The Crank-Nicolson (CN) simulation method has an oscillatory response to sharp initial transients. The technique is convenient but the oscillations make it less popular. Several ways of damping the oscillations in two types of electrochemical computations are investigated. For a simple one-dimensional system with an initial singularity, subdivision of the first time interval into a number of eq...

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...

PURPOSE Observation of a model performing fast exercise improves simultaneous exercise performance; however, the precise mechanism underpinning this effect is unknown. The aim of the present study was to investigate whether the speed of the observed exercise influenced both upper body exercise performance and the activation of a cortical action observation network (AON). METHOD In Experiment ...

We sought to determine if (i) peak vascular conductance of the calf was reduced following prolonged exposure to simulated microgravity, and (ii) if maximal cycle ergometry performed at the end of microgravity exposure stimulated a restoration of peak calf vascular conductance. To do this, peak vascular conductance of the calf was recorded following ischaemic plantar flexion exercise to fatigue ...

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 ...