The machining precision in the scroll compressor with the compliant crank mechanism is not required so high as that with the fixed throw crank, but the sealing performance is better than the later's, therefore the scroll compressor with the compliant crank mechanism operates at higher efficiency. In this study, the characters of the compliant crank mechanism are discussed, while the Oldham coup...

A partition of a non-negative integer n is a non-increasing sequence of positive integers whose sum is n. For example, The 5 partitions of 4 are 4, 3 + 1, 2 + 2, 2 + 1 + 1, and 1 + 1 + 1 + 1. To explain Ramanujan’s famous three partition congruences, the partition statistics, the rank (resp. the crank) were introduced by Dyson [8] (resp. Andrews and Garvan [3]). Atkin and Garvan [5] initiated t...

Alterations in kinetic patterns of pedal force and crank torque due to changes in surface grade (level vs. 8% uphill) and posture (seated vs. standing) were investigated during cycling on a computerized ergometer. Kinematic data from a planar cine analysis and force data from a pedal instrumented with piezoelectric crystals were recorded from multiple trials of 8 elite cyclists. These measures ...

Higher moments of the partition rank and crank statistics have been studied for their connections to combinatorial objects such as Durfee symbols, as well as for their connections to harmonic Maass forms. This paper proves the first several cases of (and strengthens) a conjecture due to Garvan, which states that the moments of the crank function are always larger than the moments of the crank f...

In 1944, Freeman Dyson conjectured the existence of a "crank" function for partitions that would provide a combinatorial proof of Ramanujan's congruence modulo 11. Forty years later, Andrews and Garvan successfully found such a function and proved the celebrated result that the crank simultaneously "explains" the three Ramanujan congruences modulo 5, 7, and 11. This note announces the proof of ...

The objective of this research was to use a pedal force decomposition approach to quantify the amount of negative muscular crank torque generated by a group of competitive cyclists across a range of pedaling rates. We hypothesized that negative muscular crank torque increases at high pedaling rates as a result of the activation dynamics associated with muscle force development and the need for ...

For its first release in 2004, CRANK was shown to effectively detect and phase anomalous scatterers from single-wavelength anomalous diffraction data. Since then, CRANK has been significantly improved and many more structures can be built automatically with single- or multiple-wavelength anomalous diffraction or single isomorphous replacement with anomalous scattering data. Here, the new algori...

UNLABELLED Maximal cycling power has been reported to decrease more rapidly when performed with increased pedaling rates. Increasing pedaling rate imposes two constraints on the neuromuscular system: 1) decreased time for muscle excitation and relaxation and 2) increased muscle shortening velocity. Using two crank lengths allows the effects of time and shortening velocity to be evaluated separa...