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The deformed oscillators formalism plays a useful role in the study of physical models. Specifically, many variants of deformed oscillators have been used to study of the quantum optics, condensed matter physics, etc. .. In this paper we construct a (q, R)-deformed crystal lattice vibration for generic atomic string and calculate statistical distribution of this vibration. This is a fundament for study of crystal lattice vibration, which would give a base for a new quantization proceduce.

Background Carpal tunnel syndrome (CTS) is the most common entrapment neuropathy which can cause severe sleep disturbance. Carpal tunnel release (CTR) is a choice for severe cases, which has shown to improve sleep quality, but the available evidence is limited. This study aimed to investigate the impact of CTR on sleep quality and hand symptoms and functions in patients with CTS. Methods This was a prospective study in 2019–2020 on patients with CTS and poor sleep quality undergoing CTR. Patients were evaluated before and at 1, 3, and 12 months after CTR by the Pittsburgh sleep quality index (PSQI) and Boston carpal tunnel syndrome questionnaires. Results There were 33 patients with 27 females (82%) and a median age of 51 years. The median time of CTS diagnosis and having sleep disorder before CTR were 12 and 6 months, respectively. The outcomes significantly improved after CTR, with the median PSQI and Boston symptom and function scores reduced from 12, 33, and 23 before CTR to 9, 14, and 11 at 1 month; 7, 13, and 9 at 3 months; and 1, 11, and 8 at 12 months postoperatively, respectively. The correlations between the PSQI and Boston symptom and function scores were > 0.6 at all time-points. Conclusions Surgical decompression significantly improves sleep quality and the hand symptoms and functions in patients with CTS. Long-term evaluations are lacking and thus are required in future studies.

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