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 mileschen 09-30-2012 11:50 PM

Problem 2.14(c)

For Problem 2.14(c), to determine the min value, the way I think would be try to solve the equation in (b) and get L. Maybe L is the second part of the min. However, how to solve the equation is a really hard question. Thus, could anyone tell me how to solve the equation or give me a hint on how to get the right answer?

 magdon 10-01-2012 05:46 AM

Re: Problem 2.14(c)

Yes, solving the equation is really hard. It is simpler to show that if takes on the value in the second part of the min, the condition in (b) is satisfied.
Quote:
 Originally Posted by mileschen (Post 5971) For Problem 2.14(c), to determine the min value, the way I think would be try to solve the equation in (b) and get L. Maybe L is the second part of the min. However, how to solve the equation is a really hard question. Thus, could anyone tell me how to solve the equation or give me a hint on how to get the right answer?

 BojanVujatovic 07-14-2014 06:29 PM

Re: Problem 2.14(c)

Quote:
 Originally Posted by magdon (Post 5975) It is simpler to show that if takes on the value in the second part of the min, the condition in (b) is satisfied.
I have difficulties solving this problem. If I assume that , then the condition in (b) is not satisfied.
(e.g. when , then and ).

I believe the right thing to do would be to assume that because the min bound will still hold and I believe the condition in (b) is then satisfied? But how do I prove that?

I appreciate any help.

 magdon 07-17-2014 09:26 AM

Re: Problem 2.14(c)

There is a typo in the equation, sorry.

The second term in the minimum should be .

Rather than solve the inequality in (b) to get this bound, you may rather just verify that this is a bound by showing that if , then the inequality in (b) is satisfied, namely .

Quote:
 Originally Posted by mileschen (Post 5971) For Problem 2.14(c), to determine the min value, the way I think would be try to solve the equation in (b) and get L. Maybe L is the second part of the min. However, how to solve the equation is a really hard question. Thus, could anyone tell me how to solve the equation or give me a hint on how to get the right answer?

 BojanVujatovic 07-20-2014 09:48 AM

Re: Problem 2.14(c)

 zhaozb15 10-01-2015 08:46 AM

Re: Problem 2.14(c)

Quote:
 Originally Posted by magdon (Post 11695) There is a typo in the equation, sorry. The second term in the minimum should be . Rather than solve the inequality in (b) to get this bound, you may rather just verify that this is a bound by showing that if , then the inequality in (b) is satisfied, namely .
If , then . Seems not correct

 ilson 10-06-2015 10:15 PM

Re: Problem 2.14(c)

Quote:
 Originally Posted by zhaozb15 (Post 12077)
I came here to say exactly this. Also, if then trivially, so can we assume that ?

 magdon 10-07-2015 07:05 AM

Re: Problem 2.14(c)

Quote:
 Originally Posted by ilson (Post 12085) I came here to say exactly this. Also, if then trivially, so can we assume that ?
Yes, the problem should state that K>1, otherwise the problem is trivial.

 RicLouRiv 07-12-2017 11:59 AM

Re: Problem 2.14(c)

I'm pretty stuck on this one -- any hints?

 ppaquay 05-21-2018 12:55 PM

Re: Problem 2.14(c)

Hi, I'm also stuck on this one. I don't know if I'm missing an algebraic argument (in verifying that 2^l > 2Kl^d) or if I'm missing something more important. Any hint would be appreciated.

 joseqft 11-11-2019 05:19 AM

Re: Problem 2.14(c)

I´ve been struggling with this problem too. Essentialiy we have to prove that the second expression in the min expression .

is a valid as explains magdon in

Quote:
 Originally Posted by magdon (Post 11695) Rather than solve the inequality in (b) to get this bound, you may rather just verify that this is a bound by showing that if , then the inequality in (b) is satisfied, namely .
this means that the inequality (1)

must be satisfied.

I have been finding upper bounds to the right hand side of (1), using the following tricks if (the case must be proved apart). , , because (this is not the seven in the exponent) and .

Then we arrive at an expression that can be compared easily with the left hand side of (1) proving that this inequality is valid.

 AlexS 01-23-2020 02:57 AM

Re: Problem 2.14(c)

Quote:
 Originally Posted by joseqft (Post 20178) I´ve been struggling with this problem too. Essentialiy we have to prove that the second expression in the min expression . is a valid as explains magdon in this means that the inequality (1) must be satisfied. I have been finding upper bounds to the right hand side of (1), using the following tricks if (the case must be proved apart). , , because (this is not the seven in the exponent) and . Then we arrive at an ASO expression that can be compared easily with the left hand side of (1) proving that this inequality is valid.
I think you will find mistake :clueless: it is not hard

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