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Method of computation of energies in the fractional quantum Hall effect regime
In a previous work, we reported exact results of energies of the ground state
in the fractional quantum Hall effect (FQHE) regime for systems with up to
electrons at the filling factor by using the
method of complex polar coordinates. In this work, we display interesting
computational details of the previous calculation and extend the calculation to
electrons at . Moreover, similar exact results
are derived at the filling for systems with up to electrons. The results that we obtained by analytical calculation are in
good agreement with their analogues ones derived by the method of Monte Carlo
in a precedent work.Comment: 9 pages, 1 figur
ACOUSTIC ANALYSIS OF THE LENGTH OF /ʃ/ AND /Ʒ/ IN ENGLISH AFFRICATES
To participate in the ongoing debate of whether affricates are single phonemes or a combination of two distinct phonemes, this paper reports the results of an acoustic study of affricates. One of the arguments that supports one phoneme analysis is based on the assumption that the length of /ʃ/ and /Ʒ/ as single phonemes tends to be shorter when they are involved within the affricates /ʃ/ and /Ʒ/ respectively. However, this assumption has not been acoustically investigated. Thus, this paper measures the duration of /ʃ/ and /Ʒ/: first when they are alone, and second when they are involved in affricates to identify any length variation between the two cases. The study is based on acoustic and statistical analyses of the recordings of Iraqi, British and American speakers of English, who were asked to pronounce words that have the two fricatives /ʃ/ and /Ʒ/ alone and in affricates as well. The results of paired samples t-tests showed a significant difference in the length of /ʃ/ and /Ʒ/ as single phonemes and their length when involved within affricates in the pronunciation of Iraqi, British and American speakers both on the group and the overall levels. These results support the one phoneme analysis of affricates. Moreover, the results indicated that Arab learners and Iraqis in particular count heavily on temporal cues rather than spectral cues in perceiving English sounds. This shows the need for more training on the part of learners and teachers, and more attention on the part of English textbook designers
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