Canadian Mathematical Bulletin最新文献

{"title":"A generalization of immanants based on partition algebra characters","authors":"John M. Campbell","doi":"10.4153/s0008439524000249","DOIUrl":"https://doi.org/10.4153/s0008439524000249","url":null,"abstract":"<p>We introduce a generalization of immanants of matrices, using partition algebra characters in place of symmetric group characters. We prove that our immanant-like function on square matrices, which we refer to as the <span>recombinant</span>, agrees with the usual definition for immanants for the special case whereby the vacillating tableaux associated with the irreducible characters correspond, according to the Bratteli diagram for partition algebra representations, to the integer partition shapes for symmetric group characters. In contrast to previously studied variants and generalizations of immanants, as in Temperley–Lieb immanants and <span>f</span>-immanants, the sum that we use to define recombinants is indexed by a full set of partition diagrams, as opposed to permutations.</p>","PeriodicalId":501184,"journal":{"name":"Canadian Mathematical Bulletin","volume":"5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142184015","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Existence of singular rotationally symmetric gradient Ricci solitons in higher dimensions","authors":"Kin Ming Hui","doi":"10.4153/s0008439524000237","DOIUrl":"https://doi.org/10.4153/s0008439524000237","url":null,"abstract":"<p>By using fixed point argument, we give a proof for the existence of singular rotationally symmetric steady and expanding gradient Ricci solitons in higher dimensions with metric <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240403061655231-0392:S0008439524000237:S0008439524000237_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$g=frac {da^2}{h(a^2)}+a^2g_{S^n}$</span></span></img></span></span> for some function <span>h</span> where <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240403061655231-0392:S0008439524000237:S0008439524000237_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$g_{S^n}$</span></span></img></span></span> is the standard metric on the unit sphere <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240403061655231-0392:S0008439524000237:S0008439524000237_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$S^n$</span></span></img></span></span> in <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240403061655231-0392:S0008439524000237:S0008439524000237_inline4.png\"><span data-mathjax-type=\"texmath\"><span>$mathbb {R}^n$</span></span></img></span></span> for any <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240403061655231-0392:S0008439524000237:S0008439524000237_inline5.png\"><span data-mathjax-type=\"texmath\"><span>$nge 2$</span></span></img></span></span>. More precisely, for any <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240403061655231-0392:S0008439524000237:S0008439524000237_inline6.png\"><span data-mathjax-type=\"texmath\"><span>$lambda ge 0$</span></span></img></span></span> and <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240403061655231-0392:S0008439524000237:S0008439524000237_inline7.png\"><span data-mathjax-type=\"texmath\"><span>$c_0&gt;0$</span></span></img></span></span>, we prove that there exist infinitely many solutions <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240403061655231-0392:S0008439524000237:S0008439524000237_inline8.png\"><span data-mathjax-type=\"texmath\"><span>${hin C^2((0,infty );mathbb {R}^+)}$</span></span></img></span></span> for the equation <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240403061655231-0392:S0008439524000237:S0008439524000237_inline9.png\"><span data-mathjax-type=\"texmath\"><span>$2r^2h(r)h_{rr}","PeriodicalId":501184,"journal":{"name":"Canadian Mathematical Bulletin","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140573286","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"OMEGA RESULTS FOR THE ERROR TERM IN THE SQUARE-FREE DIVISOR PROBLEM FOR SQUARE-FULL INTEGERS","authors":"Debika Banerjee, Makoto Minamide","doi":"10.4153/s0008439524000225","DOIUrl":"https://doi.org/10.4153/s0008439524000225","url":null,"abstract":"","PeriodicalId":501184,"journal":{"name":"Canadian Mathematical Bulletin","volume":"362 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140228041","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"ALMOST SURE CONVERGENCE OF THE NORM OF LITTLEWOOD POLYNOMIALS","authors":"Yongjiang Duan, Xiang Fang, NA Zhan","doi":"10.4153/s0008439524000213","DOIUrl":"https://doi.org/10.4153/s0008439524000213","url":null,"abstract":"","PeriodicalId":501184,"journal":{"name":"Canadian Mathematical Bulletin","volume":"30 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140238945","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"IDEALS WITH COMPONENTWISE LINEAR POWERS","authors":"Takayuki Hibi, Somayeh Moradi","doi":"10.4153/s0008439524000201","DOIUrl":"https://doi.org/10.4153/s0008439524000201","url":null,"abstract":"","PeriodicalId":501184,"journal":{"name":"Canadian Mathematical Bulletin","volume":"110 7","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140250515","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A class of Hessian quotient equations in de Sitter space","authors":"Jinyu Gao, Guanghan Li, Kuicheng Ma","doi":"10.4153/s0008439524000183","DOIUrl":"https://doi.org/10.4153/s0008439524000183","url":null,"abstract":"<p>In this paper, we consider the closed spacelike solution to a class of Hessian quotient equations in de Sitter space. Under mild assumptions, we obtain an existence result using standard degree theory based on a priori estimates.</p>","PeriodicalId":501184,"journal":{"name":"Canadian Mathematical Bulletin","volume":"294 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140203229","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Linear independence of series related to the Thue–Morse sequence along powers","authors":"Michael Coons, Yohei Tachiya","doi":"10.4153/s0008439524000195","DOIUrl":"https://doi.org/10.4153/s0008439524000195","url":null,"abstract":"<p>The Thue–Morse sequence <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240321105855809-0602:S0008439524000195:S0008439524000195_inline1.png\"><span data-mathjax-type=\"texmath\"><span>${t(n)}_{ngeqslant 0}$</span></span></img></span></span> is the indicator function of the parity of the number of ones in the binary expansion of nonnegative integers <span>n</span>, where <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240321105855809-0602:S0008439524000195:S0008439524000195_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$t(n)=1$</span></span></img></span></span> (resp. <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240321105855809-0602:S0008439524000195:S0008439524000195_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$=0$</span></span></img></span></span>) if the binary expansion of <span>n</span> has an odd (resp. even) number of ones. In this paper, we generalize a recent result of E. Miyanohara by showing that, for a fixed Pisot or Salem number <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240321105855809-0602:S0008439524000195:S0008439524000195_inline4.png\"><span data-mathjax-type=\"texmath\"><span>$beta&gt;sqrt {varphi }=1.272019ldots $</span></span></img></span></span>, the set of the numbers <span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240321105855809-0602:S0008439524000195:S0008439524000195_eqnu1.png\"><span data-mathjax-type=\"texmath\"><span>$$begin{align*}1,quad sum_{ngeqslant1}frac{t(n)}{beta^{n}},quad sum_{ngeqslant1}frac{t(n^2)}{beta^{n}},quad dots, quad sum_{ngeqslant1}frac{t(n^k)}{beta^{n}},quad dots end{align*}$$</span></span></img></span>is linearly independent over the field <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240321105855809-0602:S0008439524000195:S0008439524000195_inline5.png\"><span data-mathjax-type=\"texmath\"><span>$mathbb {Q}(beta )$</span></span></img></span></span>, where <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240321105855809-0602:S0008439524000195:S0008439524000195_inline6.png\"><span data-mathjax-type=\"texmath\"><span>$varphi :=(1+sqrt {5})/2$</span></span></img></span></span> is the golden ratio. Our result yields that for any integer <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240321105855809-0602:S0008439524000195:S0008439524000195_inline7.png\"><span data-mathjax-type=\"texmath\"><span>$kgeqslant 1$</span><","PeriodicalId":501184,"journal":{"name":"Canadian Mathematical Bulletin","volume":"156 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140203435","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Moments of the central L-values of the Asai lifts","authors":"Wenzhi Luo","doi":"10.4153/s0008439524000171","DOIUrl":"https://doi.org/10.4153/s0008439524000171","url":null,"abstract":"<p>We study some analytic properties of the Asai lifts associated with cuspidal Hilbert modular forms, and prove sharp bounds for the second moment of their central <span>L</span>-values.</p>","PeriodicalId":501184,"journal":{"name":"Canadian Mathematical Bulletin","volume":"22 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140165656","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the Complexity of Extending the Convergence Domain of Newton’s Method Under the Weak Majorant Condition","authors":"Ioannis K. Argyros, S. George","doi":"10.4153/s000843952400016x","DOIUrl":"https://doi.org/10.4153/s000843952400016x","url":null,"abstract":"","PeriodicalId":501184,"journal":{"name":"Canadian Mathematical Bulletin","volume":"46 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140085658","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Hausdorff operators on some classical spaces of analytic functions","authors":"Huayou Xie, Qingze Lin","doi":"10.4153/s0008439524000158","DOIUrl":"https://doi.org/10.4153/s0008439524000158","url":null,"abstract":"<p>In this note, we start on the study of the sufficient conditions for the boundedness of Hausdorff operators <span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240319144838897-0455:S0008439524000158:S0008439524000158_eqnu1.png\"><span data-mathjax-type=\"texmath\"><span>$$ begin{align*}(mathcal{H}_{K,mu}f)(z):=int_{mathbb{D}}K(w)f(sigma_w(z))dmu(w)end{align*} $$</span></span></img></span>on three important function spaces (i.e., derivative Hardy spaces, weighted Dirichlet spaces, and Bloch type spaces), which is a continuation of the previous works of Mirotin et al. Here, <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240319144838897-0455:S0008439524000158:S0008439524000158_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$mu $</span></span></img></span></span> is a positive Radon measure, <span>K</span> is a <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240319144838897-0455:S0008439524000158:S0008439524000158_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$mu $</span></span></img></span></span>-measurable function on the open unit disk <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240319144838897-0455:S0008439524000158:S0008439524000158_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$mathbb {D}$</span></span></img></span></span>, and <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240319144838897-0455:S0008439524000158:S0008439524000158_inline4.png\"><span data-mathjax-type=\"texmath\"><span>$sigma _w(z)$</span></span></img></span></span> is the classical Möbius transform of <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240319144838897-0455:S0008439524000158:S0008439524000158_inline5.png\"><span data-mathjax-type=\"texmath\"><span>$mathbb {D}$</span></span></img></span></span>.</p>","PeriodicalId":501184,"journal":{"name":"Canadian Mathematical Bulletin","volume":"290 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140165966","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}