BARRATT, P. R., T. KORFF, S. J. ELMER, and J. C. MARTIN. Effect of Crank Length on Joint-Specific Power during Maximal Cycling.Med. Sci. Sports Exerc., Vol. 43, No. 9, pp. 1689–1697, 2011. Previous investigators have suggested that crank length has little effect on overall short-term maximal cycling power once the effects of pedal speed and pedaling rate are accounted for. Although overall maxi...

The crank unit is defined as the basic unit of the crank-group driving mechanism for the modular design and production, and the balance methods of inertia force are researched on the crank unit in crank-group driving mechanism’s modular design. The factors affecting the balance weight’s position and mass are studied. This indicates that the product of the mass and gyration radius of the balance...

Andrews, Garvan and Liang introduced the spt-crank for vector partitions. We conjecture that for any n the sequence {NS(m,n)}m is unimodal, where NS(m,n) is the number of S-partitions of size n with crank m weight by the spt-crank. We relate this conjecture to a distributional result concerning the usual rank and crank of unrestricted partitions. This leads to a heuristic that suggests the conj...

The crank of an integer partition is an integer statistic which yields a combinatorial explanation of Ramanujan’s three famous congruences for the partition function. The existence of such a statistic was conjectured by Freeman Dyson in 1944 and realized 44 years later by George Andrews and Frank Gravan. Since then, groundbreaking work by Ken Ono, Karl Mahlburg, and others tells us that not onl...

Let spt(n) denote the total number of appearances of the smallest parts in all the partitions of n. In 1988, the second author gave new combinatorial interpretations of Ramanujan’s partition congruences mod 5, 7 and 11 in terms of a crank for weighted vector partitions. In 2008, the first author found Ramanujantype congruences for the spt-function mod 5, 7 and 13. We give new combinatorial inte...