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 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 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 کاملRelations between the Rank and the Crank
New identities and congruences involving the ranks and cranks of partitions are proved. The proof depends on a new partial differential equation connecting their generating functions.
متن کاملRank and Crank Moments for Overpartitions
We study two types of crank moments and two types of rank moments for overpartitions. We show that the crank moments and their derivatives, along with certain linear combinations of the rank moments and their derivatives, can be written in terms of quasimodular forms. We then use this fact to prove exact relations involving the moments as well as congruence properties modulo 3, 5, and 7 for som...
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ژورنال
عنوان ژورنال: Journal of the Franklin Institute
سال: 1878
ISSN: 0016-0032
DOI: 10.1016/0016-0032(78)90224-7