Comments on: Polytopes for LSL2 by Walls http://trdunlap2.wordpress.com/2008/10/14/polytopes-for-lsl2-by-walls/ What I'm working on and what I'm finding Wed, 08 Jul 2009 18:50:18 +0000 http://wordpress.com/ hourly 1 By: trdunlap2 http://trdunlap2.wordpress.com/2008/10/14/polytopes-for-lsl2-by-walls/#comment-124 trdunlap2 Thu, 16 Oct 2008 06:07:54 +0000 http://trdunlap2.wordpress.com/?p=181#comment-124 Applying L'Hopital's rule to the each formula notice that the limit as either variable goes to plus or minus infinity is the other variable. Also note that $latex \phi(4,5)=\phi(3,5)=\phi(3,4)=2$ ($latex \phi$ here denoting the formula above.) So these three cells will never three meet. This can also be seen because their normal vectors lie on a line. Applying L’Hopital’s rule to the each formula notice that the limit as either variable goes to plus or minus infinity is the other variable.

Also note that \phi(4,5)=\phi(3,5)=\phi(3,4)=2 (\phi here denoting the formula above.) So these three cells will never three meet. This can also be seen because their normal vectors lie on a line.

]]> By: trdunlap2 http://trdunlap2.wordpress.com/2008/10/14/polytopes-for-lsl2-by-walls/#comment-123 trdunlap2 Wed, 15 Oct 2008 20:32:43 +0000 http://trdunlap2.wordpress.com/?p=181#comment-123 I'm not sure what placement of planes should be possible, but I'd guess that vertices should be on the lattice, which would pose a major restriction. I’m not sure what placement of planes should be possible, but I’d guess that vertices should be on the lattice, which would pose a major restriction.

]]> By: trdunlap2 http://trdunlap2.wordpress.com/2008/10/14/polytopes-for-lsl2-by-walls/#comment-122 trdunlap2 Wed, 15 Oct 2008 20:30:02 +0000 http://trdunlap2.wordpress.com/?p=181#comment-122 If m and n are the same sign then the higher number will be on the left of the line. If they have opposite sign then the negative number will be on the left side. If m and n are the same sign then the higher number will be on the left of the line. If they have opposite sign then the negative number will be on the left side.

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