Canadian Mathematical Bulletin最新文献

{"title":"On irreducible representations of Fuchsian groups","authors":"Vikraman Balaji, Yashonidhi Pandey","doi":"10.4153/s0008439524000389","DOIUrl":"https://doi.org/10.4153/s0008439524000389","url":null,"abstract":"<p>Let <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240910160050503-0755:S0008439524000389:S0008439524000389_inline1.png\"><span data-mathjax-type=\"texmath\"><span>${mathcal {R}} subset mathbb {P}^1_{mathbb {C}}$</span></span></img></span></span> be a finite subset of markings. Let <span>G</span> be an almost simple simply-connected algebraic group over <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240910160050503-0755:S0008439524000389:S0008439524000389_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$mathbb {C}$</span></span></img></span></span>. Let <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240910160050503-0755:S0008439524000389:S0008439524000389_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$K_G$</span></span></img></span></span> denote the compact real form of <span>G</span>. Suppose for each lasso <span>l</span> around the marked point, a conjugacy class <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240910160050503-0755:S0008439524000389:S0008439524000389_inline4.png\"><span data-mathjax-type=\"texmath\"><span>$C_l$</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:20240910160050503-0755:S0008439524000389:S0008439524000389_inline5.png\"><span data-mathjax-type=\"texmath\"><span>$K_G$</span></span></img></span></span> is prescribed. The aim of this paper is to give verifiable criteria for the existence of an <span>irreducible</span> homomorphism of <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240910160050503-0755:S0008439524000389:S0008439524000389_inline6.png\"><span data-mathjax-type=\"texmath\"><span>$pi _{1}(mathbb P^1_{mathbb {C}} ,{backslash}, {mathcal {R}})$</span></span></img></span></span> into <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240910160050503-0755:S0008439524000389:S0008439524000389_inline7.png\"><span data-mathjax-type=\"texmath\"><span>$K_G$</span></span></img></span></span> such that the image of <span>l</span> lies in <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240910160050503-0755:S0008439524000389:S0008439524000389_inline8.png\"><span data-mathjax-type=\"texmath\"><span>$C_l$</span></span></img></span></span>.</p>","PeriodicalId":501184,"journal":{"name":"Canadian Mathematical Bulletin","volume":"22 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142184014","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":"Strong digraph groups","authors":"Mehmet Sefa Cihan, Gerald Williams","doi":"10.4153/s0008439524000390","DOIUrl":"https://doi.org/10.4153/s0008439524000390","url":null,"abstract":"<p>A digraph group is a group defined by non-empty presentation with the property that each relator is of the form <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240913163950622-0833:S0008439524000390:S0008439524000390_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$R(x, y)$</span></span></img></span></span>, where <span>x</span> and <span>y</span> are distinct generators and <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240913163950622-0833:S0008439524000390:S0008439524000390_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$R(cdot , cdot )$</span></span></img></span></span> is determined by some fixed cyclically reduced word <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240913163950622-0833:S0008439524000390:S0008439524000390_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$R(a, b)$</span></span></img></span></span> that involves both <span>a</span> and <span>b</span>. Associated with each such presentation is a digraph whose vertices correspond to the generators and whose arcs correspond to the relators. In this article, we consider digraph groups for strong digraphs that are digon-free and triangle-free. We classify when the digraph group is finite and show that in these cases it is cyclic, giving its order. We apply this result to the Cayley digraph of the generalized quaternion group, to circulant digraphs, and to Cartesian and direct products of strong digraphs.</p>","PeriodicalId":501184,"journal":{"name":"Canadian Mathematical Bulletin","volume":"63 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142259755","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":"General theorems for uniform asymptotic stability and boundedness in finitely delayed difference systems","authors":"Youssef N. Raffoul","doi":"10.4153/s0008439524000353","DOIUrl":"https://doi.org/10.4153/s0008439524000353","url":null,"abstract":"<p>The paper deals with boundedness of solutions and uniform asymptotic stability of the zero solution. In our current undertaking, we aim to solve two open problems that were proposed by the author in his book <span>Qualitative theory of Volterra difference equations</span> (2018, Springer, Cham). Our approach centers on finding the appropriate Lyapunov functional that satisfies specific conditions, incorporating the concept of wedges.</p>","PeriodicalId":501184,"journal":{"name":"Canadian Mathematical Bulletin","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142259756","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":"Counting elements of the congruence subgroup","authors":"Kamil Bulinski, Igor E. Shparlinski","doi":"10.4153/s0008439524000365","DOIUrl":"https://doi.org/10.4153/s0008439524000365","url":null,"abstract":"","PeriodicalId":501184,"journal":{"name":"Canadian Mathematical Bulletin","volume":"87 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141111780","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":"Minimal Subfields of Elliptic Curves","authors":"Samprit Ghosh","doi":"10.4153/s0008439524000341","DOIUrl":"https://doi.org/10.4153/s0008439524000341","url":null,"abstract":"","PeriodicalId":501184,"journal":{"name":"Canadian Mathematical Bulletin","volume":"56 10","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141112657","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 some convexity questions of Handelman","authors":"Brian Simanek","doi":"10.4153/s0008439524000316","DOIUrl":"https://doi.org/10.4153/s0008439524000316","url":null,"abstract":"<p>We resolve some questions posed by Handelman in 1996 concerning log convex <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240529095608048-0637:S0008439524000316:S0008439524000316_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$L^1$</span></span></img></span></span> functions. In particular, we give a negative answer to a question he posed concerning the integrability of <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240529095608048-0637:S0008439524000316:S0008439524000316_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$h^2(x)/h(2x)$</span></span></img></span></span> when <span>h</span> is <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240529095608048-0637:S0008439524000316:S0008439524000316_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$L^1$</span></span></img></span></span> and log convex and <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240529095608048-0637:S0008439524000316:S0008439524000316_inline4.png\"><span data-mathjax-type=\"texmath\"><span>$h(n)^{1/n}rightarrow 1$</span></span></img></span></span>.</p>","PeriodicalId":501184,"journal":{"name":"Canadian Mathematical Bulletin","volume":"2012 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141197403","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 Harnack inequality and harmonic Schwarz lemma","authors":"Rahim Kargar","doi":"10.4153/s0008439524000298","DOIUrl":"https://doi.org/10.4153/s0008439524000298","url":null,"abstract":"<p>In this paper, we study the <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240529073251569-0683:S0008439524000298:S0008439524000298_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$(s, C(s))$</span></span></img></span></span>-Harnack inequality in a domain <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240529073251569-0683:S0008439524000298:S0008439524000298_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$Gsubset mathbb {R}^n$</span></span></img></span></span> for <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240529073251569-0683:S0008439524000298:S0008439524000298_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$sin (0,1)$</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:20240529073251569-0683:S0008439524000298:S0008439524000298_inline4.png\"><span data-mathjax-type=\"texmath\"><span>$C(s)geq 1$</span></span></img></span></span> and present a series of inequalities related to <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240529073251569-0683:S0008439524000298:S0008439524000298_inline5.png\"><span data-mathjax-type=\"texmath\"><span>$(s, C(s))$</span></span></img></span></span>-Harnack functions and the Harnack metric. We also investigate the behavior of the Harnack metric under <span>K</span>-quasiconformal and <span>K</span>-quasiregular mappings, where <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240529073251569-0683:S0008439524000298:S0008439524000298_inline6.png\"><span data-mathjax-type=\"texmath\"><span>$Kgeq 1$</span></span></img></span></span>. Finally, we provide a type of harmonic Schwarz lemma and improve the Schwarz–Pick estimate for a real-valued harmonic function.</p>","PeriodicalId":501184,"journal":{"name":"Canadian Mathematical Bulletin","volume":"29 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141189008","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":"Phase retrieval on circles and lines","authors":"Isabelle Chalendar, Jonathan R. Partington","doi":"10.4153/s0008439524000304","DOIUrl":"https://doi.org/10.4153/s0008439524000304","url":null,"abstract":"<p>Let <span>f</span> and <span>g</span> be analytic functions 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:20240524113158354-0988:S0008439524000304:S0008439524000304_inline1.png\"><span data-mathjax-type=\"texmath\"><span>${mathbb D}$</span></span></img></span></span> such that <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240524113158354-0988:S0008439524000304:S0008439524000304_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$|f|=|g|$</span></span></img></span></span> on a set <span>A</span>. We give an alternative proof of the result of Perez that there exists <span>c</span> in the unit circle <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240524113158354-0988:S0008439524000304:S0008439524000304_inline3.png\"><span data-mathjax-type=\"texmath\"><span>${mathbb T}$</span></span></img></span></span> such that <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240524113158354-0988:S0008439524000304:S0008439524000304_inline4.png\"><span data-mathjax-type=\"texmath\"><span>$f=cg$</span></span></img></span></span> when <span>A</span> is the union of two lines in <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240524113158354-0988:S0008439524000304:S0008439524000304_inline5.png\"><span data-mathjax-type=\"texmath\"><span>${mathbb D}$</span></span></img></span></span> intersecting at an angle that is an irrational multiple of <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240524113158354-0988:S0008439524000304:S0008439524000304_inline6.png\"><span data-mathjax-type=\"texmath\"><span>$pi $</span></span></img></span></span>, and from this, deduce a sequential generalization of the result. Similarly, the same conclusion is valid when <span>f</span> and <span>g</span> are in the Nevanlinna class and <span>A</span> is the union of the unit circle and an interior circle, tangential or not. We also provide sequential versions of this result and analyze the case <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240524113158354-0988:S0008439524000304:S0008439524000304_inline7.png\"><span data-mathjax-type=\"texmath\"><span>$A=r{mathbb T}$</span></span></img></span></span>. Finally, we examine the most general situation when there is equality on two distinct circles in the disk, proving a result or counterexample for each possible configuration.</p>","PeriodicalId":501184,"journal":{"name":"Canadian Mathematical Bulletin","volume":"29 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141169773","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":"Pieri rules for skew dual immaculate functions","authors":"Elizabeth Niese, Sheila Sundaram, Stephanie van Willigenburg, Shiyun Wang","doi":"10.4153/s0008439524000274","DOIUrl":"https://doi.org/10.4153/s0008439524000274","url":null,"abstract":"<p>In this paper, we give Pieri rules for skew dual immaculate functions and their recently discovered row-strict counterparts. We establish our rules using a right-action analogue of the skew Littlewood–Richardson rule for Hopf algebras of Lam–Lauve–Sottile. We also obtain Pieri rules for row-strict (dual) immaculate functions.</p>","PeriodicalId":501184,"journal":{"name":"Canadian Mathematical Bulletin","volume":"24 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141061019","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":"Adjoint Reidemeister torsions of some 3-manifolds obtained by Dehn surgeries","authors":"Naoko Wakijo","doi":"10.4153/s0008439524000262","DOIUrl":"https://doi.org/10.4153/s0008439524000262","url":null,"abstract":"<p>We determine the adjoint Reidemeister torsion of a <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240508060747903-0951:S0008439524000262:S0008439524000262_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$3$</span></span></img></span></span>-manifold obtained by some Dehn surgery along <span>K</span>, where <span>K</span> is either the figure-eight knot or the <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240508060747903-0951:S0008439524000262:S0008439524000262_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$5_2$</span></span></img></span></span>-knot. As in a vanishing conjecture (Benini et al. (2020, <span>Journal of High Energy Physics</span> 2020, 57), Gang et al. (2020, <span>Journal of High Energy Physics</span> 2020, 164), and Gang et al. (2021, <span>Advances in Theoretical and Mathematical Physics</span> 25, 1819–1845)), we consider a similar conjecture and show that the conjecture holds for the 3-manifold.</p>","PeriodicalId":501184,"journal":{"name":"Canadian Mathematical Bulletin","volume":"60 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140934253","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}