Expression 23: "h" left parenthesis, "x" , right parenthesis equals left brace, 0 less than or equal to "x" less than or equal to "a" : left parenthesis, StartFraction, "x" Over "a" , EndFraction , right parenthesis Superscript, "p" , Baseline "t" , right bracehx=0≤x≤a:xapt
23
The two functions below define the exponential stream with cliff:
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Expression 25: "j" left parenthesis, "x" , right parenthesis equals left brace, 0 less than or equal to "x" less than "b" : 0 , "b" less than or equal to "x" less than "a" : left parenthesis, StartFraction, "b" Over "a" , EndFraction plus left parenthesis, StartFraction, "x" minus "b" Over "a" minus "b" , EndFraction , right parenthesis Superscript, "p" , Baseline , right parenthesis "t" , right bracejx=0≤x<b:0,b≤x<a:ba+x−ba−bpt
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Expression 26: "x" equals "b" left brace, 0 less than or equal to "y" less than or equal to StartFraction, "b" Over "a" , EndFraction "t" , right bracex=b0≤y≤bat
26
This is the traditional unlock stream, a step function where each step is a direct unlock going to the recipient:
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Expression 28: "i" left parenthesis, "x" , right parenthesis equals left brace, 0 less than or equal to "x" less than "a" : StartFraction, floor left parenthesis, StartNestedFraction, "x" times left parenthesis, "c" plus 1 , right parenthesis NestedOver "a" , EndNestedFraction , right parenthesis "t" Over "c" , EndFraction , right braceix=0≤x<a:floorx·c+1atc