Journal of the Australian Mathematical Society最新文献

{"title":"ASYMPTOTIC BEHAVIOUR OF THE LEAST ENERGY SOLUTIONS TO FRACTIONAL NEUMANN PROBLEMS","authors":"SOMNATH GANDAL, JAGMOHAN TYAGI","doi":"10.1017/s1446788724000107","DOIUrl":"https://doi.org/10.1017/s1446788724000107","url":null,"abstract":"<p>We study the asymptotic behaviour of the least energy solutions to the following class of nonlocal Neumann problems: <span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240913062454564-0570:S1446788724000107:S1446788724000107_eqnu1.png\"><span data-mathjax-type=\"texmath\"><span>$$ begin{align*} begin{cases} { d(-Delta)^{s}u+ u= vert uvert^{p-1}u } & text{in } Omega, {u>0} & text{in } Omega, { mathcal{N}_{s}u=0 } & text{in } mathbb{R}^{n}setminus overline{Omega}, end{cases} end{align*} $$</span></span></img></span></p><p>where <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240913062454564-0570:S1446788724000107:S1446788724000107_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$Omega subset mathbb {R}^{n}$</span></span></img></span></span> is a bounded domain of class <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240913062454564-0570:S1446788724000107:S1446788724000107_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$C^{1,1}$</span></span></img></span></span>, <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240913062454564-0570:S1446788724000107:S1446788724000107_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$1<p<({n+s})/({n-s}),,n>max {1, 2s }, 0<s<1, d>0$</span></span></img></span></span> and <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240913062454564-0570:S1446788724000107:S1446788724000107_inline4.png\"><span data-mathjax-type=\"texmath\"><span>$mathcal {N}_{s}u$</span></span></img></span></span> is the nonlocal Neumann derivative. We show that for small <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240913062454564-0570:S1446788724000107:S1446788724000107_inline5.png\"><span data-mathjax-type=\"texmath\"><span>$d,$</span></span></img></span></span> the least energy solutions <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240913062454564-0570:S1446788724000107:S1446788724000107_inline6.png\"><span data-mathjax-type=\"texmath\"><span>$u_d$</span></span></img></span></span> of the above problem achieve an <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240913062454564-0570:S1446788724000107:S1446788724000107_inline7.png\"><span data-mathjax-type=\"texmath\"><span>$L^{infty }$</span></span></img></span></span>-bound independent of <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/ve","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142191731","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}

{"title":"KRONECKER COEFFICIENTS FOR (DUAL) SYMMETRIC INVERSE SEMIGROUPS","authors":"VOLODYMYR MAZORCHUK, SHRADDHA SRIVASTAVA","doi":"10.1017/s1446788724000119","DOIUrl":"https://doi.org/10.1017/s1446788724000119","url":null,"abstract":"<p>We study analogues of Kronecker coefficients for symmetric inverse semigroups, for dual symmetric inverse semigroups and for the inverse semigroups of bijections between subquotients of finite sets. In all cases, we reduce the problem of determination of such coefficients to some group-theoretic and combinatorial problems. For symmetric inverse semigroups, we provide an explicit formula in terms of the classical Kronecker and Littlewood–Richardson coefficients for symmetric groups.</p>","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142191734","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}

{"title":"GEOMETRY OF CLAIRAUT CONFORMAL RIEMANNIAN MAPS","authors":"KIRAN MEENA, HEMANGI MADHUSUDAN SHAH, BAYRAM ŞAHIN","doi":"10.1017/s1446788724000090","DOIUrl":"https://doi.org/10.1017/s1446788724000090","url":null,"abstract":"&lt;p&gt;This article &lt;span&gt;introduces&lt;/span&gt; the Clairaut conformal Riemannian map. This notion includes the previously studied notions of Clairaut conformal submersion, Clairaut Riemannian submersion, and the Clairaut Riemannian map as particular cases, and is well known in the classical theory of surfaces. Toward this, we find the necessary and sufficient condition for a conformal Riemannian map &lt;span&gt;&lt;span&gt;&lt;img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240913065017866-0657:S1446788724000090:S1446788724000090_inline1.png\"&gt;&lt;span data-mathjax-type=\"texmath\"&gt;&lt;span&gt;$varphi : M to N$&lt;/span&gt;&lt;/span&gt;&lt;/img&gt;&lt;/span&gt;&lt;/span&gt; between Riemannian manifolds to be a Clairaut conformal Riemannian map with girth &lt;span&gt;&lt;span&gt;&lt;img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240913065017866-0657:S1446788724000090:S1446788724000090_inline2.png\"&gt;&lt;span data-mathjax-type=\"texmath\"&gt;&lt;span&gt;$s = e^f$&lt;/span&gt;&lt;/span&gt;&lt;/img&gt;&lt;/span&gt;&lt;/span&gt;. We show that the fibers of &lt;span&gt;&lt;span&gt;&lt;img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240913065017866-0657:S1446788724000090:S1446788724000090_inline3.png\"&gt;&lt;span data-mathjax-type=\"texmath\"&gt;&lt;span&gt;$varphi $&lt;/span&gt;&lt;/span&gt;&lt;/img&gt;&lt;/span&gt;&lt;/span&gt; are totally umbilical with mean curvature vector field the negative gradient of the logarithm of the girth function, that is, &lt;span&gt;&lt;span&gt;&lt;img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240913065017866-0657:S1446788724000090:S1446788724000090_inline4.png\"&gt;&lt;span data-mathjax-type=\"texmath\"&gt;&lt;span&gt;$-nabla f$&lt;/span&gt;&lt;/span&gt;&lt;/img&gt;&lt;/span&gt;&lt;/span&gt;. Using this, we obtain a local splitting of &lt;span&gt;M&lt;/span&gt; as a warped product and a usual product, if the horizontal space is integrable (under some appropriate hypothesis). We also provide some examples of the Clairaut conformal Riemannian maps to confirm our main theorem. We observe that the Laplacian of the logarithmic girth, that is, of &lt;span&gt;f&lt;/span&gt;, on the total manifold takes the special form. It reduces to the Laplacian on the horizontal distribution, and if it is nonnegative, the universal covering space of &lt;span&gt;M&lt;/span&gt; becomes a product manifold, under some hypothesis on &lt;span&gt;f&lt;/span&gt;. Analysis of the Laplacian of &lt;span&gt;f&lt;/span&gt; also yields the splitting of the universal covering space of &lt;span&gt;M&lt;/span&gt; as a warped product under some appropriate conditions. We calculate the sectional curvature and mixed sectional curvature of &lt;span&gt;M&lt;/span&gt; when &lt;span&gt;f&lt;/span&gt; is a distance function. We also find the relationships between the total manifold and the fibers being symmetrical and, in particular, having constant sectional curvature, and from there, we compare their universal covering spaces, if fibers are also complete, provided &lt;span&gt;f&lt;/span&gt; is a distance function. We als","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142191733","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}

{"title":"CONGRUENCE SUBGROUPS OF BRAID GROUPS AND CRYSTALLOGRAPHIC QUOTIENTS. PART I","authors":"PAOLO BELLINGERI, CELESTE DAMIANI, OSCAR OCAMPO, CHARALAMPOS STYLIANAKIS","doi":"10.1017/s1446788724000089","DOIUrl":"https://doi.org/10.1017/s1446788724000089","url":null,"abstract":"<p>This paper is the first of a two part series devoted to describing relations between congruence and crystallographic braid groups. We recall and introduce some elements belonging to congruence braid groups and we establish some (iso)-morphisms between crystallographic braid groups and corresponding quotients of congruence braid groups.</p>","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142191735","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}

{"title":"EVALUATION FUNCTIONS AND REFLEXIVITY OF BANACH SPACES OF HOLOMORPHIC FUNCTIONS","authors":"GUANGFU CAO, LI HE, JI LI, SHUQING ZHANG","doi":"10.1017/s1446788724000077","DOIUrl":"https://doi.org/10.1017/s1446788724000077","url":null,"abstract":"Let <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1446788724000077_inline1.png\"/> <jats:tex-math> $B(Omega )$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> be a Banach space of holomorphic functions on a bounded connected domain <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1446788724000077_inline2.png\"/> <jats:tex-math> $Omega $ </jats:tex-math> </jats:alternatives> </jats:inline-formula> in <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1446788724000077_inline3.png\"/> <jats:tex-math> ${{mathbb C}^n}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>. In this paper, we establish a criterion for <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1446788724000077_inline4.png\"/> <jats:tex-math> $B(Omega )$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> to be reflexive via evaluation functions on <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1446788724000077_inline5.png\"/> <jats:tex-math> $B(Omega )$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, that is, <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1446788724000077_inline6.png\"/> <jats:tex-math> $B(Omega )$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> is reflexive if and only if the evaluation functions span the dual space <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1446788724000077_inline7.png\"/> <jats:tex-math> $(B(Omega ))^{*} $ </jats:tex-math> </jats:alternatives> </jats:inline-formula>.","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141191229","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}

{"title":"TWISTED ACTIONS ON COHOMOLOGIES AND BIMODULES","authors":"VLADIMIR SHCHIGOLEV","doi":"10.1017/s1446788724000065","DOIUrl":"https://doi.org/10.1017/s1446788724000065","url":null,"abstract":"For closed subgroups <jats:italic>L</jats:italic> and <jats:italic>R</jats:italic> of a compact Lie group <jats:italic>G</jats:italic>, a left <jats:italic>L</jats:italic>-space <jats:italic>X</jats:italic>, and an <jats:italic>L</jats:italic>-equivariant continuous map <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1446788724000065_inline1.png\"/> <jats:tex-math> $A:Xto G/R$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, we introduce the twisted action of the equivariant cohomology <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1446788724000065_inline2.png\"/> <jats:tex-math> $H_R^{bullet }(mathrm {pt},Bbbk )$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> on the equivariant cohomology <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1446788724000065_inline3.png\"/> <jats:tex-math> $H_L^{bullet }(X,Bbbk )$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>. Considering this action as a right action, <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1446788724000065_inline4.png\"/> <jats:tex-math> $H_L^{bullet }(X,Bbbk )$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> becomes a bimodule together with the canonical left action of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1446788724000065_inline5.png\"/> <jats:tex-math> $H_L^{bullet }(mathrm {pt},Bbbk )$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>. Using this bimodule structure, we prove an equivariant version of the Künneth isomorphism. We apply this result to the computation of the equivariant cohomologies of Bott–Samelson varieties and to a geometric construction of the bimodule morphisms between them.","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141191868","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}

{"title":"JAZ volume 116 issue 3 Cover and Back matter","authors":"","doi":"10.1017/s1446788723000277","DOIUrl":"https://doi.org/10.1017/s1446788723000277","url":null,"abstract":"","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140982376","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}

{"title":"INDEX","authors":"","doi":"10.1017/s1446788723000289","DOIUrl":"https://doi.org/10.1017/s1446788723000289","url":null,"abstract":"","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140983800","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}

{"title":"JAZ volume 116 issue 3 Cover and Front matter","authors":"","doi":"10.1017/s1446788723000265","DOIUrl":"https://doi.org/10.1017/s1446788723000265","url":null,"abstract":"","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140986013","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}

{"title":"SPHERICAL REPRESENTATIONS FOR -FLOWS III: WEIGHT-EXTENDED BRANCHING GRAPHS","authors":"YOSHIMICHI UEDA","doi":"10.1017/s1446788724000053","DOIUrl":"https://doi.org/10.1017/s1446788724000053","url":null,"abstract":"We apply Takesaki’s and Connes’s ideas on structure analysis for type III factors to the study of links (a short term of Markov kernels) appearing in asymptotic representation theory.","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140571365","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}