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Minimal monoids generating varieties with complex subvariety lattices 用复数子变格生成品种的最小单体
IF 0.7 3区 数学
Proceedings of the Edinburgh Mathematical Society Pub Date : 2024-03-22 DOI: 10.1017/s0013091524000178
Sergey V. Gusev
{"title":"Minimal monoids generating varieties with complex subvariety lattices","authors":"Sergey V. Gusev","doi":"10.1017/s0013091524000178","DOIUrl":"https://doi.org/10.1017/s0013091524000178","url":null,"abstract":"A variety is <jats:italic>finitely universal</jats:italic> if its lattice of subvarieties contains an isomorphic copy of every finite lattice. We show that the 6-element Brandt monoid generates a finitely universal variety of monoids and, by the previous results, it is the smallest generator for a monoid variety with this property. It is also deduced that the join of two Cross varieties of monoids can be finitely universal. In particular, we exhibit a finitely universal variety of monoids with uncountably many subvarieties which is the join of two Cross varieties of monoids whose lattices of subvarieties are the 6-element and the 7-element chains, respectively.","PeriodicalId":20586,"journal":{"name":"Proceedings of the Edinburgh Mathematical Society","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140202702","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
On the structure of some One-generator braces 关于一些单发电机括号的结构
IF 0.7 3区 数学
Proceedings of the Edinburgh Mathematical Society Pub Date : 2024-03-20 DOI: 10.1017/s0013091524000154
L A Kurdachenko, I Ya. Subbotin
{"title":"On the structure of some One-generator braces","authors":"L A Kurdachenko, I Ya. Subbotin","doi":"10.1017/s0013091524000154","DOIUrl":"https://doi.org/10.1017/s0013091524000154","url":null,"abstract":"<p>We describe the one-generator braces A satisfying the condition <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240319132636021-0117:S0013091524000154:S0013091524000154_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$A^3 = langle 0 rangle$</span></span></img></span></span>.</p>","PeriodicalId":20586,"journal":{"name":"Proceedings of the Edinburgh Mathematical Society","volume":"147 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140167194","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
L2 to Lp bounds for spectral projectors on the Euclidean two-dimensional torus 欧氏二维环上谱投影的 L2 到 Lp 边界
IF 0.7 3区 数学
Proceedings of the Edinburgh Mathematical Society Pub Date : 2024-03-15 DOI: 10.1017/s0013091524000099
Ciprian Demeter, Pierre Germain
{"title":"L2 to Lp bounds for spectral projectors on the Euclidean two-dimensional torus","authors":"Ciprian Demeter, Pierre Germain","doi":"10.1017/s0013091524000099","DOIUrl":"https://doi.org/10.1017/s0013091524000099","url":null,"abstract":"We consider spectral projectors associated to the Euclidean Laplacian on the two-dimensional torus, in the case where the spectral window is narrow. Bounds for their <jats:italic>L</jats:italic><jats:sup>2</jats:sup> to <jats:italic>L<jats:sup>p</jats:sup></jats:italic> operator norm are derived, extending the classical result of Sogge; a new question on the convolution kernel of the projector is introduced. The methods employed include <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" mimetype=\"image\" xlink:href=\"S0013091524000099_inline1.png\" /> <jats:tex-math>$ell^2$</jats:tex-math> </jats:alternatives> </jats:inline-formula> decoupling, small cap decoupling and estimates of exponential sums.","PeriodicalId":20586,"journal":{"name":"Proceedings of the Edinburgh Mathematical Society","volume":"2012 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140150105","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
Canonical decompositions and algorithmic recognition of spatial graphs 空间图的典型分解和算法识别
IF 0.7 3区 数学
Proceedings of the Edinburgh Mathematical Society Pub Date : 2024-03-14 DOI: 10.1017/s0013091524000087
Stefan Friedl, Lars Munser, José Pedro Quintanilha, Yuri Santos Rego
{"title":"Canonical decompositions and algorithmic recognition of spatial graphs","authors":"Stefan Friedl, Lars Munser, José Pedro Quintanilha, Yuri Santos Rego","doi":"10.1017/s0013091524000087","DOIUrl":"https://doi.org/10.1017/s0013091524000087","url":null,"abstract":"<p>We prove that there exists an algorithm for determining whether two piecewise-linear spatial graphs are isomorphic. In its most general form, our theorem applies to spatial graphs furnished with vertex colourings, edge colourings and/or edge orientations.</p><p>We first show that spatial graphs admit canonical decompositions into blocks, that is, spatial graphs that are non-split and have no cut vertices, in a suitable topological sense. Then, we apply a result of Haken and Matveev in order to algorithmically distinguish these blocks.</p>","PeriodicalId":20586,"journal":{"name":"Proceedings of the Edinburgh Mathematical Society","volume":"55 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140128281","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
On the moduli of hypersurfaces in toric orbifolds 论环状轨道中的超曲面模量
IF 0.7 3区 数学
Proceedings of the Edinburgh Mathematical Society Pub Date : 2024-03-14 DOI: 10.1017/s0013091524000166
Dominic Bunnett
{"title":"On the moduli of hypersurfaces in toric orbifolds","authors":"Dominic Bunnett","doi":"10.1017/s0013091524000166","DOIUrl":"https://doi.org/10.1017/s0013091524000166","url":null,"abstract":"<p>We construct and study the moduli of stable hypersurfaces in toric orbifolds. Let <span>X</span> be a projective toric orbifold and <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240313101208614-0171:S0013091524000166:S0013091524000166_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$alpha in operatorname{Cl}(X)$</span></span></img></span></span> an ample class. The moduli space is constructed as a quotient of the linear system <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240313101208614-0171:S0013091524000166:S0013091524000166_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$|alpha|$</span></span></img></span></span> by <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240313101208614-0171:S0013091524000166:S0013091524000166_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$G = operatorname{Aut}(X)$</span></span></img></span></span>. Since the group <span>G</span> is non-reductive in general, we use new techniques of non-reductive geometric invariant theory. Using the <span>A</span>-discriminant of Gelfand, Kapranov and Zelevinsky, we prove semistability for quasismooth hypersurfaces of toric orbifolds. Further, we prove the existence of a quasi-projective moduli space of quasismooth hypersurfaces in a weighted projective space when the weighted projective space satisfies a certain condition. We also discuss how to proceed when this condition is not satisfied. We prove that the automorphism group of a quasismooth hypersurface of weighted projective space is finite excluding some low degrees.</p>","PeriodicalId":20586,"journal":{"name":"Proceedings of the Edinburgh Mathematical Society","volume":"11 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140128271","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
Unbounded Sturm attractors for quasilinear parabolic equations 准线性抛物方程的无界斯特姆吸引子
IF 0.7 3区 数学
Proceedings of the Edinburgh Mathematical Society Pub Date : 2024-03-08 DOI: 10.1017/s0013091524000129
Phillipo Lappicy, Juliana Fernandes
{"title":"Unbounded Sturm attractors for quasilinear parabolic equations","authors":"Phillipo Lappicy, Juliana Fernandes","doi":"10.1017/s0013091524000129","DOIUrl":"https://doi.org/10.1017/s0013091524000129","url":null,"abstract":"We analyse the asymptotic dynamics of quasilinear parabolic equations when solutions may grow up (i.e. blow up in infinite time). For such models, there is a global attractor which is unbounded and the semiflow induces a nonlinear dynamics at infinity by means of a Poincaré projection. In case the dynamics at infinity is given by a semilinear equation, then it is gradient, consisting of the so-called equilibria at infinity and their corresponding heteroclinics. Moreover, the diffusion and reaction compete for the dimensionality of the induced dynamics at infinity. If the equilibria are hyperbolic, we explicitly prove the occurrence of heteroclinics between bounded equilibria and/or equilibria at infinity. These unbounded global attractors describe the space of admissible initial data at event horizons of certain black holes.","PeriodicalId":20586,"journal":{"name":"Proceedings of the Edinburgh Mathematical Society","volume":"258 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140072551","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
A boundary maximum principle for stationary pairs of varifolds with fixed contact angle 具有固定接触角的静止变分对的边界最大原则
IF 0.7 3区 数学
Proceedings of the Edinburgh Mathematical Society Pub Date : 2024-03-08 DOI: 10.1017/s0013091524000026
Xuwen Zhang
{"title":"A boundary maximum principle for stationary pairs of varifolds with fixed contact angle","authors":"Xuwen Zhang","doi":"10.1017/s0013091524000026","DOIUrl":"https://doi.org/10.1017/s0013091524000026","url":null,"abstract":"<p>In this note, we establish a boundary maximum principle for a class of stationary pairs of varifolds satisfying a fixed contact angle condition in any compact Riemannian manifold with smooth boundary.</p>","PeriodicalId":20586,"journal":{"name":"Proceedings of the Edinburgh Mathematical Society","volume":"47 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140072452","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
Unit sphere fibrations in Euclidean space 欧几里得空间中的单位球纤维
IF 0.7 3区 数学
Proceedings of the Edinburgh Mathematical Society Pub Date : 2024-03-07 DOI: 10.1017/s0013091524000038
Daniel Asimov, Florian Frick, Michael Harrison, Wesley Pegden
{"title":"Unit sphere fibrations in Euclidean space","authors":"Daniel Asimov, Florian Frick, Michael Harrison, Wesley Pegden","doi":"10.1017/s0013091524000038","DOIUrl":"https://doi.org/10.1017/s0013091524000038","url":null,"abstract":"<p>We show that if an open set in <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240306133538207-0692:S0013091524000038:S0013091524000038_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$mathbb{R}^d$</span></span></img></span></span> can be fibered by unit <span>n</span>-spheres, then <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240306133538207-0692:S0013091524000038:S0013091524000038_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$d geq 2n+1$</span></span></img></span></span>, and if <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240306133538207-0692:S0013091524000038:S0013091524000038_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$d = 2n+1$</span></span></img></span></span>, then the spheres must be pairwise linked, and <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240306133538207-0692:S0013091524000038:S0013091524000038_inline4.png\"><span data-mathjax-type=\"texmath\"><span>$n in left{0, 1, 3, 7 right}$</span></span></img></span></span>. For these values of <span>n</span>, we construct unit <span>n</span>-sphere fibrations in <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240306133538207-0692:S0013091524000038:S0013091524000038_inline5.png\"><span data-mathjax-type=\"texmath\"><span>$mathbb{R}^{2n+1}$</span></span></img></span></span>.</p>","PeriodicalId":20586,"journal":{"name":"Proceedings of the Edinburgh Mathematical Society","volume":"70 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140055024","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
Structure of generalized Yamabe solitons and its applications 广义山叶孤子的结构及其应用
IF 0.7 3区 数学
Proceedings of the Edinburgh Mathematical Society Pub Date : 2024-03-07 DOI: 10.1017/s0013091524000117
Shun Maeta
{"title":"Structure of generalized Yamabe solitons and its applications","authors":"Shun Maeta","doi":"10.1017/s0013091524000117","DOIUrl":"https://doi.org/10.1017/s0013091524000117","url":null,"abstract":"<p>We consider the broadest concept of the gradient Yamabe soliton, the conformal gradient soliton. In this paper, we elucidate the structure of complete gradient conformal solitons under some assumption, and provide some applications to gradient Yamabe solitons. These results enhance the understanding gained from previous research. Furthermore, we give an affirmative partial answer to the Yamabe soliton version of Perelman’s conjecture.</p>","PeriodicalId":20586,"journal":{"name":"Proceedings of the Edinburgh Mathematical Society","volume":"70 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140055010","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
Proof of some conjectural congruences involving Apéry and Apéry-like numbers 涉及阿佩里数和类阿佩里数的一些猜想全等的证明
IF 0.7 3区 数学
Proceedings of the Edinburgh Mathematical Society Pub Date : 2024-03-07 DOI: 10.1017/s0013091524000075
Guo-shuai Mao, Lilong Wang
{"title":"Proof of some conjectural congruences involving Apéry and Apéry-like numbers","authors":"Guo-shuai Mao, Lilong Wang","doi":"10.1017/s0013091524000075","DOIUrl":"https://doi.org/10.1017/s0013091524000075","url":null,"abstract":"<p>In this paper, we mainly prove the following conjectures of Sun [16]: Let <span>p</span> &gt; 3 be a prime. Then<span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240306144432913-0876:S0013091524000075:S0013091524000075_eqnU1.png\"><span data-mathjax-type=\"texmath\"><span>begin{align*}&amp;A_{2p}equiv A_2-frac{1648}3p^3B_{p-3} ({rm{mod}} p^4),&amp;A_{2p-1}equiv A_1+frac{16p^3}3B_{p-3} ({rm{mod}} p^4),&amp;A_{3p}equiv A_3-36738p^3B_{p-3} ({rm{mod}} p^4),end{align*}</span></span></img></span></p><p contenttype=\"noindent\">where <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240306144432913-0876:S0013091524000075:S0013091524000075_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$A_n=sum_{k=0}^nbinom{n}k^2binom{n+k}{k}^2$</span></span></img></span></span> is the <span>n</span>th Apéry number, and <span>B<span>n</span></span> is the <span>n</span>th Bernoulli number.</p>","PeriodicalId":20586,"journal":{"name":"Proceedings of the Edinburgh Mathematical Society","volume":"8 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140055029","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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