To find the trading time generator, first we solve 
1 = dY_{1}^{D} + dY_{2}^{D}
+ dY_{3}^{D} = 0.5^{D} + 0.25^{D} + 0.75^{D}. 
The Mathematica command is 
FindRoot[0.5^D + 0.25^D + 0.75^D == 1,{D,1}] 
The approximate solution is D = 1.73051. 
With this value of D we find the trading time generators
dT_{1}, dT_{2}, and dT_{3}: 
dT_{1} = dY_{1}^{D} = .5^{1.73051} = 0.301345, 
dT_{2} = dY_{2}^{D} = .25^{1.73051} = 0.0908091, and 
dT_{3} = dY_{3}^{D} = .75^{1.73051} = 0.607844. 

Here is the trading timeclock time generator. 
