Maybe this is dumb, but isn't that a variant of the Knapsack problem?

Asaf Karagila

Neat, I got 175 points today. I have 34 minutes to get 25 more :-D

Srivatsan

@AsafKaragila Yes, the current policy is clear. And this question wouldn't fall under set theory, whether or not [elementary-set-theory] fits.

Asaf Karagila

@Srivatsan Quite.

Srivatsan

@tb Variant, yes. But we are now looking at the least k subsets of the original set. Presumbly these near-minimum sets could have greater structure (that is to say, this problem might not be NP-complete).

(where subsets are ordered according to the sum of the elements)

t.b.

@Srivatsan I see. Meanwhile J.M. has posted an answer/comment.

Srivatsan

23:34

My impression is that this problem is quite different from knapsack. Whether it is a standard problem, I have no idea.

@tb With all due respect to JM, that's quite a non-answer. =)

[Of course, I am sure JM intended to post it as a comment; just saying.]

t.b.

Well, I'm sure y'all can resolve that without my participation :)

Srivatsan

Ok, I'm off for dinner. Bye!

t.b.

bye

robjohn

@Jonas: I have some bad news.

Jonas Teuwen

@robjohn Oh?

@robjohn Oh. Thanks 8-).

robjohn

23:47

I don't think it's bounded under the conditions given.

Asaf Karagila

Tick tock, will I break the 200 limit today or not?

Jonas Teuwen

@robjohn And it doesn't help if $t \lesssim \min(1, |y|^{-1})$ right? 8-)?

No it doesn't because that is the same as $t \in (0, T]$.

@robjohn Thanks. I'll adapt my argument then.

robjohn

I could bound the one part, but when I went to bound the second part, the counter-example was pretty clear.

I needed to bound $\left|e^{-t^2}x-y\right|^2$ below, but I couldn't in the second case.

Asaf Karagila

@tb How far are you from Epic?

t.b.

@AsafKaragila No idea

robjohn

23:53

@AsafKaragila I'm lucky to get 50 today :-)

Asaf Karagila

math.stackexchange.com/reputation - check the bottom.

@robjohn Two more votes and I hit 200, four more and I hit the cap.

t.b.

@robjohn that's more than me :) 36 unless some answers happen to be deleted

robjohn

@AsafKaragila :-p

Asaf Karagila

@tb Nice. If I hit the cap today, we can get an Epic badge together... it'll be my 14th ;-)

t.b.

@AsafKaragila oh, that's the amount of rep today :)

Jonas Teuwen

23:55

@robjohn I'm standing in front of the ruins of my world image.

robjohn

@JonasTeuwen Why is that?

Asaf Karagila

Hah. I see. :-P

Jonas Teuwen

@robjohn Because my inequality fails!

robjohn

@JonasTeuwen Is it that critical?

Jonas Teuwen

I don't think so. I have the condition $t \min(|x|, |y|) \leqslant C$. I think I only need the part with the $|x|$ in there. I just wanted to state the result in a more general form which might be useful in the future.

t.b.

23:57

@AsafKaragila I don't understand what you're saying here. Reputation source can be any vote type, upvotes, accepted answers, bounties...any net increase from votes (not association) totaling >= 200.

Asaf Karagila