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Let R be a commutative Noetherian ring with identity and C a semidualizing module for R. Let C (R) and ℐ C (R) denote, respectively, the classes of C -projective and C -injective R -modules. We show that their induced Ext bifunctors Ext C i (− , ∼) and Ext ℐ C i (− , ∼) coincide for all i ≥ 0 if and only if C is projective. Also, we provide some other criteria for C to be projective by using some special cotorsion theories. [ABSTRACT FROM AUTHOR]

Our aim in this article is to study a problem originally raised by Grothendieck. We show that the approximately Cohen–Macaulay property is preserved for the tensor product of algebras over a field k . We also discuss the converse problem. [ABSTRACT FROM AUTHOR]

Background: Ataxia telangiectasia (AT) is an autosomal recessive multisystem disorder. Most patients have progressive cerebellar ataxia, oculocutaneous telangiectasia, frequent pulmonary infection, and an increased risk of malignancies. Although N-acetyl-dl-leucine (ADLL) has shown some efficacy in patients with AT, its more pharmacologically active enantiomer, N-acetyl-l-leucine (NALL), has just recently been investigated in ataxic individuals. The current study assessed the efficacy of NALL in patients with AT., Methods: This 2 × 2 crossover, double-blind, randomized clinical trial was conducted on 20 patients with AT. After excluding four patients, 16 subjects (eight females, eight males; mean age 9.8 ± 3.5 years) with a definitive genetic diagnosis of AT were randomly assigned to one of two study groups, with one group receiving 1-4 g/day NALL or a placebo for six weeks. Subjects then had a 4-week washout before crossing over to the other treatment for an additional six weeks. The Spinocerebellar Ataxia Functional Index (SCAFI) and the Scale for Assessment and Rating of Ataxia (SARA) score assessed patients' motor function. Quality of life (QOL) was evaluated by a specialist using the PedsQL questionnaire. Fasting blood samples were taken from all subjects before and after each intervention to determine potential side effects., Results: Although patients' nausea and constipation were improved, the results failed to reveal any significant benefits of NALL treatment on ataxia symptoms. NALL treatment had no significant effects on SARA, SCAFI-9HPT (9-hole peg test) nondominant, SCAFI-9HPT dominant, or SCAFI-8WMT (8 m walking time) (p > 0.05). Our patient's Physical Health score in Child self-report and Parent proxy-report did not significantly change in the treatment group compared to the placebo (p > 0.05). Furthermore, there were no significant changes in energy and macronutrient intake after NALL treatment. None of the volunteers reported serious or moderate side effects., Conclusions: To the best of our knowledge, this was the first placebo-controlled, randomized clinical trial exploring NALL's potential effects for treating AT. Despite improvements in some symptomss, NALL intervention failed to improve motor function significantly. However, patients' nausea and constipation were improved by NALL, which can be a relevant benefit clinically., Competing Interests: Declaration of competing interest None., (© 2024 European Paediatric Neurology Society. Published by Elsevier Ltd. All rights reserved.)

Ataxia-telangiectasia (AT) is a rare autosomal recessive disorder with no available curative treatment. Although the positive effects of N-acetyl-DL-leucine on cerebellar ataxia have been reported previously, there is little evidence of N-acetyl-DL-leucine's effects in patients with AT. This study assessed the effect of 16 weeks N-acetyl-DL-leucine supplementation on ataxia symptoms in a 9-year-old female with AT. The subject consumed 4 g/day N-acetyl-DL-leucine (2 g in the morning and 2 g in the evening) for 16 weeks. Safety was assessed via clinical blood chemistry prior to the intervention and after 6 and 16 weeks. Additionally, The Scale for the Assessment and Rating of Ataxia (SARA) score was used to assess the drug's effects on ataxia symptoms at baseline, 6, 12, and 16 weeks. Quality of life has also been evaluated by a specialist using the PedsQL questionnaire.Despite some initial (first week only) nausea and constipation, supplementation with N-acetyl-DL-leucine was well tolerated and safe according to blood chemistry measures. The SARA score progressively improved, and by week 16 had improved by 11.0 points (48.88%). Parent and self-reported quality of life assessments indicated physical, emotional, social, and school functions all improved by 16 weeks. Supplementation with N-acetyl-DL-leucine at a dose of 4 g/day for 16 weeks was well tolerated and significantly improved ataxia symptoms and quality of life measures in a young child with AT., (© 2022. The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.)

Oral dexamethasone was administered at a dose of 0.075 mg/kg/day for a boy with ataxia-telangiectasia. The SARA score was improved by 7.0 points after dexamethasone treatment over a period of 28 days. The body weight was increased by 1.4 kg after 4 weeks leading to dose titration to 0.05 mg/kg/day., Competing Interests: The authors declare that there is no conflict of interest., (© 2022 The Authors. Clinical Case Reports published by John Wiley & Sons Ltd.)

Saffron, the dried stigmas of Crocus sativus L., is mainly used as a food coloring and flavoring agent. This agricultural product is used in traditional medicine for the treatment of several diseases including asthma, liver disease, menstruation disorders, and, of special interest in this review, metabolic syndrome. Saffron and its active components including crocin, crocetin, and safranal are potential therapeutic candidates for attenuating MetS complications including hypertension, hyperglycemia, obesity, and dyslipidemia. This review summarizes the protective role of saffron and its constituents in the pathogenesis of MetS for a better understanding and hence a better management of this disease.