Expression 6: "p" left parenthesis, "x" , "i" , right parenthesis equals "k" Superscript, "i" , Baseline "V" times left parenthesis, "x" minus "X" left parenthesis, "i" , right parenthesis , right parenthesis minus StartFraction, "g" Over 2 , EndFraction left parenthesis, "x" minus "X" left parenthesis, "i" , right parenthesis , right parenthesis squared left brace, 0 less than or equal to "x" minus "X" left parenthesis, "i" , right parenthesis less than or equal to "k" Superscript, "i" , Baseline "L" , right bracepx,i=kiV·x−Xi−g2x−Xi20≤x−Xi≤kiL
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Expression 7: "X" Subscript, 0 , Baseline left parenthesis, "i" , right parenthesis equals negative StartFraction, "L" Over 2 , EndFraction plus "L" Start sum from "j" equals 0 to "i" minus 1, end sum, "k" Superscript, "j" , BaselineX0i=−L2+Li−1∑j=0kj
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Expression 8: "X" left parenthesis, "i" , right parenthesis equals "L" left parenthesis, StartFraction, 1 minus "k" Superscript, "i" , Baseline Over 1 minus "k" , EndFraction minus .5 , right parenthesisXi=L1−ki1−k−.5
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Expression 9: "p" left parenthesis, "x" , left bracket, 0...1 5 , right bracket , right parenthesispx,0...15
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Expression 10: mod left parenthesis, StartFraction, log left parenthesis, 1 minus left parenthesis, 1 minus "k" , right parenthesis left parenthesis, StartNestedFraction, "x" NestedOver "L" , EndNestedFraction plus .5 , right parenthesis , right parenthesis Over log left parenthesis, "k" , right parenthesis , EndFraction , 1 , right parenthesismodlog1−1−kxL+.5logk,1
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Expression 11: "I" left parenthesis, "x" , right parenthesis equals floor left parenthesis, StartFraction, log left parenthesis, 1 minus left parenthesis, 1 minus "k" , right parenthesis left parenthesis, StartNestedFraction, "x" NestedOver "L" , EndNestedFraction plus .5 , right parenthesis , right parenthesis Over log left parenthesis, "k" , right parenthesis , EndFraction , right parenthesisIx=floorlog1−1−kxL+.5logk
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Expression 12: "p" left parenthesis, "x" , "I" left parenthesis, "x" , right parenthesis , right parenthesispx,Ix