{"title":"Hausdorff dimension of sets defined by almost convergent binary expansion sequences","authors":"Q. Song","doi":"10.1017/S0017089523000046","DOIUrl":"https://doi.org/10.1017/S0017089523000046","url":null,"abstract":"Abstract In this paper, we study the Hausdorff dimension of sets defined by almost convergent binary expansion sequences. More precisely, the Hausdorff dimension of the following set \u0000begin{align*} bigg{xin[0,1);:;frac{1}{n}sum_{k=a}^{a+n-1}x_{k}longrightarrowalphatextrm{ uniformly in }ainmathbb{N}textrm{ as }nrightarrowinftybigg} end{align*}\u0000 is determined for any \u0000$ alphain[0,1] $\u0000 . This completes a question considered by Usachev [Glasg. Math. J. 64 (2022), 691–697] where only the dimension for rational \u0000$ alpha $\u0000 is given.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":"65 1","pages":"450 - 456"},"PeriodicalIF":0.5,"publicationDate":"2023-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47513362","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Some characterizations of expanding and steady Ricci solitons","authors":"Márcio S. Santos","doi":"10.1017/S0017089523000034","DOIUrl":"https://doi.org/10.1017/S0017089523000034","url":null,"abstract":"Abstract In this short note, we deal with complete noncompact expanding and steady Ricci solitons of dimension \u0000$ngeq 3.$\u0000 More precisely, under an integrability assumption, we obtain a characterization for the generalized cigar Ricci soliton and the Gaussian Ricci soliton.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":"65 1","pages":"446 - 449"},"PeriodicalIF":0.5,"publicationDate":"2023-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44363017","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Laura A Barnes, Yinuo Xu, Ana Sanchez-Azofra, Esteban A Moya, Michelle P Zhang, Laura E Crotty Alexander, Atul Malhotra, Omar Mesarwi
{"title":"Duration of intermittent hypoxia impacts metabolic outcomes and severity of murine NAFLD.","authors":"Laura A Barnes, Yinuo Xu, Ana Sanchez-Azofra, Esteban A Moya, Michelle P Zhang, Laura E Crotty Alexander, Atul Malhotra, Omar Mesarwi","doi":"10.3389/frsle.2023.1215944","DOIUrl":"10.3389/frsle.2023.1215944","url":null,"abstract":"<p><strong>Rationale: </strong>Obstructive sleep apnea (OSA) is associated with metabolic dysfunction, including progression of nonalcoholic fatty liver disease (NAFLD). Chronic intermittent hypoxia (IH) as a model of OSA worsens hepatic steatosis and fibrosis in rodents with diet induced obesity. However, IH also causes weight loss, thus complicating attempts to co-model OSA and NAFLD. We sought to determine the effect of various durations of IH exposure on metabolic and liver-related outcomes in a murine NAFLD model. We hypothesized that longer IH duration would worsen the NAFLD phenotype.</p><p><strong>Methods: </strong>Male C57BL/6J mice (<i>n</i> = 32) were fed a high <i>trans</i>-fat diet for 24 weeks, to induce NAFLD with severe steatohepatitis. Mice were exposed to an IH profile modeling severe OSA, for variable durations (0, 6, 12, or 18 weeks). Intraperitoneal glucose tolerance test was measured at baseline and at six-week intervals. Liver triglycerides, collagen and other markers of NAFLD were measured at sacrifice.</p><p><strong>Results: </strong>Mice exposed to IH for 12 weeks gained less weight (<i>p</i> = 0.023), and had lower liver weight (<i>p</i> = 0.008) relative to room air controls. These effects were not observed in the other IH groups. IH of longer duration transiently worsened glucose tolerance, but this effect was not seen in the groups exposed to shorter durations of IH. IH exposure for 12 or 18 weeks exacerbated liver fibrosis, with the largest increase in hepatic collagen observed in mice exposed to IH for 12 weeks.</p><p><strong>Discussion: </strong>Duration of IH significantly impacts clinically relevant outcomes in a NAFLD model, including body weight, fasting glucose, glucose tolerance, and liver fibrosis.</p>","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":"44 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10704994/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78628155","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Galois representations of superelliptic curves","authors":"Ariel Pacetti, Angel Villanueva","doi":"10.1017/S0017089522000386","DOIUrl":"https://doi.org/10.1017/S0017089522000386","url":null,"abstract":"Abstract A superelliptic curve over a discrete valuation ring \u0000$mathscr{O}$\u0000 of residual characteristic p is a curve given by an equation \u0000$mathscr{C};:; y^n=,f(x)$\u0000 , with \u0000$textrm{Disc}(,f)neq 0$\u0000 . The purpose of this article is to describe the Galois representation attached to such a curve under the hypothesis that f(x) has all its roots in the fraction field of \u0000$mathscr{O}$\u0000 and that \u0000$p nmid n$\u0000 . Our results are inspired on the algorithm given in Bouw and WewersGlasg (Math. J. 59(1) (2017), 77–108.) but our description is given in terms of a cluster picture as defined in Dokchitser et al. (Algebraic curves and their applications, Contemporary Mathematics, vol. 724 (American Mathematical Society, Providence, RI, 2019), 73–135.).","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":"65 1","pages":"356 - 382"},"PeriodicalIF":0.5,"publicationDate":"2022-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48469136","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}