• Communications of the Korean Mathematical Society
• /
• v.38 no.4
• /
• pp.1029-1044
• /
• 2023

The purpose of this paper is to introduce the concept of joint essential numerical spectrum 𝜎_en(·) of q-tuple of operators on a Banach space and to study its properties. This notion generalize the notion of the joint essential numerical range.

• Clinics in Shoulder and Elbow
• /
• v.27 no.1
• /
• pp.45-51
• /
• 2024

Background: It is essential to distinguish between symptomatic- and asymptomatic radiographic acromioclavicular (AC) osteoarthritis (OA) because AC-targeted physical examinations are dubious. This study aimed to determine the diagnostic value of a preoperative AC injection in discriminating between symptomatic- and asymptomatic radiographic AC OA based on patient arthroscopic distal clavicle resection (aDCR) outcomes. Methods: Forty-eight patients who underwent aDCR for AC OA were included. Their satisfaction was objectified using a 5-point Likert scale and patient willingness to repeat the surgery. The Oxford Shoulder Score (OSS), the Subjective Shoulder Value (SSV), and the Numerical Rating Scale (NRS) were used to assess postoperative shoulder function and pain. Patients were subdivided into groups based on their good or minimal reaction to an AC injection (good reaction: ≥7 consecutive days of pain reduction, Minimal reaction: <7 consecutive days of pain reduction). Results: Twenty-seven patients had a good reaction and 21 patients had a minimal reaction to the AC injection (median follow-up, 45.0 months; range, 31.0-52.8 months). No significant differences were found in level of satisfaction (P=0.234) or willingness to repeat the surgery (P=0.861). No significant differences were found in OSS (P=0.612), SSV (P=0.641), NRS at rest (P=0.684) or during activity (P=0.422). Conclusions: This study found no significant differences between patients with a good reaction or a minimal reaction to an AC injection after aDCR surgery. The outcomes of this study seem to suggest that a distinction between symptomatic and asymptomatic radiographic AC OA is unnecessary, as all patients were equally satisfied with the outcome.