From han@npac.syr.edu Mon Feb 21 11:54:18 1994
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From: han@npac.syr.edu (Leping Han)
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Date: Mon, 21 Feb 1994 11:54:14 -0500
Message-Id: <199402211654.LAA05315@ace.syr.edu>
To: paulc@npac.syr.edu
Subject: formula for the appendix
Status: R

Paul:

The followings are the formula for the matrix in table 1.

I modified them correspondingly, please double check them against
the top part( a portion of C code ).


  e[0] = -6.;
  e[1] = -4.;
  e[2] = -2.;
  e[3] = 0.;
  e[4] = 2.;
  e[5] = 4.;
  e[6] = 6.;

  for (i=0;i<7;i++) {
    a[i] = exp(-e[i]*beta);
  }

  x[0] = a[6];
  x[1] = a[5] -a[6];
  x[2] = a[4] - 2*a[5] + a[6];
  x[3] = a[3] - 3*a[4] + 3*a[5] - a[6];
  x[4] = a[2] - 2*a[3] + 2*a[4] -2*a[5] + a[6];
  x[5] = a[1]/2.0 - a[2] + a[3] - 2*a[4] + 5*a[5]/2.0 - a[6];
  x[6] = a[0] - 3*a[1] + 3*a[2] - 2*a[3] + 3*a[4] -3*a[5] + a[6];


  prob[i][j] = matrix[i][j]*x[j]/a[i];



 
\begin{eqnarray}
% i = 1 
\nonumber
P(A_1,1) & = & e^{-12K} \\
\nonumber
P(B_1,1) & = & 6(e^{-10K} - e^{-12K}) \\
\nonumber
P(C_1,1) & = & 9(e^{-8K} - 2e^{-10K}  + e^{-12K}) \\
\nonumber
P(D_1,1) & = & 2(e^{-6K} - 3e^{-8K} + 3e^{-10K} - e^{-12K}) \\
\nonumber
P(E_1,1) & = & 3(e^{-4K} - 2e^{-6K} + 2e^{-8K} - 2e^{-10K} + e^{-12K}) \\
\nonumber
P(F_1,1) & = & 3(e^{-2K} - 2e^{-4K} + 2e^{-6K} - 4e^{-8K} +
               5e^{-10K} - 2e^{-12K}) \\
\nonumber
P(G_1,1) & = & 1 - 3e^{-2K} + 3e^{-4K} - 2e^{-6K} +
               3e^{-8K} - 3e^{-10K} + e^{-12K} \\
\nonumber
\\
% i = 2
\nonumber
P(A_1,2) & = & e^{-10K} \\
\nonumber
P(B_1,2) & = & 5(e^{-8K} - e^{-10K}) \\
\nonumber
P(C_1,2) & = & 6(e^{-6K} - 2e^{-8K}  + e^{-10K}) \\
\nonumber
P(D_1,2) & = & 2(e^{-4K} - 3e^{-6K} + 3e^{-8K} - 2e^{-10K}) \\
\nonumber
P(E_1,2) & = & 2(e^{-2K} - 2e^{-4K} + 2e^{-6K} -2e^{-8K} + e^{-10K}) \\
\nonumber
P(F_1,2) & = & 1 - 2e^{-2K} + 2e^{-4K} - 4e^{-6K} +
               5e^{-8K} - 2e^{-10K} \\
\nonumber
\\
% i = 3
\nonumber
P(A_1,3) & = & e^{-8K} \\
\nonumber
P(B_1,3) & = & 4(e^{-6K} - e^{-8K}) \\
\nonumber
P(C_1,3) & = & 4(e^{-4K} - 2e^{-6K} + e^{-8K}) \\ 
\nonumber
P(D_1,3) & = & 2(e^{-2K} - 3e^{-4K} + 3e^{-6K} - e^{-8K}) \\ 
\nonumber 
P(E_1,3) & = & 1 - 2e^{-2K} + 2e^{-4K} -2e^{-6K} + e^{-8K} \\
\nonumber
\\
% i = 4
\nonumber
P(A_1,4) & = & e^{-6K} \\
\nonumber
P(B_1,4) & = & 3(e^{-4K} - e^{-6K}) \\
\nonumber
P(C_1,4) & = & 3(e^{-2K} -2e^{-4K} + e^{-6K}) \\
\nonumber
P(D_1,4) & = & 1 - 3e^{-2K} +  3e^{-4K} - e^{-6K} \\
\nonumber
\\
% i = 5
\nonumber
P(A_1,5) & = & e^{-4K} \\
\nonumber
P(B_1,5) & = & 2(e^{-2K} - e^{-4K}) \\
\nonumber
P(C_1,5) & = & 1 - 2e^{-2K}  + e^{-4K} \\
\nonumber
\\
% i = 6
\nonumber
P(A_1,6) & = & e^{-2K} \\
\nonumber
P(B_1,6) & = & 1 - e^{-2K} \\
\nonumber
\\
% i = 7
\nonumber
P(A_1,7) & = & 1 \\
\nonumber
\end{eqnarray}

Han

From han@npac.syr.edu Sun Feb 20 23:46:04 1994
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	id AA21328; Sun, 20 Feb 94 23:46:02 EST
From: han@npac.syr.edu (Leping Han)
Received: from localhost (han@localhost) by altair.syr.edu (8.6.4/8.6.4) id XAA17330 for paulc; Sun, 20 Feb 1994 23:46:01 -0500
Date: Sun, 20 Feb 1994 23:46:01 -0500
Message-Id: <199402210446.XAA17330@altair.syr.edu>
To: paulc@npac.syr.edu
Subject: probabilty\
Status: RO

this is the probabilties for the
7x7 matrix at beta = 0.738
beta=0.738
  0.000143  0.002886  0.014614  0.010962  0.098132  0.419626  0.453636
  0.000624  0.010525  0.042630  0.047964  0.286246  0.612012  0.000000
  0.002729  0.036839  0.124348  0.209862  0.626222  0.000000  0.000000
  0.011938  0.120890  0.408054  0.459117  0.000000  0.000000  0.000000
  0.052235  0.352630  0.595135  0.000000  0.000000  0.000000  0.000000
  0.228550  0.771450  0.000000  0.000000  0.000000  0.000000  0.000000
  1.000000  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000

Han

