منابع مشابه
Influence of crank length and crank-axle height on standing arm-crank (grinding) power.
OBJECTIVE To determine the optimal crank length and crank-axle height for maximum power production during standing arm cranking ("grinding"). METHODS Nine elite professional America's Cup grinders (age = 36 +/- 2 yr, body mass = 104 +/- 1 kg, body fat = 13% +/- 2%) performed eight maximal 6-s sprints on an adjustable standing arm-crank ergometer fitted with an SRM power crank. The protocol in...
متن کاملDyson’s Crank Distribution Conjecture
Bringmann and Dousse recently established a conjecture of Dyson dealing with the limiting asymptotics of the Andrews-Garvan crank statistic for integer partitions. A direct “sieving” technique is used to establish this conjecture and establish the range of validity. Unlike the approach of Bringmann and Dousse, the technique readily yields the analogous result for Dyson’s partition rank and all ...
متن کاملRamanujan's congruences and Dyson's crank.
T he achievement of Karl Mahlburg in this issue of PNAS (1) adds a lustrous chapter to a unique mathematical object: the crank. In 1944, the crank was first hinted at by Freeman Dyson (2), then an undergraduate at Cambridge University. He had written an article, titled Some Guesses in the Theory of Partitions, for Eureka, the undergraduate mathematics journal of Cambridge. Dyson discovered the ...
متن کاملOn Spt-crank Type Functions
In a recent paper, Andrews, Dixit, and Yee introduced a new spt-type function spt ω (n), which is closely related to Ramanujan’s third order mock theta function ω(q). Garvan and Jennings-Shaffer introduce a crank function which explains congruences for spt ω (n). In this note, we study asymptotic behavior of this crank function and confirm a positivity conjecture of the crank asymptotically. We...
متن کاملDyson's Crank of a Partition
holds. He was thus led to conjecture the existence of some other partition statistic (which he called the crank); this unknown statistic should provide a combinatorial interpretation of ^-p(lln + 6) in the same way that (1.1) and (1.2) treat the primes 5 and 7. In [4, 5], one of us was able to find a crank relative to vector partitions as follows: For a partition 7r, let #(7r) be the number of ...
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ژورنال
عنوان ژورنال: Structure
سال: 2004
ISSN: 0969-2126
DOI: 10.1016/j.str.2004.07.018