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FERMAT’S LAST THEOREM OVER AND 再来一遍费马最后定理
IF 0.7 3区 数学
Canadian Journal of Mathematics-Journal Canadien De Mathematiques Pub Date : 2022-11-21 DOI: 10.4153/s0008414x22000633
Imin Chen, Aisosa Efemwonkieke, David Sun
{"title":"FERMAT’S LAST THEOREM OVER AND","authors":"Imin Chen, Aisosa Efemwonkieke, David Sun","doi":"10.4153/s0008414x22000633","DOIUrl":"https://doi.org/10.4153/s0008414x22000633","url":null,"abstract":"","PeriodicalId":55284,"journal":{"name":"Canadian Journal of Mathematics-Journal Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76572386","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Correspondence theorems for Hopf algebroids with applications to affine groupoids Hopf代数群的对应定理及其在仿射群上的应用
IF 0.7 3区 数学
Canadian Journal of Mathematics-Journal Canadien De Mathematiques Pub Date : 2022-11-14 DOI: 10.4153/s0008414x23000238
L. EL KAOUTIT, Aryan Ghobadi, P. Saracco, J. Vercruysse
{"title":"Correspondence theorems for Hopf algebroids with applications to affine groupoids","authors":"L. EL KAOUTIT, Aryan Ghobadi, P. Saracco, J. Vercruysse","doi":"10.4153/s0008414x23000238","DOIUrl":"https://doi.org/10.4153/s0008414x23000238","url":null,"abstract":"We provide a correspondence between one-sided coideal subrings and one-sided ideal two-sided coideals in an arbitrary bialgebroid. We prove that, under some expected additional conditions, this correspondence becomes bijective for Hopf algebroids. As an application, we investigate normal Hopf ideals in commutative Hopf algebroids (affine groupoid schemes) in connection with the study of normal affine subgroupoids.","PeriodicalId":55284,"journal":{"name":"Canadian Journal of Mathematics-Journal Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88727652","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Riesz-type criteria for L-functions in the Selberg class Selberg类中l函数的riesz型准则
IF 0.7 3区 数学
Canadian Journal of Mathematics-Journal Canadien De Mathematiques Pub Date : 2022-11-05 DOI: 10.4153/s0008414x23000354
Shivajee Gupta, A. Vatwani
{"title":"Riesz-type criteria for L-functions in the Selberg class","authors":"Shivajee Gupta, A. Vatwani","doi":"10.4153/s0008414x23000354","DOIUrl":"https://doi.org/10.4153/s0008414x23000354","url":null,"abstract":"We formulate a generalization of Riesz-type criteria in the setting of $L$-functions belonging to the Selberg class. We obtain a criterion which is sufficient for the Grand Riemann Hypothesis (GRH) for $L$-functions satisfying axioms of the Selberg class without imposing the Ramanujan hypothesis on their coefficients. We also construct a subclass of the Selberg class and prove a necessary criterion for GRH for $L$-functions in this subclass. Identities of Ramanujan-Hardy-Littlewood type are also established in this setting, specific cases of which yield new transformation formulas involving special values of the Meijer $G$-function of the type $G^{n 0}_{0 n}$.","PeriodicalId":55284,"journal":{"name":"Canadian Journal of Mathematics-Journal Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78661854","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Abel universal functions 阿贝尔泛函数
IF 0.7 3区 数学
Canadian Journal of Mathematics-Journal Canadien De Mathematiques Pub Date : 2022-10-26 DOI: 10.4153/S0008414X22000578
S. Charpentier, A. Mouze
{"title":"Abel universal functions","authors":"S. Charpentier, A. Mouze","doi":"10.4153/S0008414X22000578","DOIUrl":"https://doi.org/10.4153/S0008414X22000578","url":null,"abstract":"Abstract Given a sequence \u0000$varrho =(r_n)_nin [0,1)$\u0000 tending to \u0000$1$\u0000 , we consider the set \u0000${mathcal {U}}_A({mathbb {D}},varrho )$\u0000 of Abel universal functions consisting of holomorphic functions f in the open unit disk \u0000$mathbb {D}$\u0000 such that for any compact set K included in the unit circle \u0000${mathbb {T}}$\u0000 , different from \u0000${mathbb {T}}$\u0000 , the set \u0000${zmapsto f(r_n cdot )vert _K:nin mathbb {N}}$\u0000 is dense in the space \u0000${mathcal {C}}(K)$\u0000 of continuous functions on K. It is known that the set \u0000${mathcal {U}}_A({mathbb {D}},varrho )$\u0000 is residual in \u0000$H(mathbb {D})$\u0000 . We prove that it does not coincide with any other classical sets of universal holomorphic functions. In particular, it is not even comparable in terms of inclusion to the set of holomorphic functions whose Taylor polynomials at \u0000$0$\u0000 are dense in \u0000${mathcal {C}}(K)$\u0000 for any compact set \u0000$Ksubset {mathbb {T}}$\u0000 different from \u0000${mathbb {T}}$\u0000 . Moreover, we prove that the class of Abel universal functions is not invariant under the action of the differentiation operator. Finally, an Abel universal function can be viewed as a universal vector of the sequence of dilation operators \u0000$T_n:fmapsto f(r_n cdot )$\u0000 acting on \u0000$H(mathbb {D})$\u0000 . Thus, we study the dynamical properties of \u0000$(T_n)_n$\u0000 such as the multiuniversality and the (common) frequent universality. All the proofs are constructive.","PeriodicalId":55284,"journal":{"name":"Canadian Journal of Mathematics-Journal Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74729135","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Application of capacities to space–time fractional dissipative equations I: regularity and the blow-up set 容量在时空分数阶耗散方程中的应用I:正则性与爆破集
IF 0.7 3区 数学
Canadian Journal of Mathematics-Journal Canadien De Mathematiques Pub Date : 2022-10-25 DOI: 10.4153/s0008414x22000566
Pengtao Li, Zhichun Zhai
{"title":"Application of capacities to space–time fractional dissipative equations I: regularity and the blow-up set","authors":"Pengtao Li, Zhichun Zhai","doi":"10.4153/s0008414x22000566","DOIUrl":"https://doi.org/10.4153/s0008414x22000566","url":null,"abstract":"Abstract We apply capacities to explore the space–time fractional dissipative equation: (0.1) \u0000$$ begin{align} left{begin{aligned} &partial^{beta}_{t}u(t,x)=-nu(-Delta)^{alpha/2}u(t,x)+f(t,x),quad (t,x)inmathbb R^{1+n}_{+}, &u(0,x)=varphi(x), xinmathbb R^{n}, end{aligned}right. end{align} $$\u0000 where \u0000$alpha>n$\u0000 and \u0000$beta in (0,1)$\u0000 . In this paper, we focus on the regularity and the blow-up set of mild solutions to (0.1). First, we establish the Strichartz-type estimates for the homogeneous term \u0000$R_{alpha ,beta }(varphi )$\u0000 and inhomogeneous term \u0000$G_{alpha ,beta }(g)$\u0000 , respectively. Second, we obtain some space–time estimates for \u0000$G_{alpha ,beta }(g).$\u0000 Based on these estimates, we prove that the continuity of \u0000$R_{alpha ,beta }(varphi )(t,x)$\u0000 and the Hölder continuity of \u0000$G_{alpha ,beta }(g)(t,x)$\u0000 on \u0000$mathbb {R}^{1+n}_+,$\u0000 which implies a Moser–Trudinger-type estimate for \u0000$G_{alpha ,beta }.$\u0000 Then, for a newly introduced \u0000$L^{q}_{t}L^p_{x}$\u0000 -capacity related to the space–time fractional dissipative operator \u0000$partial ^{beta }_{t}+(-Delta )^{alpha /2},$\u0000 we perform the geometric-measure-theoretic analysis and establish its basic properties. Especially, we estimate the capacity of fractional parabolic balls in \u0000$mathbb {R}^{1+n}_+$\u0000 by using the Strichartz estimates and the Moser–Trudinger-type estimate for \u0000$G_{alpha ,beta }.$\u0000 A strong-type estimate of the \u0000$L^{q}_{t}L^p_{x}$\u0000 -capacity and an embedding of Lorentz spaces are also derived. Based on these results, especially the Strichartz-type estimates and the \u0000$L^{q}_{t}L^p_{x}$\u0000 -capacity of fractional parabolic balls, we deduce the size, i.e., the Hausdorff dimension, of the blow-up set of solutions to (0.1).","PeriodicalId":55284,"journal":{"name":"Canadian Journal of Mathematics-Journal Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72391809","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Reconstruction problems of convex bodies from surface area measures and lightness functions 基于表面积测度和亮度函数的凸体重构问题
IF 0.7 3区 数学
Canadian Journal of Mathematics-Journal Canadien De Mathematiques Pub Date : 2022-10-03 DOI: 10.4153/S0008414X22000505
G. Leng, Chang Liu, Dongmeng Xi
{"title":"Reconstruction problems of convex bodies from surface area measures and lightness functions","authors":"G. Leng, Chang Liu, Dongmeng Xi","doi":"10.4153/S0008414X22000505","DOIUrl":"https://doi.org/10.4153/S0008414X22000505","url":null,"abstract":"Abstract First, we build a computational procedure to reconstruct the convex body from a pre-given surface area measure. Nontrivially, we prove the convergence of this procedure. Then, the sufficient and necessary conditions of a Sobolev binary function to be a lightness function of a convex body are investigated. Finally, we present a computational procedure to compute the curvature function from a pre-given lightness function, and then we reconstruct the convex body from this curvature function by using the first procedure. The convergence is also proved. The main computations in both procedures are simply about the spherical harmonics.","PeriodicalId":55284,"journal":{"name":"Canadian Journal of Mathematics-Journal Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84287393","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
CJM volume 74 issue 5 Cover and Front matter CJM第74卷第5期封面和封面问题
IF 0.7 3区 数学
Canadian Journal of Mathematics-Journal Canadien De Mathematiques Pub Date : 2022-10-01 DOI: 10.4153/s0008414x2200044x
Ming Xu, Vladimir S. Matveev
{"title":"CJM volume 74 issue 5 Cover and Front matter","authors":"Ming Xu, Vladimir S. Matveev","doi":"10.4153/s0008414x2200044x","DOIUrl":"https://doi.org/10.4153/s0008414x2200044x","url":null,"abstract":"","PeriodicalId":55284,"journal":{"name":"Canadian Journal of Mathematics-Journal Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87143996","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
CJM volume 74 issue 5 Cover and Back matter CJM第74卷第5期封面和封底
IF 0.7 3区 数学
Canadian Journal of Mathematics-Journal Canadien De Mathematiques Pub Date : 2022-10-01 DOI: 10.4153/s0008414x22000451
{"title":"CJM volume 74 issue 5 Cover and Back matter","authors":"","doi":"10.4153/s0008414x22000451","DOIUrl":"https://doi.org/10.4153/s0008414x22000451","url":null,"abstract":"","PeriodicalId":55284,"journal":{"name":"Canadian Journal of Mathematics-Journal Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84861241","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
THE COLORED JONES POLYNOMIAL OF THE FIGURE-EIGHT KNOT AND A QUANTUM MODULARITY 数字8结的彩色琼斯多项式和量子模性
IF 0.7 3区 数学
Canadian Journal of Mathematics-Journal Canadien De Mathematiques Pub Date : 2022-09-16 DOI: 10.4153/s0008414x23000172
H. Murakami
{"title":"THE COLORED JONES POLYNOMIAL OF THE FIGURE-EIGHT KNOT AND A QUANTUM MODULARITY","authors":"H. Murakami","doi":"10.4153/s0008414x23000172","DOIUrl":"https://doi.org/10.4153/s0008414x23000172","url":null,"abstract":"We study the asymptotic behavior of the $N$-dimensional colored Jones polynomial of the figure-eight knot evaluated at $expbigl((u+2ppii)/Nbigr)$, where $u$ is a small real number and $p$ is a positive integer. We show that it is asymptotically equivalent to the product of the $p$-dimensional colored Jones polynomial evaluated at $expbigl(4Npi^2/(u+2ppii)bigr)$ and a term that grows exponentially with growth rate determined by the Chern--Simons invariant. This indicates a quantum modularity of the colored Jones polynomial.","PeriodicalId":55284,"journal":{"name":"Canadian Journal of Mathematics-Journal Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80845780","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Global existence of the strong solution to the 3D incompressible micropolar equations with fractional partial dissipation 具有分数阶部分耗散的三维不可压缩微极方程强解的整体存在性
IF 0.7 3区 数学
Canadian Journal of Mathematics-Journal Canadien De Mathematiques Pub Date : 2022-09-13 DOI: 10.4153/S0008414X22000414
Yujun Liu
{"title":"Global existence of the strong solution to the 3D incompressible micropolar equations with fractional partial dissipation","authors":"Yujun Liu","doi":"10.4153/S0008414X22000414","DOIUrl":"https://doi.org/10.4153/S0008414X22000414","url":null,"abstract":"Abstract In this paper, we considered the global strong solution to the 3D incompressible micropolar equations with fractional partial dissipation. Whether or not the classical solution to the 3D Navier–Stokes equations can develop finite-time singularity remains an outstanding open problem, so does the same issue on the 3D incompressible micropolar equations. We establish the global-in-time existence and uniqueness strong solutions to the 3D incompressible micropolar equations with fractional partial velocity dissipation and microrotation diffusion with the initial data \u0000$(mathbf {u}_0, mathbf {w}_0)in H^1(mathbb {R}^3)$\u0000 .","PeriodicalId":55284,"journal":{"name":"Canadian Journal of Mathematics-Journal Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90650954","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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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