Interpolating classical partitions of the set of positive integers
RAMANUJAN JOURNAL
Authors: Krandel, Jared; Chen, Weiru
Abstract
We construct an easily described family of partitions of the positive integers into n disjoint sets with essentially the same structure for every n = 2. In a special case, it interpolates between the Beatty 1 f + 1 f2 = 1 partitioning (n = 2) and the 2-adic partitioning in the limit as n.8. We then analyze how membership of elements in the sets of one partition relates to membership in the sets of another. We investigate in detail the interactions of two Beatty partitions with one another and the interactions of the f Beatty partition mentioned above with its "extension" to three sets given by the construction detailed in the first part. In the first case, we obtain detailed results, whereas in the second case we place some restrictions on the interaction but cannot obtain exhaustive results.
Quantitative acoustic metrics of vowel production in mandarin-speakers with post-stroke spastic dysarthria
CLINICAL LINGUISTICS & PHONETICS
Authors: Ge, Shengnan; Wan, Qin; Yin, Minmin; Wang, Yongli; Huang, Zhaoming
Abstract
Impairment of vowel production in dysarthria has been highly valued. This study aimed to explore the vowel production of Mandarin-speakers with post-stroke spastic dysarthria in connected speech and to explore the influence of gender and tone on the vowel production. Multiple vowel acoustic metrics, including F1 range, F2 range, vowel space area (VSA), vowel articulation index (VAI) and formant centralization ratio (FCR), were analyzed from vowel tokens embedded in connected speech produced. The participants included 25 clients with spastic dysarthria secondary to stroke (15 males, 10 females) and 25 speakers with no history of neurological disease (15 males, 10 females). Variance analyses were conducted and the results showed that the main effects of population, gender, and tone on F2 range, VSA, VAI, and FCR were all significant. Vowel production became centralized in the clients with post-stroke spastic dysarthria. Vowel production was found to be more centralized in males compared to females. Vowels in neutral tone (T0) were the most centralized among the other tones. The quantitative acoustic metrics of F2 range, VSA, VAI, and FCR were effective in predicting vowel production in Mandarin-speaking clients with post-stroke spastic dysarthria, and hence may be used as powerful tools to assess the speech performance for this population.