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Decidability problem for exponential equations in finitely presented groups 有限存在群中指数方程的可判定性问题
IF 0.6 4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2022-11-22 DOI: 10.4153/S0008439522000698
O. Bogopolski, A. Ivanov
{"title":"Decidability problem for exponential equations in finitely presented groups","authors":"O. Bogopolski, A. Ivanov","doi":"10.4153/S0008439522000698","DOIUrl":"https://doi.org/10.4153/S0008439522000698","url":null,"abstract":"Abstract We study the following decision problem: given an exponential equation \u0000$a_1g_1^{x_1}a_2g_2^{x_2}dots a_ng_n^{x_n}=1$\u0000 over a recursively presented group G, decide if it has a solution with all \u0000$x_i$\u0000 in \u0000$mathbb {Z}$\u0000 . We construct a finitely presented group G where this problem is decidable for equations with one variable and is undecidable for equations with two variables. We also study functions estimating possible solutions of such an equation through the lengths of its coefficients with respect to a given generating set of G. Another result concerns Turing degrees of some natural fragments of the above problem.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44524963","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}
引用次数: 1
Norms on complex matrices induced by random vectors 随机向量诱导的复矩阵范数
IF 0.6 4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2022-11-15 DOI: 10.4153/S0008439522000741
Ángel Chávez, S. Garcia, Jackson Hurley
{"title":"Norms on complex matrices induced by random vectors","authors":"Ángel Chávez, S. Garcia, Jackson Hurley","doi":"10.4153/S0008439522000741","DOIUrl":"https://doi.org/10.4153/S0008439522000741","url":null,"abstract":"Abstract We introduce a family of norms on the \u0000$n times n$\u0000 complex matrices. These norms arise from a probabilistic framework, and their construction and validation involve probability theory, partition combinatorics, and trace polynomials in noncommuting variables. As a consequence, we obtain a generalization of Hunter’s positivity theorem for the complete homogeneous symmetric polynomials.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49456108","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}
引用次数: 2
Słociński–Wold decompositions for row isometries Słociński-Wold分解行等距
IF 0.6 4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2022-11-14 DOI: 10.4153/S0008439522000686
Adam H. Fuller
{"title":"Słociński–Wold decompositions for row isometries","authors":"Adam H. Fuller","doi":"10.4153/S0008439522000686","DOIUrl":"https://doi.org/10.4153/S0008439522000686","url":null,"abstract":"Abstract Słociński gave sufficient conditions for commuting isometries to have a nice Wold-like decomposition. In this note, we provide analogous results for row isometries satisfying certain commutation relations. Other than known results for doubly commuting row isometries, we provide sufficient conditions for a Wold decomposition based on the Lebesgue decomposition of the row isometries.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41475756","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}
引用次数: 0
A multiplicative Kowalski–Słodkowski theorem for $C^star $ -algebras $C^star$-代数的乘法Kowalski–Słodkowski定理
IF 0.6 4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2022-11-02 DOI: 10.4153/S0008439522000662
C. Touré, R. Brits, Geethika Sebastian
{"title":"A multiplicative Kowalski–Słodkowski theorem for \u0000$C^star $\u0000 -algebras","authors":"C. Touré, R. Brits, Geethika Sebastian","doi":"10.4153/S0008439522000662","DOIUrl":"https://doi.org/10.4153/S0008439522000662","url":null,"abstract":"Abstract We present here a multiplicative version of the classical Kowalski–Słodkowski theorem, which identifies the characters among the collection of all functionals on a complex and unital Banach algebra A. In particular, we show that, if A is a \u0000$C^star $\u0000 -algebra, and if \u0000$phi :Ato mathbb C $\u0000 is a continuous function satisfying \u0000$ phi (x)phi (y) in sigma (xy) $\u0000 for all \u0000$x,yin A$\u0000 (where \u0000$sigma $\u0000 denotes the spectrum), then either \u0000$phi $\u0000 is a character of A or \u0000$-phi $\u0000 is a character of A.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42053749","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On a conjecture of M. R. Murty and V. K. Murty 论Murty先生和v.k. Murty的猜想
IF 0.6 4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2022-10-25 DOI: 10.4153/S0008439522000650
Yuchen Ding
{"title":"On a conjecture of M. R. Murty and V. K. Murty","authors":"Yuchen Ding","doi":"10.4153/S0008439522000650","DOIUrl":"https://doi.org/10.4153/S0008439522000650","url":null,"abstract":"Abstract Let \u0000$omega ^*(n)$\u0000 be the number of primes p such that \u0000$p-1$\u0000 divides n. Recently, M. R. Murty and V. K. Murty proved that \u0000$$ begin{align*}x(loglog x)^3llsum_{nle x}omega^*(n)^2ll xlog x.end{align*} $$\u0000 They further conjectured that there is some positive constant C such that \u0000$$ begin{align*}sum_{nle x}omega^*(n)^2sim Cxlog x,end{align*} $$\u0000 as \u0000$xrightarrow infty $\u0000 . In this short note, we give the correct order of the sum by showing that \u0000$$ begin{align*}sum_{nle x}omega^*(n)^2asymp xlog x.end{align*} $$","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42280774","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}
引用次数: 0
Projective freeness and stable rank of algebras of complex-valued BV functions 复值BV函数代数的射影自由与稳定秩
IF 0.6 4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2022-10-19 DOI: 10.4153/S000843952300005X
A. Brudnyi
{"title":"Projective freeness and stable rank of algebras of complex-valued BV functions","authors":"A. Brudnyi","doi":"10.4153/S000843952300005X","DOIUrl":"https://doi.org/10.4153/S000843952300005X","url":null,"abstract":"Abstract The paper investigates the algebraic properties of weakly inverse-closed complex Banach function algebras generated by functions of bounded variation on a finite interval. It is proved that such algebras have Bass stable rank 1 and are projective-free if they do not contain nontrivial idempotents. These properties are derived from a new result on the vanishing of the second Čech cohomology group of the polynomially convex hull of a continuum of a finite linear measure described by the classical H. Alexander theorem.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43189482","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}
引用次数: 0
Nearly sharp Lang–Weil bounds for a hypersurface 超曲面的近锐Lang-Weil界
IF 0.6 4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2022-10-18 DOI: 10.4153/S0008439522000625
Kaloyan Slavov
{"title":"Nearly sharp Lang–Weil bounds for a hypersurface","authors":"Kaloyan Slavov","doi":"10.4153/S0008439522000625","DOIUrl":"https://doi.org/10.4153/S0008439522000625","url":null,"abstract":"Abstract We improve to nearly optimal the known asymptotic and explicit bounds for the number of \u0000$mathbb {F}_q$\u0000 -rational points on a geometrically irreducible hypersurface over a (large) finite field. The proof involves a Bertini-type probabilistic combinatorial technique. Namely, we slice the given hypersurface with a random plane.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42649683","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}
引用次数: 1
Some remarks on approximation in several complex variables 关于几种复变量近似的几点说明
IF 0.6 4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2022-10-17 DOI: 10.4153/S0008439522000613
J. Falcó, P. Gauthier, Myrto Manolaki, V. Nestoridis
{"title":"Some remarks on approximation in several complex variables","authors":"J. Falcó, P. Gauthier, Myrto Manolaki, V. Nestoridis","doi":"10.4153/S0008439522000613","DOIUrl":"https://doi.org/10.4153/S0008439522000613","url":null,"abstract":"Abstract In Gauthier, Manolaki, and Nestoridis (2021, Advances in Mathematics 381, 107649), in order to correct a false Mergelyan-type statement given in Gamelin and Garnett (1969, Transactions of the American Mathematical Society 143, 187–200) on uniform approximation on compact sets K in \u0000$mathbb C^d$\u0000 , the authors introduced a natural function algebra \u0000$A_D(K)$\u0000 which is smaller than the classical one \u0000$A(K)$\u0000 . In the present paper, we investigate when these two algebras coincide and compare them with the classes of all plausibly approximable functions by polynomials or rational functions or functions holomorphic on open sets containing the compact set K. Finally, we introduce a notion of O-hull of K and strengthen known results.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44229267","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}
引用次数: 0
A note about charts built by Eriksson-Bique and Soultanis on metric measure spaces 关于Eriksson-Bique和Soultanis在度量度量空间上建立的图表的注释
IF 0.6 4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2022-10-13 DOI: 10.4153/s0008439523000486
Luca Gennaioli, N. Gigli
{"title":"A note about charts built by Eriksson-Bique and Soultanis on metric measure spaces","authors":"Luca Gennaioli, N. Gigli","doi":"10.4153/s0008439523000486","DOIUrl":"https://doi.org/10.4153/s0008439523000486","url":null,"abstract":"\u0000 This note is motivated by recent studies by Eriksson-Bique and Soultanis about the construction of charts in general metric measure spaces. We analyze their construction and provide an alternative and simpler proof of the fact that these charts exist on sets of finite Hausdorff dimension. The observation made here offers also some simplification about the study of the relation between the reference measure and the charts in the setting of \u0000 \u0000 \u0000 \u0000$text {RCD}$\u0000\u0000 \u0000 spaces.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46462070","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}
引用次数: 0
A note on the column-row property 列-行属性的注释
IF 0.6 4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2022-10-13 DOI: 10.4153/s0008439523000322
Samya Kumar Ray, S. Sarkar
{"title":"A note on the column-row property","authors":"Samya Kumar Ray, S. Sarkar","doi":"10.4153/s0008439523000322","DOIUrl":"https://doi.org/10.4153/s0008439523000322","url":null,"abstract":"In this article, we study the following question asked by Michael Hartz in a recent paper cite{Hartz}: textit{which operator spaces satisfy the column-row property?} We provide a complete classification of the column-row property for non-commutative $L_{p}$-spaces over semifinite von Neumann algebras. We study other relevant properties of operator spaces that are related to the column-row property and discuss their existence and non-existence for various natural examples of operator spaces.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48389717","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}
引用次数: 0
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