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-   -   Question 20 (http://book.caltech.edu/bookforum/showthread.php?t=1464)

victe 09-09-2012 05:01 PM

Question 20
 
I think there is two possible true answers to this question.

yaser 09-09-2012 09:43 PM

Re: Question 11
 
Quote:

Originally Posted by victe (Post 5070)
I think there is two possible true answers to this question.

Could you pmail me why you think so?

the cyclist 09-10-2012 09:32 AM

Re: Question 11
 
Quote:

Originally Posted by victe (Post 5070)
I think there is two possible true answers to this question.

Hm. I don't think so. I can say the following without giving away too much info:

Out of the first four statements, I am sure three of them are false, because I can create simple counterexamples for them. For the remaining statement, I am not sure yet. (I am neither sure it is true, nor do I have a counterexample.)

So, I have narrowed it down to that one statement or "none of the above". Regardless, I am very confident that there are not two true statements in the list.

TonySuarez 09-10-2012 09:38 AM

Re: Question 11
 
:D

Couldn't resist (but in the end perhaps I'll have to swallow...)

feallertmalty 09-10-2012 09:47 AM

Re: Question 11
 
Quote:

Couldn't resist (but in the end perhaps I'll have to swallow...)
You narrated . On no other word

victe 09-12-2012 06:20 AM

Re: Question 11
 
Quote:

Originally Posted by TonySuarez (Post 5091)
:D

Couldn't resist (but in the end perhaps I'll have to swallow...)

In the end I was wrong.
I derived mathematically the true solution, and there is only one correct answer. Only, the statement should indicate some property on the functions to be met, but with the roles that are often used is understood.
Indeed, there are very simple counterexamples for all incorrect answers.

TonySuarez 09-14-2012 11:05 AM

Re: Question 11
 
Quote:

Originally Posted by TonySuarez (Post 5091)
:D

Couldn't resist (but in the end perhaps I'll have to swallow...)

I just jumped in, and delivered the final.
Worst than I expected :-(, lowered my percentile somewhat... but that's life...

So, in the end I had to swallow Q11, FYI :-(

fgpancorbo 09-14-2012 08:25 PM

Re: Question 11
 
Quote:

Originally Posted by the cyclist (Post 5090)
Hm. I don't think so. I can say the following without giving away too much info:

Out of the first four statements, I am sure three of them are false, because I can create simple counterexamples for them. For the remaining statement, I am not sure yet. (I am neither sure it is true, nor do I have a counterexample.)

So, I have narrowed it down to that one statement or "none of the above". Regardless, I am very confident that there are not two true statements in the list.

I find myself in a similar situation! I spent a couple of hours trying to come up with the counter example to no avail. I then went analytical and I see no easy way to prove it. Still 4 days, so there is time for inspiration :D.

yaser 09-14-2012 09:42 PM

Re: Question 11
 
Quote:

Originally Posted by fgpancorbo (Post 5292)
I find myself in a similar situation! I spent a couple of hours trying to come up with the counter example to no avail. I then went analytical and I see no easy way to prove it. Still 4 days, so there is time for inspiration :D.

Hint (from Mr. Hints himself :)): Cauchy.

I hope this helps more than it confuses.

fgpancorbo 09-14-2012 10:01 PM

Re: Question 11
 
Quote:

Originally Posted by yaser (Post 5295)
Hint (from Mr. Hints himself :)): Cauchy.

I hope this helps more than it confuses.

:D, sure, Cauchy like in "Cauchy-Schwarz"? I don't want to sound cocky but I thought about bringing that ammunition myself except that I was unable to identify the inner product but now that I think about it... there is that cross term that looks very much like one... Interesting. Correction; I said earlier that I had the proof, but I still have to work out the details on paper. I just did it in my mind; the actual details are a bit more elaborated but I don't see a problem getting there :D.

samirbajaj 09-15-2012 12:49 PM

Re: Question 11
 
Quote:

Originally Posted by yaser (Post 5295)
Hint (from Mr. Hints himself :)): Cauchy.

I hope this helps more than it confuses.

OK, you just signed up to explain this after the Final deadline.

If you forget, I will remind you :-)

Thanks.

-Samir

yaser 09-15-2012 03:36 PM

Re: Question 11
 
Quote:

Originally Posted by samirbajaj (Post 5320)
OK, you just signed up to explain this after the Final deadline.

The deadline is this coming Tuesday, right?

fgpancorbo 09-15-2012 09:24 PM

Re: Question 11
 
Quote:

Originally Posted by fgpancorbo (Post 5296)
:D, sure, Cauchy like in "Cauchy-Schwarz"? I don't want to sound cocky but I thought about bringing that ammunition myself except that I was unable to identify the inner product but now that I think about it... there is that cross term that looks very much like one... Interesting. Correction; I said earlier that I had the proof, but I still have to work out the details on paper. I just did it in my mind; the actual details are a bit more elaborated but I don't see a problem getting there :D.

OK, I finally got it :D. It's a bit more technical that I originally thought. If I am allowed, I think that there is another hint needed, and that's the http://en.wikipedia.org/wiki/Inequal...The_inequality . Professor Yaser, feel free to remove this comment if I am giving too much out. Maybe there is a easier way, but I needed both equalities, http://en.wikipedia.org/wiki/Cauchy%...arz_inequality and http://en.wikipedia.org/wiki/Inequal...The_inequality to prove the option for which I was unable to find a counter example.

samirbajaj 09-16-2012 11:01 AM

Re: Question 11
 
Quote:

Originally Posted by yaser (Post 5325)
The deadline is this coming Tuesday, right?


Right.

I can imagine a connection between the hint and the problem, but I couldn't formally pin it down, and instead had to fall back on my intuition (which may be wrong).

I'd love to see a brief explanation related to this after Tuesday.

Thank you.

-Samir

yaser 09-16-2012 11:25 AM

Re: Question 11
 
Quote:

Originally Posted by samirbajaj (Post 5354)
I'd love to see a brief explanation related to this after Tuesday.

I am sure an *ANSWER* thread will be forthcoming.


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