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The nonclassical diffusion equations with time-dependent memory kernels and a new class of nonlinearities 具有时变记忆核的非经典扩散方程及一类新的非线性
IF 0.5 4区 数学
Glasgow Mathematical Journal Pub Date : 2022-02-21 DOI: 10.1017/S0017089522000027
L. T. Thuy, N. Toan
{"title":"The nonclassical diffusion equations with time-dependent memory kernels and a new class of nonlinearities","authors":"L. T. Thuy, N. Toan","doi":"10.1017/S0017089522000027","DOIUrl":"https://doi.org/10.1017/S0017089522000027","url":null,"abstract":"Abstract In this study, we consider the nonclassical diffusion equations with time-dependent memory kernels \u0000begin{equation*} u_{t} - Delta u_t - Delta u - int_0^infty k^{prime}_{t}(s) Delta u(t-s) ds + f( u) = g end{equation*}\u0000 on a bounded domain \u0000$Omega subset mathbb{R}^N,, Ngeq 3$\u0000 . Firstly, we study the existence and uniqueness of weak solutions and then, we investigate the existence of the time-dependent global attractors \u0000$mathcal{A}={A_t}_{tinmathbb{R}}$\u0000 in \u0000$H_0^1(Omega)times L^2_{mu_t}(mathbb{R}^+,H_0^1(Omega))$\u0000 . Finally, we prove that the asymptotic dynamics of our problem, when \u0000$k_t$\u0000 approaches a multiple \u0000$mdelta_0$\u0000 of the Dirac mass at zero as \u0000$tto infty$\u0000 , is close to the one of its formal limit \u0000begin{equation*}u_{t} - Delta u_{t} - (1+m)Delta u + f( u) = g. end{equation*}\u0000 The main novelty of our results is that no restriction on the upper growth of the nonlinearity is imposed and the memory kernel \u0000$k_t(!cdot!)$\u0000 depends on time, which allows for instance to describe the dynamics of aging materials.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49075907","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
Homotopy commutativity in Hermitian symmetric spaces 厄密对称空间中的同伦交换性
IF 0.5 4区 数学
Glasgow Mathematical Journal Pub Date : 2022-01-31 DOI: 10.1017/S0017089522000118
D. Kishimoto, Masahiro Takeda, Yichen Tong
{"title":"Homotopy commutativity in Hermitian symmetric spaces","authors":"D. Kishimoto, Masahiro Takeda, Yichen Tong","doi":"10.1017/S0017089522000118","DOIUrl":"https://doi.org/10.1017/S0017089522000118","url":null,"abstract":"Abstract Ganea proved that the loop space of \u0000$mathbb{C} P^n$\u0000 is homotopy commutative if and only if \u0000$n=3$\u0000 . We generalize this result to that the loop spaces of all irreducible Hermitian symmetric spaces but \u0000$mathbb{C} P^3$\u0000 are not homotopy commutative. The computation also applies to determining the homotopy nilpotency class of the loop spaces of generalized flag manifolds \u0000$G/T$\u0000 for a maximal torus T of a compact, connected Lie group G.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44703460","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
KMS states on $C_c^{*}(mathbb{N}^2)$ KMS在$C_c^{*}(mathbb{N}^2)$上的状态
IF 0.5 4区 数学
Glasgow Mathematical Journal Pub Date : 2022-01-30 DOI: 10.1017/S0017089523000071
Anbu Arjunan, Sruthymurali, S. Sundar
{"title":"KMS states on \u0000$C_c^{*}(mathbb{N}^2)$","authors":"Anbu Arjunan, Sruthymurali, S. Sundar","doi":"10.1017/S0017089523000071","DOIUrl":"https://doi.org/10.1017/S0017089523000071","url":null,"abstract":"Abstract Let \u0000$C_c^{*}(mathbb{N}^{2})$\u0000 be the universal \u0000$C^{*}$\u0000 -algebra generated by a semigroup of isometries \u0000${v_{(m,n)},:, m,n in mathbb{N}}$\u0000 whose range projections commute. We analyse the structure of KMS states on \u0000$C_{c}^{*}(mathbb{N}^2)$\u0000 for the time evolution determined by a homomorphism \u0000$c,:,mathbb{Z}^{2} to mathbb{R}$\u0000 . In contrast to the reduced version \u0000$C_{red}^{*}(mathbb{N}^{2})$\u0000 , we show that the set of KMS states on \u0000$C_{c}^{*}(mathbb{N}^{2})$\u0000 has a rich structure. In particular, we exhibit uncountably many extremal KMS states of type I, II and III.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44842606","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
Hausdorff dimension of the set of almost convergent sequences 几乎收敛序列集合的Hausdorff维数
IF 0.5 4区 数学
Glasgow Mathematical Journal Pub Date : 2022-01-06 DOI: 10.1017/S0017089521000446
A. Usachev
{"title":"Hausdorff dimension of the set of almost convergent sequences","authors":"A. Usachev","doi":"10.1017/S0017089521000446","DOIUrl":"https://doi.org/10.1017/S0017089521000446","url":null,"abstract":"Abstract The paper deals with the sets of numbers from [0,1] such that their binary representation is almost convergent. The aim of the study is to compute the Hausdorff dimensions of such sets. Previously, the results of this type were proved for a single summation method (e.g. Cesàro, Abel, Toeplitz). This study extends the results to a wide range of matrix summation methods.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43570293","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
GMJ volume 64 issue 1 Cover and Front matter GMJ第64卷第1期封面和封面问题
IF 0.5 4区 数学
Glasgow Mathematical Journal Pub Date : 2021-12-07 DOI: 10.1017/s0017089521000392
{"title":"GMJ volume 64 issue 1 Cover and Front matter","authors":"","doi":"10.1017/s0017089521000392","DOIUrl":"https://doi.org/10.1017/s0017089521000392","url":null,"abstract":"","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45316539","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
GMJ volume 64 issue 1 Cover and Back matter GMJ第64卷第1期封面和封底
IF 0.5 4区 数学
Glasgow Mathematical Journal Pub Date : 2021-12-07 DOI: 10.1017/s0017089521000409
{"title":"GMJ volume 64 issue 1 Cover and Back matter","authors":"","doi":"10.1017/s0017089521000409","DOIUrl":"https://doi.org/10.1017/s0017089521000409","url":null,"abstract":"","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43425166","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 parabolic subgroups of symplectic reflection groups 关于辛反射群的抛物子群
IF 0.5 4区 数学
Glasgow Mathematical Journal Pub Date : 2021-12-02 DOI: 10.1017/S0017089522000416
G. Bellamy, J. Schmitt, U. Thiel
{"title":"On parabolic subgroups of symplectic reflection groups","authors":"G. Bellamy, J. Schmitt, U. Thiel","doi":"10.1017/S0017089522000416","DOIUrl":"https://doi.org/10.1017/S0017089522000416","url":null,"abstract":"Abstract Using Cohen’s classification of symplectic reflection groups, we prove that the parabolic subgroups, that is, stabilizer subgroups, of a finite symplectic reflection group, are themselves symplectic reflection groups. This is the symplectic analog of Steinberg’s Theorem for complex reflection groups. Using computational results required in the proof, we show the nonexistence of symplectic resolutions for symplectic quotient singularities corresponding to three exceptional symplectic reflection groups, thus reducing further the number of cases for which the existence question remains open. Another immediate consequence of our result is that the singular locus of the symplectic quotient singularity associated to a symplectic reflection group is pure of codimension two.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43462559","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
Abelian actions on compact nonorientable Riemann surfaces 紧致非定向黎曼曲面上的阿贝尔作用
IF 0.5 4区 数学
Glasgow Mathematical Journal Pub Date : 2021-12-02 DOI: 10.1017/S0017089521000410
Jesús Rodríguez
{"title":"Abelian actions on compact nonorientable Riemann surfaces","authors":"Jesús Rodríguez","doi":"10.1017/S0017089521000410","DOIUrl":"https://doi.org/10.1017/S0017089521000410","url":null,"abstract":"Abstract Given an integer \u0000$g>2$\u0000 , we state necessary and sufficient conditions for a finite Abelian group to act as a group of automorphisms of some compact nonorientable Riemann surface of genus g. This result provides a new method to obtain the symmetric cross-cap number of Abelian groups. We also compute the least symmetric cross-cap number of Abelian groups of a given order and solve the maximum order problem for Abelian groups acting on nonorientable Riemann surfaces.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48163514","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
Casting light on shadow Somos sequences 在阴影上投射灯光Somos序列
IF 0.5 4区 数学
Glasgow Mathematical Journal Pub Date : 2021-11-21 DOI: 10.1017/S0017089522000167
A. Hone
{"title":"Casting light on shadow Somos sequences","authors":"A. Hone","doi":"10.1017/S0017089522000167","DOIUrl":"https://doi.org/10.1017/S0017089522000167","url":null,"abstract":"Abstract Recently Ovsienko and Tabachnikov considered extensions of Somos and Gale-Robinson sequences, defined over the algebra of dual numbers. Ovsienko used the same idea to construct so-called shadow sequences derived from other nonlinear recurrence relations exhibiting the Laurent phenomenon, with the original motivation being the hope that these examples should lead to an appropriate notion of a cluster superalgebra, incorporating Grassmann variables. Here, we present various explicit expressions for the shadow of Somos-4 sequences and describe the solution of a general Somos-4 recurrence defined over the \u0000$mathbb{C}$\u0000 -algebra of dual numbers from several different viewpoints: analytic formulae in terms of elliptic functions, linear difference equations, and Hankel determinants.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42125167","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: 7
Conjugacy growth in the higher Heisenberg groups 高海森堡群的共轭增长
IF 0.5 4区 数学
Glasgow Mathematical Journal Pub Date : 2021-11-11 DOI: 10.1017/S0017089522000428
Alex Evetts
{"title":"Conjugacy growth in the higher Heisenberg groups","authors":"Alex Evetts","doi":"10.1017/S0017089522000428","DOIUrl":"https://doi.org/10.1017/S0017089522000428","url":null,"abstract":"Abstract We calculate asymptotic estimates for the conjugacy growth function of finitely generated class 2 nilpotent groups whose derived subgroups are infinite cyclic, including the so-called higher Heisenberg groups. We prove that these asymptotics are stable when passing to commensurable groups, by understanding their twisted conjugacy growth. We also use these estimates to prove that, in certain cases, the conjugacy growth series cannot be a holonomic function.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43119586","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
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