9,500 research outputs found
Finite Form of the Quintuple Product Identity
The celebrated quintuple product identity follows surprisingly from an
almost-trivial algebraic identity, which is the limiting case of the
terminating q-Dixon formula.Comment: 1 pag
Arithmetic Properties of Overpartition Pairs
Bringmann and Lovejoy introduced a rank for overpartition pairs and
investigated its role in congruence properties of , the number of
overpartition pairs of n. In particular, they applied the theory of Klein forms
to show that there exist many Ramanujan-type congruences for the number
. In this paper, we shall derive two Ramanujan-type identities and
some explicit congruences for . Moreover, we find three ranks as
combinatorial interpretations of the fact that is divisible by
three for any n. We also construct infinite families of congruences for
modulo 3, 5, and 9.Comment: 19 page
Influence of dynamic inflow on the helicopter vertical response
A study was conducted to investigate the effects of dynamic inflow on rotor-blade flapping and vertical motion of the helicopter in hover. Linearized versions of two dynamic inflow models, one developed by Carpenter and Fridovich and the other by Pitt and Peters, were incorporated in simplified rotor-body models and were compared for variations in thrust coefficient and the blade Lock number. In addition, a comparison was made between the results of the linear analysis, and the transient and frequency responses measured in flight on the CH-47B variable-stability helicopter. Results indicate that the correlations are good, considering the simplified model used. The linear analysis also shows that dynamic inflow plays a key role in destabilizing the flapping mode. The destabilized flapping mode, along with the inflow mode that the dynamic inflow introduces, results in a large initial overshoot in the vertical acceleration response to an abrupt input in the collective pitch. This overshoot becomes more pronounced as either the thrust coefficient or the blade Lock number is reduced. Compared with Carpenter's inflow model, Pitt's model tends to produce more oscillatory responses because of the less stable flapping mode predicted by it
Antennas for 20/30 GHz and beyond
Antennas of 20/30 GHz and higher frequency, due to the small wavelength, offer capabilities for many space applications. With the government-sponsored space programs (such as ACTS) in recent years, the industry has gone through the learning curve of designing and developing high-performance, multi-function antennas in this frequency range. Design and analysis tools (such as the computer modelling used in feedhorn design and reflector surface and thermal distortion analysis) are available. The components/devices (such as BFN's, weight modules, feedhorns and etc.) are space-qualified. The manufacturing procedures (such as reflector surface control) are refined to meet the stringent tolerance accompanying high frequencies. The integration and testing facilities (such as Near-Field range) also advance to facilitate precision assembling and performance verification. These capabilities, essential to the successful design and development of high-frequency spaceborne antennas, shall find more space applications (such as ESGP) than just communications
Han's Bijection via Permutation Codes
We show that Han's bijection when restricted to permutations can be carried
out in terms of the cyclic major code and the cyclic inversion code. In other
words, it maps a permutation with a cyclic major code to a permutation with a cyclic inversion code . We also show that the fixed points of Han's map can be characterized by
the strong fixed points of Foata's second fundamental transformation. The
notion of strong fixed points is related to partial Foata maps introduced by
Bj\"orner and Wachs.Comment: 12 pages, to appear in European J. Combi
A Bijection between Atomic Partitions and Unsplitable Partitions
In the study of the algebra of symmetric functions in
noncommutative variables, Bergeron and Zabrocki found a free generating set
consisting of power sum symmetric functions indexed by atomic partitions. On
the other hand, Bergeron, Reutenauer, Rosas, and Zabrocki studied another free
generating set of consisting of monomial symmetric functions
indexed by unsplitable partitions. Can and Sagan raised the question of finding
a bijection between atomic partitions and unsplitable partitions. In this
paper, we provide such a bijection.Comment: 6 page
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