发布求助
文献互助 智能选刊 最新文献

Proceedings of the Edinburgh Mathematical Society最新文献

筛选
英文 中文
Generalized Divisor Functions in Arithmetic Progressions: II 等差数列中的广义除数函数2
IF 0.7 3区 数学
Proceedings of the Edinburgh Mathematical Society Pub Date : 2023-11-16 DOI: 10.1017/s0013091523000664
D. T. Nguyen
{"title":"Generalized Divisor Functions in Arithmetic Progressions: II","authors":"D. T. Nguyen","doi":"10.1017/s0013091523000664","DOIUrl":"https://doi.org/10.1017/s0013091523000664","url":null,"abstract":"We obtain a new bound on the second moment of modified shifted convolutions of the generalized threefold divisor function and show that, for applications, the modified version is sufficient.","PeriodicalId":20586,"journal":{"name":"Proceedings of the Edinburgh Mathematical Society","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138526200","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: 3
On the Difference of Two Fourth Powers 关于两次四次方之差
3区 数学
Proceedings of the Edinburgh Mathematical Society Pub Date : 2023-11-10 DOI: 10.1017/s0013091523000706
Nguyen Xuan Tho
{"title":"On the Difference of Two Fourth Powers","authors":"Nguyen Xuan Tho","doi":"10.1017/s0013091523000706","DOIUrl":"https://doi.org/10.1017/s0013091523000706","url":null,"abstract":"Abstract We investigate the equation $D=x^4-y^4$ in field extensions. As an application, for a prime number p , we find solutions to $p=x^4-y^4$ if $pequiv 11$ (mod 16) and $p^3=x^4-y^4$ if $pequiv 3$ (mod 16) in all cubic extensions of $mathbb{Q}(i)$ .","PeriodicalId":20586,"journal":{"name":"Proceedings of the Edinburgh Mathematical Society","volume":"93 12","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135092056","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
Multiplicity and Stability of Normalized Solutions to Non-autonomous Schrödinger Equation with Mixed Non-linearities 混合非线性非自治Schrödinger方程归一化解的多重性与稳定性
3区 数学
Proceedings of the Edinburgh Mathematical Society Pub Date : 2023-11-09 DOI: 10.1017/s0013091523000676
Xinfu Li, Li Xu, Meiling Zhu
{"title":"Multiplicity and Stability of Normalized Solutions to Non-autonomous Schrödinger Equation with Mixed Non-linearities","authors":"Xinfu Li, Li Xu, Meiling Zhu","doi":"10.1017/s0013091523000676","DOIUrl":"https://doi.org/10.1017/s0013091523000676","url":null,"abstract":"Abstract This paper first studies the multiplicity of normalized solutions to the non-autonomous Schrödinger equation with mixed nonlinearities begin{equation*} begin{cases} -Delta u=lambda u+h(epsilon x)|u|^{q-2}u+eta |u|^{p-2}u,quad xin mathbb{R}^N, int_{mathbb{R}^N}|u|^2,textrm{d}x=a^2, end{cases} end{equation*} where $a, epsilon, eta gt 0$ , q is L 2 -subcritical, p is L 2 -supercritical, $lambdain mathbb{R}$ is an unknown parameter that appears as a Lagrange multiplier and h is a positive and continuous function. It is proved that the numbers of normalized solutions are at least the numbers of global maximum points of h when ϵ is small enough. The solutions obtained are local minimizers and probably not ground state solutions for the lack of symmetry of the potential h . Secondly, the stability of several different sets consisting of the local minimizers is analysed. Compared with the results of the corresponding autonomous equation, the appearance of the potential h increases the number of the local minimizers and the number of the stable sets. In particular, our results cover the Sobolev critical case $p=2N/(N-2)$ .","PeriodicalId":20586,"journal":{"name":"Proceedings of the Edinburgh Mathematical Society","volume":" 47","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135241988","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
Reversibility of affine transformations 仿射变换的可逆性
3区 数学
Proceedings of the Edinburgh Mathematical Society Pub Date : 2023-11-08 DOI: 10.1017/s001309152300069x
Krishnendu Gongopadhyay, Tejbir Lohan, Chandan Maity
{"title":"Reversibility of affine transformations","authors":"Krishnendu Gongopadhyay, Tejbir Lohan, Chandan Maity","doi":"10.1017/s001309152300069x","DOIUrl":"https://doi.org/10.1017/s001309152300069x","url":null,"abstract":"Abstract An element g in a group G is called reversible if g is conjugate to g −1 in G . An element g in G is strongly reversible if g is conjugate to g −1 by an involution in G . The group of affine transformations of $mathbb D^n$ may be identified with the semi-direct product $mathrm{GL}(n, mathbb D) ltimes mathbb D^n $ , where $mathbb D:=mathbb R, mathbb C$ or $ mathbb H $ . This paper classifies reversible and strongly reversible elements in the affine group $mathrm{GL}(n, mathbb D) ltimes mathbb D^n $ .","PeriodicalId":20586,"journal":{"name":"Proceedings of the Edinburgh Mathematical Society","volume":" 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135341269","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
Rigidity of Ext and Tor via Flat–Cotorsion Theory 基于平扭理论的Ext和Tor的刚度
3区 数学
Proceedings of the Edinburgh Mathematical Society Pub Date : 2023-11-03 DOI: 10.1017/s0013091523000573
Lars Winther Christensen, Luigi Ferraro, Peder Thompson
{"title":"Rigidity of Ext and Tor via Flat–Cotorsion Theory","authors":"Lars Winther Christensen, Luigi Ferraro, Peder Thompson","doi":"10.1017/s0013091523000573","DOIUrl":"https://doi.org/10.1017/s0013091523000573","url":null,"abstract":"Abstract Let $mathfrak{p}$ be a prime ideal in a commutative noetherian ring R and denote by $k(mathfrak{p})$ the residue field of the local ring $R_mathfrak{p}$ . We prove that if an R -module M satisfies $operatorname{Ext}_R^{n}(k(mathfrak{p}),M)=0$ for some $ngeqslantdim R$ , then $operatorname{Ext}_R^i(k(mathfrak{p}),M)=0$ holds for all $i geqslant n$ . This improves a result of Christensen, Iyengar and Marley by lowering the bound on n . We also improve existing results on Tor-rigidity. This progress is driven by the existence of minimal semi-flat-cotorsion replacements in the derived category as recently proved by Nakamura and Thompson.","PeriodicalId":20586,"journal":{"name":"Proceedings of the Edinburgh Mathematical Society","volume":"218 S699","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135775005","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
Cohomology of a Real Toric Variety and Shellability of Posets Arising from a Graph 图上实环簇的上同调性及序集的可壳性
3区 数学
Proceedings of the Edinburgh Mathematical Society Pub Date : 2023-11-03 DOI: 10.1017/s001309152300055x
Boram Park, Seonjeong Park
{"title":"Cohomology of a Real Toric Variety and Shellability of Posets Arising from a Graph","authors":"Boram Park, Seonjeong Park","doi":"10.1017/s001309152300055x","DOIUrl":"https://doi.org/10.1017/s001309152300055x","url":null,"abstract":"Abstract Given a graph G without loops, the pseudograph associahedron P G is a smooth polytope, so there is a projective smooth toric variety X G corresponding to P G . Taking the real locus of X G , we have the projective smooth real toric variety $X^{mathbb{R}}_G$ . The integral cohomology groups of $X^{mathbb{R}}_G$ can be computed by studying the topology of certain posets of even subgraphs of G ; such a poset is neither pure nor shellable in general. We completely characterize the graphs whose posets of even subgraphs are always shellable. It follows that we get a family of projective smooth real toric varieties whose integral cohomology groups are torsion-free or have only 2-torsion.","PeriodicalId":20586,"journal":{"name":"Proceedings of the Edinburgh Mathematical Society","volume":"32 125","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135820852","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
Bohr Radius for Banach Spaces on Simply Connected Domains 单连通域上Banach空间的Bohr半径
3区 数学
Proceedings of the Edinburgh Mathematical Society Pub Date : 2023-11-03 DOI: 10.1017/s0013091523000688
Vasudevarao Allu, Himadri Halder
{"title":"Bohr Radius for Banach Spaces on Simply Connected Domains","authors":"Vasudevarao Allu, Himadri Halder","doi":"10.1017/s0013091523000688","DOIUrl":"https://doi.org/10.1017/s0013091523000688","url":null,"abstract":"Abstract Let $H^{infty}(Omega,X)$ be the space of bounded analytic functions $f(z)=sum_{n=0}^{infty} x_{n}z^{n}$ from a proper simply connected domain Ω containing the unit disk $mathbb{D}:={zin mathbb{C}:|z| lt 1}$ into a complex Banach space X with $leftlVert frightrVert_{H^{infty}(Omega,X)} leq 1$ . Let $phi={phi_{n}(r)}_{n=0}^{infty}$ with $phi_{0}(r)leq 1$ such that $sum_{n=0}^{infty} phi_{n}(r)$ converges locally uniformly with respect to $r in [0,1)$ . For $1leq p,q lt infty$ , we denote begin{equation*} R_{p,q,phi}(f,Omega,X)= sup left{r geq 0: leftlVert x_{0}rightrVert^p phi_{0}(r) + left(sum_{n=1}^{infty} leftlVert x_{n}rightrVertphi_{n}(r)right)^q leq phi_{0}(r)right} end{equation*} and define the Bohr radius associated with ϕ by begin{equation*}R_{p,q,phi}(Omega,X)=inf left{R_{p,q,phi}(f,Omega,X): leftlVert frightrVert_{H^{infty}(Omega,X)} leq 1right}.end{equation*} In this article, we extensively study the Bohr radius $R_{p,q,phi}(Omega,X)$ , when X is an arbitrary Banach space, and $X=mathcal{B}(mathcal{H})$ is the algebra of all bounded linear operators on a complex Hilbert space $mathcal{H}$ . Furthermore, we establish the Bohr inequality for the operator-valued Cesáro operator and Bernardi operator.","PeriodicalId":20586,"journal":{"name":"Proceedings of the Edinburgh Mathematical Society","volume":"237 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135775120","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
PEM series 2 volume 66 issue 4 Cover and Front matter PEM 系列 2 第 66 卷第 4 期 封面和封底
IF 0.7 3区 数学
Proceedings of the Edinburgh Mathematical Society Pub Date : 2023-11-01 DOI: 10.1017/s001309152300072x
{"title":"PEM series 2 volume 66 issue 4 Cover and Front matter","authors":"","doi":"10.1017/s001309152300072x","DOIUrl":"https://doi.org/10.1017/s001309152300072x","url":null,"abstract":"","PeriodicalId":20586,"journal":{"name":"Proceedings of the Edinburgh Mathematical Society","volume":"14 1","pages":"f1 - f2"},"PeriodicalIF":0.7,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139302420","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
PEM series 2 volume 66 issue 4 Cover and Back matter PEM 系列 2 第 66 卷第 4 期封面和封底事项
IF 0.7 3区 数学
Proceedings of the Edinburgh Mathematical Society Pub Date : 2023-11-01 DOI: 10.1017/s0013091523000731
{"title":"PEM series 2 volume 66 issue 4 Cover and Back matter","authors":"","doi":"10.1017/s0013091523000731","DOIUrl":"https://doi.org/10.1017/s0013091523000731","url":null,"abstract":"","PeriodicalId":20586,"journal":{"name":"Proceedings of the Edinburgh Mathematical Society","volume":"22 1","pages":"b1 - b2"},"PeriodicalIF":0.7,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139298789","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
Stable solutions to double phase problems involving a nonlocal term – erratum 涉及非局部项的双相问题的稳定解--勘误表
IF 0.7 3区 数学
Proceedings of the Edinburgh Mathematical Society Pub Date : 2023-11-01 DOI: 10.1017/s0013091523000718
Belgacem Rahal, Phuong Le
{"title":"Stable solutions to double phase problems involving a nonlocal term – erratum","authors":"Belgacem Rahal, Phuong Le","doi":"10.1017/s0013091523000718","DOIUrl":"https://doi.org/10.1017/s0013091523000718","url":null,"abstract":"","PeriodicalId":20586,"journal":{"name":"Proceedings of the Edinburgh Mathematical Society","volume":"78 1","pages":"1229 - 1229"},"PeriodicalIF":0.7,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139291868","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
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信