{"title":"Long time dynamics of nonequilibrium electroconvection","authors":"Fizay-Noah Lee","doi":"10.1090/tran/9171","DOIUrl":"https://doi.org/10.1090/tran/9171","url":null,"abstract":"<p>The Nernst-Planck-Stokes (NPS) system models electroconvection of ions in a fluid. We consider the system, for two oppositely charged ionic species, on three dimensional bounded domains with Dirichlet boundary conditions for the ionic concentrations (modelling ion selectivity), Dirichlet boundary conditions for the electrical potential (modelling an applied potential), and no-slip boundary conditions for the fluid velocity. In this paper, we obtain quantitative bounds on solutions of the NPS system in the long time limit, which we use to prove (1) the existence of a compact global attractor with finite fractal (box-counting) dimension and (2) space-time averaged electroneutrality <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"rho almost-equals 0\"> <mml:semantics> <mml:mrow> <mml:mi>ρ</mml:mi> <mml:mo>≈</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">rho approx 0</mml:annotation> </mml:semantics> </mml:math> </inline-formula> in the singular limit of Debye length going to zero, <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"epsilon right-arrow 0\"> <mml:semantics> <mml:mrow> <mml:mi>ϵ</mml:mi> <mml:mo stretchy=\"false\">→</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">epsilon to 0</mml:annotation> </mml:semantics> </mml:math> </inline-formula>.</p>","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140932116","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Quantum symmetries of Hadamard matrices","authors":"Daniel Gromada","doi":"10.1090/tran/9153","DOIUrl":"https://doi.org/10.1090/tran/9153","url":null,"abstract":"<p>We define quantum automorphisms and isomorphisms of Hadamard matrices. We show that every Hadamard matrix of size <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper N greater-than-or-equal-to 4\"> <mml:semantics> <mml:mrow> <mml:mi>N</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">Nge 4</mml:annotation> </mml:semantics> </mml:math> </inline-formula> has quantum symmetries and that all Hadamard matrices of a fixed size are mutually quantum isomorphic. These results pass also to the corresponding Hadamard graphs. We also define quantum Hadamard matrices acting on quantum spaces and bring an example thereof over matrix algebras.</p>","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141519509","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Guido De Philippis, Nicola Fusco, Massimiliano Morini
{"title":"Regularity of capillarity droplets with obstacle","authors":"Guido De Philippis, Nicola Fusco, Massimiliano Morini","doi":"10.1090/tran/9152","DOIUrl":"https://doi.org/10.1090/tran/9152","url":null,"abstract":"<p>In this paper we study the regularity properties of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper Lamda\"> <mml:semantics> <mml:mi mathvariant=\"normal\">Λ</mml:mi> <mml:annotation encoding=\"application/x-tex\">Lambda</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-minimizers of the capillarity energy in a half space with the wet part constrained to be confined inside a given planar region. Applications to a model for nanowire growth are also provided.</p>","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140932027","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Patterns of structural reflection in the large-cardinal hierarchy","authors":"Joan Bagaria, Philipp Lücke","doi":"10.1090/tran/9120","DOIUrl":"https://doi.org/10.1090/tran/9120","url":null,"abstract":"<p>We unveil new patterns of Structural Reflection in the large-cardinal hierarchy below the first measurable cardinal. Namely, we give two different characterizations of strongly unfoldable and subtle cardinals in terms of a weak form of the principle of Structural Reflection, and also in terms of weak product structural reflection. Our analysis prompts the introduction of the new notion of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper C Superscript left-parenthesis n right-parenthesis\"> <mml:semantics> <mml:msup> <mml:mi>C</mml:mi> <mml:mrow> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>n</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> </mml:msup> <mml:annotation encoding=\"application/x-tex\">C^{(n)}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-strongly unfoldable cardinal for every natural number <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"n\"> <mml:semantics> <mml:mi>n</mml:mi> <mml:annotation encoding=\"application/x-tex\">n</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, and we show that these cardinals form a natural hierarchy between strong unfoldable and subtle cardinals analogous to the known hierarchies of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper C Superscript left-parenthesis n right-parenthesis\"> <mml:semantics> <mml:msup> <mml:mi>C</mml:mi> <mml:mrow> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>n</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> </mml:msup> <mml:annotation encoding=\"application/x-tex\">C^{(n)}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-extendible and <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper Sigma Subscript n\"> <mml:semantics> <mml:msub> <mml:mi mathvariant=\"normal\">Σ<!-- Σ --></mml:mi> <mml:mi>n</mml:mi> </mml:msub> <mml:annotation encoding=\"application/x-tex\">Sigma _n</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-strong cardinals. These results show that the relatively low region of the large-cardinal hierarchy comprised between the first strongly unfoldable and the first subtle cardinals is completely analogous to the much higher region between the first strong and the first Woodin cardinals, and also to the much further upper region of the hierarchy ranging between the first supercompact and the first Vopěnka cardinals.</p>","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140932031","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Band projections in spaces of regular operators","authors":"David Muñoz-Lahoz, Pedro Tradacete","doi":"10.1090/tran/9162","DOIUrl":"https://doi.org/10.1090/tran/9162","url":null,"abstract":"<p>We introduce inner band projections in the space of regular operators on a Dedekind complete Banach lattice and study some structural properties of this class. In particular, we provide a new characterization of atomic order continuous Banach lattices as those for which all band projections in the corresponding space of regular operators are inner. We also characterize the multiplication operators <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L Subscript upper A Baseline upper R Subscript upper B\"> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi>L</mml:mi> <mml:mi>A</mml:mi> </mml:msub> <mml:msub> <mml:mi>R</mml:mi> <mml:mi>B</mml:mi> </mml:msub> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">L_AR_B</mml:annotation> </mml:semantics> </mml:math> </inline-formula> which are band projections precisely as those with <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper A comma upper B\"> <mml:semantics> <mml:mrow> <mml:mi>A</mml:mi> <mml:mo>,</mml:mo> <mml:mi>B</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">A,B</mml:annotation> </mml:semantics> </mml:math> </inline-formula> being band projections up to a scalar multiple.</p>","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141060513","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On Nielsen realization and manifold models for classifying spaces","authors":"James Davis, Wolfgang Lück","doi":"10.1090/tran/9155","DOIUrl":"https://doi.org/10.1090/tran/9155","url":null,"abstract":"<p>We consider the problem of whether, for a given virtually torsionfree discrete group <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper Gamma\"> <mml:semantics> <mml:mi mathvariant=\"normal\">Γ</mml:mi> <mml:annotation encoding=\"application/x-tex\">Gamma</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, there exists a cocompact proper topological <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper Gamma\"> <mml:semantics> <mml:mi mathvariant=\"normal\">Γ</mml:mi> <mml:annotation encoding=\"application/x-tex\">Gamma</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-manifold, which is equivariantly homotopy equivalent to the classifying space for proper actions. This problem is related to Nielsen Realization. We will make the assumption that the expected manifold model has a zero-dimensional singular set. Then we solve the problem in the case, for instance, that <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper Gamma\"> <mml:semantics> <mml:mi mathvariant=\"normal\">Γ</mml:mi> <mml:annotation encoding=\"application/x-tex\">Gamma</mml:annotation> </mml:semantics> </mml:math> </inline-formula> contains a normal torsionfree subgroup <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"pi\"> <mml:semantics> <mml:mi>π</mml:mi> <mml:annotation encoding=\"application/x-tex\">pi</mml:annotation> </mml:semantics> </mml:math> </inline-formula> such that <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"pi\"> <mml:semantics> <mml:mi>π</mml:mi> <mml:annotation encoding=\"application/x-tex\">pi</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is hyperbolic and <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"pi\"> <mml:semantics> <mml:mi>π</mml:mi> <mml:annotation encoding=\"application/x-tex\">pi</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is the fundamental group of an aspherical closed manifold of dimension greater or equal to five and <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper Gamma slash pi\"> <mml:semantics> <mml:mrow> <mml:mi mathvariant=\"normal\">Γ</mml:mi> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>π</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">Gamma /pi</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a finite cyclic group of odd order.</p>","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142176290","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Bounded differentials on the unit disk and the associated geometry","authors":"Song Dai, Qiongling Li","doi":"10.1090/tran/9154","DOIUrl":"https://doi.org/10.1090/tran/9154","url":null,"abstract":"<p>For a harmonic diffeomorphism between the Poincaré disks, Wan [J. Differential Geom. 35 (1992), pp. 643–657] showed the equivalence between the boundedness of the Hopf differential and the quasi-conformality. In this paper, we will generalize this result from quadratic differentials to <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"r\"> <mml:semantics> <mml:mi>r</mml:mi> <mml:annotation encoding=\"application/x-tex\">r</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-differentials. We study the relationship between bounded holomorphic <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"r\"> <mml:semantics> <mml:mi>r</mml:mi> <mml:annotation encoding=\"application/x-tex\">r</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-differentials/<inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis r minus 1 right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>r</mml:mi> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">(r-1)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-differential and the induced curvature of the associated harmonic maps from the unit disk to the symmetric space <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper S upper L left-parenthesis r comma double-struck upper R right-parenthesis slash upper S upper O left-parenthesis r right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mi>S</mml:mi> <mml:mi>L</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>r</mml:mi> <mml:mo>,</mml:mo> <mml:mrow> <mml:mi mathvariant=\"double-struck\">R</mml:mi> </mml:mrow> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>S</mml:mi> <mml:mi>O</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>r</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">SL(r,mathbb R)/SO(r)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> arising from cyclic/subcyclic Higgs bundles. Also, we show the equivalence between the boundedness of holomorphic differentials and having a negative upper bound of the induced curvature on hyperbolic affine spheres in <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper R cubed\"> <mml:semantics> <mml:msup> <mml:mrow> <mml:mi mathvariant=\"double-struck\">R</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> </mml:msup> <mml:annotation encoding=\"application/x-tex\">mathbb {R}^3</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, maximal surfaces in <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"doub","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141519513","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Nonexpansive maps in nonlinear smooth spaces","authors":"Pedro Pinto","doi":"10.1090/tran/9166","DOIUrl":"https://doi.org/10.1090/tran/9166","url":null,"abstract":"<p>We introduce the notion of a nonlinear smooth space generalizing both <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper C upper A upper T left-parenthesis 0 right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mi>CAT</mml:mi> <mml:mo></mml:mo> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mn>0</mml:mn> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">operatorname {CAT}(0)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> spaces as well as smooth Banach spaces. We show that this notion allows for a unified treatment of several results in functional analysis. Namely, we substantiate the usefulness of this setting by establishing a nonlinear generalization of an important result due to Reich in Banach spaces. On par with the linear context, this nonlinear version entails a convergence proof of several other methods. Here, we establish the convergence of a general form of the Halpern-type schema for resolvent-like families of functions. We furthermore prove the convergence of the viscosity generalization of Halpern’s iteration (even for families of maps) generalizing a result due to Chang. This work is set in the context of the ‘proof mining’ program, and the results are complemented with quantitative information like rates of convergence and of metastability (in the sense of T. Tao).</p>","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141519512","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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