S.O.S. Mathematics CyberBoard

Your Resource for mathematics help on the web!
It is currently Fri, 9 Oct 2015 14:55:26 UTC

All times are UTC [ DST ]

Post new topic Reply to topic  [ 3 posts ] 
Author Message
 Post subject: A strong inequality
PostPosted: Thu, 11 Jun 2009 22:39:37 UTC 

Joined: Sun, 23 Mar 2008 10:55:47 UTC
Posts: 29
Prove that


 Post subject: Re: A strong inequality
PostPosted: Fri, 12 Jun 2009 07:35:49 UTC 
User avatar

Joined: Mon, 29 Dec 2008 17:49:32 UTC
Posts: 7323
Location: NCTS/TPE, Taiwan
mathemagics wrote:
Prove that


Rearrange, so it suffices to show 3>e-log(1-(e-1)/e^2). Then it is just a matter of using enough terms in the series expansion (e.g. taking 7 terms approximation for e and log) so the remainder term doesn't matter.

Spin(2)&=U(1)=SO(2)&&\text{are obvious}\\
Spin(3)&=Sp(1)=SU(2)&&\text{by }q\mapsto(\mathop{\mathrm{Im}}\mathbb{H}\ni p\mapsto qp\bar{q})\\
Spin(4)&=Sp(1)\times Sp(1)&&\text{by }(q_1,q_2)\mapsto(\mathbb{H}\ni p\mapsto q_1p\bar{q_2})\\
Spin(5)&=Sp(2)&&\text{by }\mathbb{HP}^1\cong S^4_{round}\hookrightarrow\mathbb{R}^5\\
Spin(6)&=SU(4)&&\text{by the irrep }\Lambda_+\mathbb{C}^4

 Post subject:
PostPosted: Fri, 12 Jun 2009 13:20:06 UTC 
Member of the 'S.O.S. Math' Hall of Fame
User avatar

Joined: Wed, 1 Oct 2003 04:45:43 UTC
Posts: 9950
I really want to use Bernoulli's inequality somehow...

Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 3 posts ] 

All times are UTC [ DST ]

Who is online

Users browsing this forum: No registered users

You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum

Search for:
Jump to:  
Contact Us | S.O.S. Mathematics Homepage
Privacy Statement | Search the "old" CyberBoard

users online during the last hour
Powered by phpBB © 2001, 2005-2015 phpBB Group.
Copyright © 1999-2015 MathMedics, LLC. All rights reserved.
Math Medics, LLC. - P.O. Box 12395 - El Paso TX 79913 - USA