Proceedings of the Royal Society of Edinburgh Section A-Mathematics最新文献

{"title":"Remarks on a formula of Ramanujan","authors":"Andrés Chirre, Steven M. Gonek","doi":"10.1017/prm.2023.136","DOIUrl":"https://doi.org/10.1017/prm.2023.136","url":null,"abstract":"Assuming an averaged form of Mertens’ conjecture and that the ordinates of the non-trivial zeros of the Riemann zeta function are linearly independent over the rationals, we analyse the finer structure of the terms in a well-known formula of Ramanujan.","PeriodicalId":54560,"journal":{"name":"Proceedings of the Royal Society of Edinburgh Section A-Mathematics","volume":"6 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139758154","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}

{"title":"On the existence of a nodal solution for p-Laplacian equations depending on the gradient","authors":"F. Faraci, D. Puglisi","doi":"10.1017/prm.2023.135","DOIUrl":"https://doi.org/10.1017/prm.2023.135","url":null,"abstract":"<p>In the present paper we deal with a quasi-linear elliptic equation depending on a sublinear nonlinearity involving the gradient. We prove the existence of a nontrivial nodal solution employing the theory of invariant sets of descending flow together with sub-supersolution techniques, gradient regularity arguments, strong comparison principle for the <span><span><span data-mathjax-type=\"texmath\"><span>$p$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240130151231725-0751:S030821052300135X:S030821052300135X_inline2.png\"/></span></span>-Laplace operator. The same conclusion is obtained for an eigenvalue problem under a different set of assumptions.</p>","PeriodicalId":54560,"journal":{"name":"Proceedings of the Royal Society of Edinburgh Section A-Mathematics","volume":"103 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139647806","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}

{"title":"Regular matrices of unbounded linear operators","authors":"Paolo Leonetti","doi":"10.1017/prm.2024.1","DOIUrl":"https://doi.org/10.1017/prm.2024.1","url":null,"abstract":"<p>Let <span><span><span data-mathjax-type=\"texmath\"><span>$X,,Y$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240130151803585-0502:S0308210524000015:S0308210524000015_inline1.png\"/></span></span> be Banach spaces and fix a linear operator <span><span><span data-mathjax-type=\"texmath\"><span>$T in mathcal {L}(X,,Y)$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240130151803585-0502:S0308210524000015:S0308210524000015_inline2.png\"/></span></span> and ideals <span><span><span data-mathjax-type=\"texmath\"><span>$mathcal {I},, mathcal {J}$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240130151803585-0502:S0308210524000015:S0308210524000015_inline3.png\"/></span></span> on the nonnegative integers. We obtain Silverman–Toeplitz type theorems on matrices <span><span><span data-mathjax-type=\"texmath\"><span>$A=(A_{n,k}: n,,k in omega )$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240130151803585-0502:S0308210524000015:S0308210524000015_inline4.png\"/></span></span> of linear operators in <span><span><span data-mathjax-type=\"texmath\"><span>$mathcal {L}(X,,Y)$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240130151803585-0502:S0308210524000015:S0308210524000015_inline5.png\"/></span></span>, so that<span><span data-mathjax-type=\"texmath\"><span>[ mathcal{J}text{-}lim Aboldsymbol{x}=T(mathcal{I}text{-}lim boldsymbol{x}) ]</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240130151803585-0502:S0308210524000015:S0308210524000015_eqnU1.png\"/></span>for every <span><span><span data-mathjax-type=\"texmath\"><span>$X$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240130151803585-0502:S0308210524000015:S0308210524000015_inline6.png\"/></span></span>-valued sequence <span><span><span data-mathjax-type=\"texmath\"><span>$boldsymbol {x}=(x_0,,x_1,,ldots )$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240130151803585-0502:S0308210524000015:S0308210524000015_inline7.png\"/></span></span> which is <span><span><span data-mathjax-type=\"texmath\"><span>$mathcal {I}$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240130151803585-0502:S0308210524000015:S0308210524000015_inline8.png\"/></span></span>-convergent (and bounded). This allows us to establish the relationship between the classical Silv","PeriodicalId":54560,"journal":{"name":"Proceedings of the Royal Society of Edinburgh Section A-Mathematics","volume":"32 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139647939","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}

{"title":"Sharp gradient estimate, rigidity and almost rigidity of Green functions on non-parabolic RCD(0, N) spaces","authors":"Shouhei Honda, Yuanlin Peng","doi":"10.1017/prm.2024.131","DOIUrl":"https://doi.org/10.1017/prm.2024.131","url":null,"abstract":"<p>Inspired by a result in T. H. Colding. (16). <span>Acta. Math.</span> <span>209</span>(2) (2012), 229-263 [16] of Colding, the present paper studies the Green function <span><span><span data-mathjax-type=\"texmath\"><span>$G$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240116102450072-0592:S0308210523001312:S0308210523001312_inline2.png\"/></span></span> on a non-parabolic <span><span><span data-mathjax-type=\"texmath\"><span>$operatorname {RCD}(0,,N)$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240116102450072-0592:S0308210523001312:S0308210523001312_inline3.png\"/></span></span> space <span><span><span data-mathjax-type=\"texmath\"><span>$(X,, mathsf {d},, mathfrak {m})$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240116102450072-0592:S0308210523001312:S0308210523001312_inline4.png\"/></span></span> for some finite <span><span><span data-mathjax-type=\"texmath\"><span>$N&gt;2$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240116102450072-0592:S0308210523001312:S0308210523001312_inline5.png\"/></span></span>. Defining <span><span><span data-mathjax-type=\"texmath\"><span>$mathsf {b}_x=G(x,, cdot )^{frac {1}{2-N}}$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240116102450072-0592:S0308210523001312:S0308210523001312_inline6.png\"/></span></span> for a point <span><span><span data-mathjax-type=\"texmath\"><span>$x in X$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240116102450072-0592:S0308210523001312:S0308210523001312_inline7.png\"/></span></span>, which plays a role of a smoothed distance function from <span><span><span data-mathjax-type=\"texmath\"><span>$x$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240116102450072-0592:S0308210523001312:S0308210523001312_inline8.png\"/></span></span>, we prove that the gradient <span><span><span data-mathjax-type=\"texmath\"><span>$|nabla mathsf {b}_x|$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240116102450072-0592:S0308210523001312:S0308210523001312_inline9.png\"/></span></span> has the canonical pointwise representative with the sharp upper bound in terms of the <span><span><span data-mathjax-type=\"texmath\"><span>$N$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240116102450072-0592:S0308210523001312:S0308210523001312_","PeriodicalId":54560,"journal":{"name":"Proceedings of the Royal Society of Edinburgh Section A-Mathematics","volume":"23 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139481144","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}

{"title":"Nonexpansive and noncontractive mappings on the set of quantum pure states","authors":"Michiya Mori, Peter Šemrl","doi":"10.1017/prm.2024.133","DOIUrl":"https://doi.org/10.1017/prm.2024.133","url":null,"abstract":"<p>Wigner's theorem characterizes isometries of the set of all rank one projections on a Hilbert space. In metric geometry, nonexpansive maps and noncontractive maps are well-studied generalizations of isometries. We show that under certain conditions Wigner symmetries can be characterized as nonexpansive or noncontractive maps on the set of all projections of rank one. The assumptions required for such characterizations are injectivity or surjectivity and they differ in the finite and the infinite-dimensional case. Motivated by a recently obtained optimal version of Uhlhorn's generalization of Wigner's theorem, we also give a description of nonexpansive maps which satisfy a condition that is much weaker than surjectivity. Such maps do not need to be Wigner symmetries. The optimality of all presented results is shown by counterexamples.</p>","PeriodicalId":54560,"journal":{"name":"Proceedings of the Royal Society of Edinburgh Section A-Mathematics","volume":"52 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139481093","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}

{"title":"Classification of simple smooth modules over the Heisenberg–Virasoro algebra","authors":"Haijun Tan, Yufeng Yao, Kaiming Zhao","doi":"10.1017/prm.2024.132","DOIUrl":"https://doi.org/10.1017/prm.2024.132","url":null,"abstract":"<p>In this paper, we classify simple smooth modules over the mirror Heisenberg–Virasoro algebra <span><span><span data-mathjax-type=\"texmath\"><span>${mathfrak {D}}$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240116103651863-0511:S0308210523001324:S0308210523001324_inline1.png\"/></span></span>, and simple smooth modules over the twisted Heisenberg–Virasoro algebra <span><span><span data-mathjax-type=\"texmath\"><span>$bar {mathfrak {D}}$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240116103651863-0511:S0308210523001324:S0308210523001324_inline2.png\"/></span></span> with non-zero level. To this end we generalize Sugawara operators to smooth modules over the Heisenberg algebra, and develop new techniques. As applications, we characterize simple Whittaker modules and simple highest weight modules over <span><span><span data-mathjax-type=\"texmath\"><span>${mathfrak {D}}$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240116103651863-0511:S0308210523001324:S0308210523001324_inline3.png\"/></span></span>. A vertex-algebraic interpretation of our result is the classification of simple weak twisted and untwisted modules over the Heisenberg–Virasoro vertex algebras. We also present a few examples of simple smooth <span><span><span data-mathjax-type=\"texmath\"><span>${mathfrak {D}}$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240116103651863-0511:S0308210523001324:S0308210523001324_inline4.png\"/></span></span>-modules and <span><span><span data-mathjax-type=\"texmath\"><span>$bar {mathfrak {D}}$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240116103651863-0511:S0308210523001324:S0308210523001324_inline5.png\"/></span></span>-modules induced from simple modules over finite dimensional solvable Lie algebras, that are not tensor product modules of Virasoro modules and Heisenberg modules. This is very different from the case of simple highest weight modules over <span><span><span data-mathjax-type=\"texmath\"><span>$mathfrak {D}$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240116103651863-0511:S0308210523001324:S0308210523001324_inline6.png\"/></span></span> and <span><span><span data-mathjax-type=\"texmath\"><span>$bar {mathfrak {D}}$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240116103651863-0511:S0308210523001324:S0308210523001324_inline7.png\"/></span></span> which are always tensor products of simple Virasoro modules and simple Heisenberg m","PeriodicalId":54560,"journal":{"name":"Proceedings of the Royal Society of Edinburgh Section A-Mathematics","volume":"19 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139480944","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}

{"title":"Cavitation of a spherical body under mechanical and self-gravitational forces","authors":"Pablo V. Negrón–Marrero, Jeyabal Sivaloganathan","doi":"10.1017/prm.2023.125","DOIUrl":"https://doi.org/10.1017/prm.2023.125","url":null,"abstract":"<p>In this paper, we look for minimizers of the energy functional for isotropic compressible elasticity taking into consideration the effect of a gravitational field induced by the body itself. We consider two types of problems: the displacement problem in which the outer boundary of the body is subjected to a Dirichlet-type boundary condition, and the one with zero traction on the boundary but with an internal pressure function. For a spherically symmetric body occupying the unit ball <span><span><span data-mathjax-type=\"texmath\"><span>$mathcal {B}in mathbb {R}^3$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240106111107785-0833:S0308210523001257:S0308210523001257_inline1.png\"/></span></span>, the minimization is done within the class of radially symmetric deformations. We give conditions for the existence of such minimizers, for satisfaction of the Euler–Lagrange equations, and show that for large displacements or large internal pressures, the minimizer must develop a cavity at the centre. We discuss a numerical scheme for approximating the minimizers for the displacement problem, together with some simulations that show the dependence of the cavity radius and minimum energy on the displacement and mass density of the body.</p>","PeriodicalId":54560,"journal":{"name":"Proceedings of the Royal Society of Edinburgh Section A-Mathematics","volume":"45 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139397124","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}

{"title":"Adhesion and volume filling in one-dimensional population dynamics under Dirichlet boundary condition","authors":"Hyung Jun Choi, Seonghak Kim, Youngwoo Koh","doi":"10.1017/prm.2023.129","DOIUrl":"https://doi.org/10.1017/prm.2023.129","url":null,"abstract":"<p>We generalize the one-dimensional population model of Anguige &amp; Schmeiser [1] reflecting the cell-to-cell adhesion and volume filling and classify the resulting equation into the six types. Among these types, we fix one that yields a class of advection-diffusion equations of forward-backward-forward type and prove the existence of infinitely many global-in-time weak solutions to the initial-Dirichlet boundary value problem when the maximum value of an initial population density exceeds a certain threshold. Such solutions are extracted from the method of convex integration by Müller &amp; Šverák [12]; they exhibit fine-scale density mixtures over a finite time interval, then become smooth and identical, and decay exponentially and uniformly to zero as time approaches infinity. TE check: Please check the reference citation in abstract.</p>","PeriodicalId":54560,"journal":{"name":"Proceedings of the Royal Society of Edinburgh Section A-Mathematics","volume":"33 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139398466","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}

{"title":"Nowhere scattered multiplier algebras","authors":"Eduard Vilalta","doi":"10.1017/prm.2023.123","DOIUrl":"https://doi.org/10.1017/prm.2023.123","url":null,"abstract":"<p>We study sufficient conditions under which a nowhere scattered <span><span><span data-mathjax-type=\"texmath\"><span>$mathrm {C}^*$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240104121729565-0175:S0308210523001233:S0308210523001233_inline1.png\"/></span></span>-algebra <span><span><span data-mathjax-type=\"texmath\"><span>$A$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240104121729565-0175:S0308210523001233:S0308210523001233_inline2.png\"/></span></span> has a nowhere scattered multiplier algebra <span><span><span data-mathjax-type=\"texmath\"><span>$mathcal {M}(A)$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240104121729565-0175:S0308210523001233:S0308210523001233_inline3.png\"/></span></span>, that is, we study when <span><span><span data-mathjax-type=\"texmath\"><span>$mathcal {M}(A)$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240104121729565-0175:S0308210523001233:S0308210523001233_inline4.png\"/></span></span> has no nonzero, elementary ideal-quotients. In particular, we prove that a <span><span><span data-mathjax-type=\"texmath\"><span>$sigma$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240104121729565-0175:S0308210523001233:S0308210523001233_inline5.png\"/></span></span>-unital <span><span><span data-mathjax-type=\"texmath\"><span>$mathrm {C}^*$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240104121729565-0175:S0308210523001233:S0308210523001233_inline6.png\"/></span></span>-algebra <span><span><span data-mathjax-type=\"texmath\"><span>$A$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240104121729565-0175:S0308210523001233:S0308210523001233_inline7.png\"/></span></span> of</p><ol><li><p><span>(i)</span> finite nuclear dimension, or</p></li><li><p><span>(ii)</span> real rank zero, or</p></li><li><p><span>(iii)</span> stable rank one with <span><span><span data-mathjax-type=\"texmath\"><span>$k$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240104121729565-0175:S0308210523001233:S0308210523001233_inline8.png\"/></span></span>-comparison,</p></li></ol> is nowhere scattered if and only if <span><span><span data-mathjax-type=\"texmath\"><span>$mathcal {M}(A)$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240104121729565-0175:S0308210523001233:S0308210523001233","PeriodicalId":54560,"journal":{"name":"Proceedings of the Royal Society of Edinburgh Section A-Mathematics","volume":"1 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139103518","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}

{"title":"On Calderon's problem for the connection Laplacian","authors":"Ravil Gabdurakhmanov, Gerasim Kokarev","doi":"10.1017/prm.2023.127","DOIUrl":"https://doi.org/10.1017/prm.2023.127","url":null,"abstract":"<p>We consider Calderón's problem for the connection Laplacian on a real-analytic vector bundle over a manifold with boundary. We prove a uniqueness result for this problem when all geometric data are real-analytic, recovering the topology and geometry of a vector bundle up to a gauge transformation and an isometry of the base manifold.</p>","PeriodicalId":54560,"journal":{"name":"Proceedings of the Royal Society of Edinburgh Section A-Mathematics","volume":"17 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139105524","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}