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Packing Characteristics of Different Shaped Proppants for use with Hydrofracing - A Numerical Investigation using 3D FEMDEM
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Unlimited parity alternating partitions
We introduce a new type of partitions that consists of partitions whose
different parts alternate in parity (e.g., ). Various properties of
this partition function are studied. In particular, we obtain its asymptotic
behavior by employing Ingham's Tauberian theorem
Note on sums involving the Euler function
In this note, we provide refined estimates of the following sums involving
the Euler totient function: where denotes the integral part of real
. The above summations were recently considered by Bordell\`es et al. and
Wu.Comment: Bull. Aust. Math. Soc., accepte
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