A family of rank-n (n = 5, 6, 7, 8) three-qubit mixed states are constructed. The explicit expressions for the three-tangle and optimal decompositions for all these states are given. The CKW relations for these states are also discussed.

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Background Acne vulgaris (AV) is a common dermatosis. For moderate to severe AV, isotretinoin is the first-line treatment. Chemical peeling with supramolecular salicylic acid (SSA) was developed with water solubility and advanced skin penetration properties. In the present study, we investigated the efficacy and safety of oral low-dose isotretinoin combined with 30% SSA chemical peeling. Methods Thirty-three moderate-to-severe acne patients were enrolled and received oral low-dose (0.2-0.4 mg/kg/d) isotretinoin and were then randomly assigned to receive 30% SSA or not on each side of the face with 2-week intervals for four sessions. Photos, the number of lesions, GAGS score, skin indices (melanin, erythema, pore, and texture), hydration, and transepidermal water loss (TEWL) were assessed at 0, 2, 4, 6, and 10 weeks. Side effects, efficacy, and satisfactory rates were recorded.Results A total of 29 patients completed the study. Oral isotretinoin combined with SSA decreased response time compared to isotretinoin monotherapy, with significantly improved GAGS score, count of lesions, and efficacy (%) at 4-6 weeks. Skin indices of melanin, erythema, pore, and texture evaluated at week 10 were improved as well. Oral isotretinoin with or without SSA was effective by the lesion clearance; only SSA significantly improved the TEWL. All the side effects were temporary and tolerable, and no adverse effects were observed. ConclusionOral low-dose isotretinoin combined with 30% SSA is safe and effective, which advanced the onset of action and improves lesion clearance.Abbreviation: SD, standard deviation.

Necrolytic migratory erythema is most commonly associated with glucagonoma syndrome. We report a rare case of glucagonoma syndrome with necrolytic migratory erythema presenting as pruritic papules and follicular pustules in a 57-year-old woman; showing eosinophilic infiltration on histology. However, the final diagnosis was confirmed by demonstrating neuroendocrine tumour on histopathological examination of the liver metastases. Nutrition therapy was administered as a palliative treatment. This case also highlights the atypical clinical features and nonspecific histology of necrolytic migratory erythema which makes the diagnosis difficult.

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