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Mazdak Farrokhzad edited c) Imposing a restriction.tex
about 10 years ago
Commit id: d1f1d4ab7317444ed69247f93cf0b19eb3ab8a79
deletions | additions
diff --git a/c) Imposing a restriction.tex b/c) Imposing a restriction.tex
index add85c4..958b4e0 100644
--- a/c) Imposing a restriction.tex
+++ b/c) Imposing a restriction.tex
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\delta(x,i) &= min\left[ i, \ceil{\frac{x}{c}} \right]\\
A_1 &= \sum_{k=1}^{\delta(x,i)}\Big[ 2(k - 1) \Big]\\
&= 2\sum_{k=1}^{\delta(x,i)}\Big[ k \Big] - \sum_{k=1}^{\delta(x,i)}\Big[ 1 \Big]\\
&= \delta(x,i)(\delta(x,i) + 1) - \delta(x,i)
A_2 &= \Big( 2\delta(x,i) - 1 \Big)\Big( i-\delta(x,i) \Big)\\
&= 2i\delta(x,i) + \delta(x,i) - 2\delta(x,i)^2 - i\\
T(i,x) &= A_1 + A_2