Pub Date : 2023-03-13DOI: 10.1017/S0017089523000046
Q. Song
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 begin{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*} is determined for any $ alphain[0,1] $ . This completes a question considered by Usachev [Glasg. Math. J. 64 (2022), 691–697] where only the dimension for rational $ alpha $ is given.
{"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}
Pub Date : 2023-03-13DOI: 10.1017/S0017089523000034
Márcio S. Santos
Abstract In this short note, we deal with complete noncompact expanding and steady Ricci solitons of dimension $ngeq 3.$ More precisely, under an integrability assumption, we obtain a characterization for the generalized cigar Ricci soliton and the Gaussian Ricci soliton.
{"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}
Pub Date : 2023-01-01Epub Date: 2023-08-25DOI: 10.3389/frsle.2023.1215944
Laura A Barnes, Yinuo Xu, Ana Sanchez-Azofra, Esteban A Moya, Michelle P Zhang, Laura E Crotty Alexander, Atul Malhotra, Omar Mesarwi
Rationale: 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.
Methods: Male C57BL/6J mice (n = 32) were fed a high trans-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.
Results: Mice exposed to IH for 12 weeks gained less weight (p = 0.023), and had lower liver weight (p = 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.
Discussion: Duration of IH significantly impacts clinically relevant outcomes in a NAFLD model, including body weight, fasting glucose, glucose tolerance, and liver fibrosis.
理由：阻塞性睡眠呼吸暂停（OSA阻塞性睡眠呼吸暂停（OSA）与代谢功能障碍有关，包括非酒精性脂肪肝（NAFLD）的恶化。慢性间歇性缺氧（IH）作为 OSA 的一种模型，会加重饮食诱发肥胖的啮齿类动物的肝脏脂肪变性和纤维化。然而，间歇性缺氧也会导致体重减轻，从而使同时模拟 OSA 和非酒精性脂肪肝的尝试变得更加复杂。我们试图确定小鼠非酒精性脂肪肝模型中不同持续时间的 IH 暴露对代谢和肝脏相关结果的影响。我们假设，较长的 IH 持续时间会恶化 NAFLD 表型：雄性 C57BL/6J 小鼠（n = 32）连续 24 周摄入高反式脂肪饮食，以诱发非酒精性脂肪肝和严重的脂肪性肝炎。小鼠在不同时间段（0、6、12 或 18 周）暴露于模拟严重 OSA 的 IH 配置文件中。在基线和每隔六周测量腹腔内葡萄糖耐量试验。牺牲时测量肝脏甘油三酯、胶原蛋白和其他非酒精性脂肪肝标志物：结果：与室内空气对照组相比，接触 IH 12 周的小鼠体重增加较少（p = 0.023），肝脏重量较轻（p = 0.008）。其他 IH 组未观察到这些影响。持续时间较长的 IH 会短暂恶化葡萄糖耐量，但在接触较短时间 IH 的组别中未发现这种影响。IH暴露12周或18周会加剧肝纤维化，在IH暴露12周的小鼠中观察到肝胶原蛋白增幅最大：讨论：IH持续时间对非酒精性脂肪肝模型的临床相关结果有重大影响，包括体重、空腹血糖、糖耐量和肝纤维化。
{"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}
Pub Date : 2022-11-24DOI: 10.1017/S0017089522000386
Ariel Pacetti, Angel Villanueva
Abstract A superelliptic curve over a discrete valuation ring $mathscr{O}$ of residual characteristic p is a curve given by an equation $mathscr{C};:; y^n=,f(x)$ , with $textrm{Disc}(,f)neq 0$ . 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 $mathscr{O}$ and that $p nmid n$ . 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.).
{"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}
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