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The Asymptotic Behavior of Compositions of the Euler and Carmichael Functions
The Asymptotic Behavior Compositions the Euler Carmichael Functions Number Theory
2012/6/14
We compare the asymptotic behavior of Carmichael's lambda function composed with Euler's totient function to the asymptotic behavior of Carmichael's lambda function composed with itself. We establish ...
Generalized Compositions of Natural Numbers
optimal control optimal synthesis atom cooling
2011/2/21
Frictionless atom cooling in harmonic traps is formulated as a time-optimal control problem and a synthesis of optimal controlled trajectories is obtained.