Canadian Mathematical Bulletin最新文献

{"title":"The degree one Laguerre–Pólya class and the shuffle-word-embedding conjecture","authors":"James E. Pascoe, Hugo J. Woerdeman","doi":"10.4153/s0008439524000146","DOIUrl":"https://doi.org/10.4153/s0008439524000146","url":null,"abstract":"<p>We discuss the class of functions, which are well approximated on compacta by the geometric mean of the eigenvalues of a unital (completely) positive map into a matrix algebra or more generally a type <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240313102706185-0312:S0008439524000146:S0008439524000146_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$II_1$</span></span></img></span></span> factor, using the notion of a Fuglede–Kadison determinant. In two variables, the two classes are the same, but in three or more noncommuting variables, there are generally functions arising from type <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240313102706185-0312:S0008439524000146:S0008439524000146_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$II_1$</span></span></img></span></span> von Neumann algebras, due to the recently established failure of the Connes embedding conjecture. The question of whether or not approximability holds for scalar inputs is shown to be equivalent to a restricted form of the Connes embedding conjecture, the so-called shuffle-word-embedding conjecture.</p>","PeriodicalId":501184,"journal":{"name":"Canadian Mathematical Bulletin","volume":"34 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140125687","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":"Theoretical study of a -Hilfer fractional differential system in Banach spaces","authors":"Oualid Zentar, Mohamed Ziane, Mohammed Al Horani","doi":"10.4153/s0008439524000134","DOIUrl":"https://doi.org/10.4153/s0008439524000134","url":null,"abstract":"<p>In this work, we study the existence of solutions of nonlinear fractional coupled system of <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240312122704388-0228:S0008439524000134:S0008439524000134_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$varphi $</span></span></img></span></span>-Hilfer type in the frame of Banach spaces. We improve a property of a measure of noncompactness in a suitably selected Banach space. Darbo’s fixed point theorem is applied to obtain a new existence result. Finally, the validity of our result is illustrated through an example.</p>","PeriodicalId":501184,"journal":{"name":"Canadian Mathematical Bulletin","volume":"45 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140115188","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":"Some examples of noncommutative projective Calabi–Yau schemes","authors":"Yuki Mizuno","doi":"10.4153/s0008439524000110","DOIUrl":"https://doi.org/10.4153/s0008439524000110","url":null,"abstract":"<p>In this article, we construct some examples of noncommutative projective Calabi–Yau schemes by using noncommutative Segre products and quantum weighted hypersurfaces. We also compare our constructions with commutative Calabi–Yau varieties and examples constructed in Kanazawa (2015, <span>Journal of Pure and Applied Algebra</span> 219, 2771–2780). In particular, we show that some of our constructions are essentially new examples of noncommutative projective Calabi–Yau schemes.</p>","PeriodicalId":501184,"journal":{"name":"Canadian Mathematical Bulletin","volume":"187 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139923296","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":"Nowhere constant families of maps and resolvability","authors":"István Juhász, Jan van Mill","doi":"10.4153/s0008439524000109","DOIUrl":"https://doi.org/10.4153/s0008439524000109","url":null,"abstract":"<p>If <span>X</span> is a topological space and <span>Y</span> is any set, then we call a family <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240221124122868-0846:S0008439524000109:S0008439524000109_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$mathcal {F}$</span></span></img></span></span> of maps from <span>X</span> to <span>Y nowhere constant</span> if for every non-empty open set <span>U</span> in <span>X</span> there is <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240221124122868-0846:S0008439524000109:S0008439524000109_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$f in mathcal {F}$</span></span></img></span></span> with <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240221124122868-0846:S0008439524000109:S0008439524000109_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$|f[U]|&gt; 1$</span></span></img></span></span>, i.e., <span>f</span> is not constant on <span>U</span>. We prove the following result that improves several earlier results in the literature.</p><p>If <span>X</span> is a topological space for which <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240221124122868-0846:S0008439524000109:S0008439524000109_inline4.png\"><span data-mathjax-type=\"texmath\"><span>$C(X)$</span></span></img></span></span>, the family of all continuous maps of <span>X</span> to <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240221124122868-0846:S0008439524000109:S0008439524000109_inline5.png\"><span data-mathjax-type=\"texmath\"><span>$mathbb {R}$</span></span></img></span></span>, is nowhere constant and <span>X</span> has a <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240221124122868-0846:S0008439524000109:S0008439524000109_inline6.png\"><span data-mathjax-type=\"texmath\"><span>$pi $</span></span></img></span></span>-base consisting of connected sets then <span>X</span> is <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240221124122868-0846:S0008439524000109:S0008439524000109_inline7.png\"><span data-mathjax-type=\"texmath\"><span>$mathfrak {c}$</span></span></img></span></span>-resolvable.</p>","PeriodicalId":501184,"journal":{"name":"Canadian Mathematical Bulletin","volume":"34 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139923520","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":"Relations for quadratic Hodge integrals via stable maps","authors":"Georgios Politopoulos","doi":"10.4153/s0008439524000080","DOIUrl":"https://doi.org/10.4153/s0008439524000080","url":null,"abstract":"<p>Following Faber–Pandharipande, we use the virtual localization formula for the moduli space of stable maps to <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240207132305625-0891:S0008439524000080:S0008439524000080_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$mathbb {P}^{1}$</span></span></img></span></span> to compute relations between Hodge integrals. We prove that certain generating series of these integrals are polynomials.</p>","PeriodicalId":501184,"journal":{"name":"Canadian Mathematical Bulletin","volume":"131 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139762502","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 CHARACTERIZATION OF RANDOM ANALYTIC FUNCTIONS SATISFYING BLASCHKE-TYPE CONDITIONS","authors":"Yongjiang Duan, Xiang Fang, NA Zhan","doi":"10.4153/s0008439524000079","DOIUrl":"https://doi.org/10.4153/s0008439524000079","url":null,"abstract":"","PeriodicalId":501184,"journal":{"name":"Canadian Mathematical Bulletin","volume":"5 12","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139616716","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":"How to determine a curve singularity","authors":"J. Elias","doi":"10.4153/s000843952400002x","DOIUrl":"https://doi.org/10.4153/s000843952400002x","url":null,"abstract":"<p>We characterize the finite codimension sub-<span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240127042025273-0301:S000843952400002X:S000843952400002X_inline1.png\"><span data-mathjax-type=\"texmath\"><span>${mathbf {k}}$</span></span></img></span></span>-algebras of <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240127042025273-0301:S000843952400002X:S000843952400002X_inline2.png\"><span data-mathjax-type=\"texmath\"><span>${mathbf {k}}[![t]!]$</span></span></img></span></span> as the solutions of a computable finite family of higher differential operators. For this end, we establish a duality between such a sub-algebras and the finite codimension <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240127042025273-0301:S000843952400002X:S000843952400002X_inline3.png\"><span data-mathjax-type=\"texmath\"><span>${mathbf {k}}$</span></span></img></span></span>-vector spaces of <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240127042025273-0301:S000843952400002X:S000843952400002X_inline4.png\"><span data-mathjax-type=\"texmath\"><span>${mathbf {k}}[u]$</span></span></img></span></span>, this ring acts on <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240127042025273-0301:S000843952400002X:S000843952400002X_inline5.png\"><span data-mathjax-type=\"texmath\"><span>${mathbf {k}}[![t]!]$</span></span></img></span></span> by differentiation.</p>","PeriodicalId":501184,"journal":{"name":"Canadian Mathematical Bulletin","volume":"329 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139589878","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 rigid analytic proof that the Abel–Jacobi map extends to compact-type models","authors":"Taylor Dupuy, Joseph Rabinoff","doi":"10.4153/s0008439524000031","DOIUrl":"https://doi.org/10.4153/s0008439524000031","url":null,"abstract":"<p>Let <span>K</span> be a non-Archimedean valued field with valuation ring <span>R</span>. Let <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240207131109559-0437:S0008439524000031:S0008439524000031_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$C_eta $</span></span></img></span></span> be a <span>K</span>-curve with compact-type reduction, so its Jacobian <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240207131109559-0437:S0008439524000031:S0008439524000031_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$J_eta $</span></span></img></span></span> extends to an abelian <span>R</span>-scheme <span>J</span>. We prove that an Abel–Jacobi map <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240207131109559-0437:S0008439524000031:S0008439524000031_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$iota colon C_eta to J_eta $</span></span></img></span></span> extends to a morphism <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240207131109559-0437:S0008439524000031:S0008439524000031_inline4.png\"><span data-mathjax-type=\"texmath\"><span>$Cto J$</span></span></img></span></span>, where <span>C</span> is a compact-type <span>R</span>-model of <span>J</span>, and we show this is a closed immersion when the special fiber of <span>C</span> has no rational components. To do so, we apply a rigid-analytic “fiberwise” criterion for a morphism to extend to integral models, and geometric results of Bosch and Lütkebohmert on the analytic structure of <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240207131109559-0437:S0008439524000031:S0008439524000031_inline5.png\"><span data-mathjax-type=\"texmath\"><span>$J_eta $</span></span></img></span></span>.</p>","PeriodicalId":501184,"journal":{"name":"Canadian Mathematical Bulletin","volume":"22 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139762317","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 EXTENSION OF BOUNDED HOLOMORPHIC MAPS FROM GLEASON PARTS OF THE MAXIMAL IDEAL SPACE OF","authors":"Alexander Brudnyi","doi":"10.4153/s0008439524000018","DOIUrl":"https://doi.org/10.4153/s0008439524000018","url":null,"abstract":"","PeriodicalId":501184,"journal":{"name":"Canadian Mathematical Bulletin","volume":"53 22","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139446029","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 root of unity ambiguity in a formula for the Brumer–Stark units","authors":"Matthew H. Honnor","doi":"10.4153/s0008439523001005","DOIUrl":"https://doi.org/10.4153/s0008439523001005","url":null,"abstract":"<p>We prove a conjectural formula for the Brumer–Stark units. Dasgupta and Kakde have shown the formula is correct up to a bounded root of unity. In this paper, we resolve the ambiguity in their result. We also remove an assumption from Dasgupta–Kakde’s result on the formula.</p>","PeriodicalId":501184,"journal":{"name":"Canadian Mathematical Bulletin","volume":"50 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139481587","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}