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Classification of noncommutative monoid structures on normal affine surfaces Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-07-15 Boris Bilich
Abstract:In 2021, Dzhunusov and Zaitseva classified two-dimensional normal affine commutative algebraic monoids. In this work, we extend this classification to noncommutative monoid structures on normal affine surfaces. We prove that two-dimensional algebraic monoids are toric. We also show how to find all monoid structures on a normal toric surface. Every such structure is induced by a comultiplication
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The Szlenk index of 𝐿_{𝑝}(𝑋) and 𝐴_{𝑝} Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-07-15 Ryan Causey
Abstract:Given a Banach space $X$, a $w^*$-compact subset of $X^*$, and $1
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On real hypersurfaces of 𝕊²×𝕊² Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-06-30 Dong Gao, Zejun Hu, Hui Ma, Zeke Yao
Abstract:In this paper, regarding the Riemannian product $\mathbb {S}^2\times \mathbb {S}^2$ of two unit $2$-spheres as a Kähler surface, we study its real hypersurfaces with typical geometric properties. First, we classify the real hypersurfaces of $\mathbb {S}^2\times \mathbb {S}^2$ with isometric Reeb flow and then, by using a Simons’ type inequality, a characterization of these compact real hypersurfaces
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Minimal free resolutions of fiber products Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-06-30 Hugh Geller
Abstract:We consider a local (or standard graded) ring $R$ with ideals $\mathcal {I}’$, $\mathcal {I}$, $\mathcal {J}’$, and $\mathcal {J}$ satisfying certain Tor-vanishing constraints. We construct free resolutions for quotient rings $R/\langle \mathcal {I}’, \mathcal {I}\mathcal {J}, \mathcal {J}’\rangle$, give conditions for the quotient to be realized as a fiber product, and give criteria for the
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On the Waldschmidt constant of square-free principal Borel ideals Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-06-30 Eduardo Camps Moreno, Craig Kohne, Eliseo Sarmiento, Adam Van Tuyl
Abstract:Fix a square-free monomial $m \in S = \mathbb {K}[x_1,\ldots ,x_n]$. The square-free principal Borel ideal generated by $m$, denoted $\operatorname {sfBorel}(m)$, is the ideal generated by all the square-free monomials that can be obtained via Borel moves from the monomial $m$. We give upper and lower bounds for the Waldschmidt constant of $\operatorname {sfBorel}(m)$ in terms of the support
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The Orlicz Minkowski Problem for general measures Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-06-30 Fengfan Xie
Abstract:The existence of a solution to the volume normalized Orlicz Minkowski problem is proved for general measures. This solves a limit case of Lutwak-Yang-Zhang’s existence theorem to the problem.
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Determinantal formulas for dual Grothendieck polynomials Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-06-22 Alimzhan Amanov, Damir Yeliussizov
Abstract:We prove Jacobi–Trudi-type determinantal formulas for skew dual Grothendieck polynomials which are $K$-theoretic deformations of Schur polynomials. We also obtain a bialternant-type formula analogous to the classical definition of Schur polynomials.
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Fragmentation norm and relative quasimorphisms Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-06-22 Michael Brandenbursky, Jarek Kędra
Abstract:We prove that manifolds with complicated enough fundamental group admit measure-preserving homeomorphisms which have positive stable fragmentation norm with respect to balls of bounded measure.
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A note on discrete spherical averages over sparse sequences Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-06-22 Brian Cook
Abstract:This note presents an example of an increasing sequence $(\lambda _l)_{l=1}^\infty$ such that the maximal operators associated to the normalized discrete spherical convolution averages \[ \sup _{l\geq 1}\frac {1}{r(\lambda _l)}\left |\sum _{|x|^2=\lambda _l}f(y-x)\right |,\] defined for functions $f:\mathbb {Z}^n\to \mathbb {C}$, are bounded on $\ell ^p$ for all $p>1$ when the ambient dimension
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Almost everywhere convergence of spectral sums for self-adjoint operators Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-06-17 Peng Chen, Xuan Thinh Duong, Lixin Yan
Abstract:Let $L$ be a non-negative self-adjoint operator acting on the space $L^2(X)$, where $X$ is a positive measure space. Let ${ L}=\int _0^{\infty } \lambda dE_{ L}({\lambda })$ be the spectral resolution of $L$ and $S_R({ L})f=\int _0^R dE_{ L}(\lambda ) f$ denote the spherical partial sums in terms of the resolution of ${ L}$. In this article we give a sufficient condition on $L$ such that \begin{equation*}
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On the Jacobian ideal of an almost generic hyperplane arrangement Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-06-16 Ricardo Burity, Aron Simis, Ştefan Tohǎneanu
Abstract:Let $\mathcal {A}$ denote a central hyperplane arrangement of rank $n$ in affine space $\mathbb {K}^n$ over a field $\mathbb {K}$ of characteristic zero and let $l_1,\ldots , l_m\in R≔\mathbb {K}[x_1,\ldots ,x_n]$ denote the linear forms defining the corresponding hyperplanes, along with the corresponding defining polynomial $f≔l_1\cdots l_m\in R$. The focus of the paper is on the ideal $J_f\subset
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A rigidity theorem for parabolic 2-Hessian equations Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-06-16 Yan He, Cen Pan, Ni Xiang
Abstract:In this paper, we consider the entire solution to the parabolic $2$-Hessian equation $-u_t\sigma _2(D^2 u)=1$ in $\mathbb {R}^n\times (-\infty ,0]$. We prove a rigidity theorem for the parabolic $2$-Hessian equation in $\mathbb {R}^n\times (-\infty ,0]$ by establishing Pogorelov type estimates for $2$-convex-monotone solutions.
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𝐹-thresholds and test ideals of Thom-Sebastiani type polynomials Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-06-16 Manuel González Villa, Delio Jaramillo-Velez, Luis Núñez-Betancourt
Abstract:We provide a formula for $F$-thresholds of a Thom-Sebastiani type polynomial over a perfect field of prime characteristic. We also compute the first test ideal of Thom-Sebastiani type polynomials. Finally, we apply our results to find hypersurfaces where the log canonical thresholds equal the $F$-pure thresholds for infinitely many prime numbers.
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A Feynman–Kac approach to a paper of Chung and Feller on fluctuations in the coin-tossing game Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-06-16 F. Grünbaum
Abstract:A classical result of K. L. Chung and W. Feller deals with the partial sums $S_k$ arising in a fair coin-tossing game. If $N_n$ is the number of “positive” terms among $S_1$, $S_2$, …, $S_n$ then the quantity $P(N_{2n} = 2r)$ takes an elegant form. We lift the restriction on an even number of tosses and give a simple expression for $P(N_{2n+1} = r)$, $r = 0$, $1$, $2$, …, $2n+1$. We get to
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Multiplicative ergodic theorem of semi-discrete dynamic system Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-06-10 Jiahui Feng, Xue Yang
Abstract:In this paper, Multiplicative Ergodic Theorem (MET) on manifolds with semi-discrete time variable is proved. Considering that there is no cocycle property with any semi-discrete time variable $t\in \mathbb {T}$, we define the quasi-cocycle property on forward and backward time scales. We obtain the skew-product quasi-flow with semi-discrete time variable $t\in \mathbb {T}$. For dynamic equations
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Filtered 𝐴-infinity structures in complex geometry Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-06-10 Joana Cirici, Anna Sopena-Gilboy
Abstract:We prove a filtered version of the Homotopy Transfer Theorem which gives an $A$-infinity algebra structure on any page of the spectral sequence associated to a filtered dg-algebra. We then develop various applications to the study of the geometry and topology of complex manifolds, using the Hodge filtration, as well as to complex algebraic varieties, using mixed Hodge theory.
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Boundedness theorems for flowers and sharps Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-06-10 J. Aguilera, A. Freund, M. Rathjen, A. Weiermann
Abstract:We show that the $\Sigma ^1_1$- and $\Sigma ^1_2$-boundedness theorems extend to the category of continuous dilators. We then apply these results to conclude the corresponding theorems for the category of sharps of real numbers, thus establishing another connection between Proof Theory and Set Theory, and extending work of Girard-Normann [J. Symbolic Logic 57 (1992), pp. 659–676] and Kechris-Woodin
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On Laurent biorthogonal polynomials and Painlevé-type equations Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-06-03 Xiao-Lu Yue, Xiang-Ke Chang, Xing-Biao Hu, Ya-Jie Liu
Abstract:In this paper, we investigate Laurent biorthogonal polynomials with a weight function of three parameters, i.e. $z^\alpha e^{-t_1z-\frac {t_2}{z}}, z\in (0,+\infty )$, $(t_1>0,\ t_2>0,\ \alpha \in \mathbb {R})$. First, the structure relation of the Laurent biorthogonal polynomials is found with the aid of biorthogonality. Then we derive an alternate discrete Painlevé II by considering the
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On abstract homomorphisms of some special unitary groups Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-06-03 Igor Rapinchuk, Joshua Ruiter
Abstract:We analyze the abstract representations of the groups of rational points of even-dimensional quasi-split special unitary groups associated with quadratic field extensions. We show that, under certain assumptions, such representations have a standard description, as predicted by a conjecture of Borel and Tits [Ann. of Math. (2) 97 (1973), pp. 499–571]. Our method extends the approach introduced
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Spun normal surfaces in 3-manifolds III: Boundary slopes Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-06-03 E. Kang, J. Rubinstein
Abstract:Spun normal surfaces are a useful way of representing proper essential surfaces, using ideal triangulations for 3-manifolds with tori and Klein bottle boundaries. In this paper, we consider spinning essential surfaces in an irreducible $P^2$-irreducible, anannular, atoroidal 3-manifold with tori and Klein bottle boundary components. We can assume that such a 3-manifold is equipped with an
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Constant rank theorems for Li-Yau-Hamilton type matrices of heat equations Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-06-03 Shujun Shi, Wei Zhang
Abstract:In this paper, we prove constant rank theorems for Li-Yau-Hamilton type matrices of heat equations on Riemannian manifolds as well as on Kähler manifolds under some curvature conditions.
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A note on stability of syzygy bundles on Enriques and bielliptic surfaces Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-06-03 Jayan Mukherjee, Debaditya Raychaudhury
Abstract:In this note, we prove that the syzygy bundle $M_L$ is cohomologically stable with respect to $L$ for any ample and globally generated line bundle $L$ on an Enriques (resp. bielliptic) surface over an algebraically closed field of characteristic $\neq 2$ (resp. $\neq 2,3$). In particular our result on complex Enriques surfaces improves the result of Torres-López and Zamora [Beitr. Algebra
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Random 2-cell embeddings of multistars Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-06-03 Jesse Campion Loth, Kevin Halasz, Tomáš Masařík, Bojan Mohar, Robert Šámal
Abstract:Random 2-cell embeddings of a given graph $G$ are obtained by choosing a random local rotation around every vertex. We analyze the expected number of faces, $\mathbb {E}[F_G]$, of such an embedding which is equivalent to studying its average genus. So far, tight results are known for two families called monopoles and dipoles. We extend the dipole result to a more general family called multistars
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Bernstein-Sato polynomials for general ideals vs. principal ideals Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-06-03 Mircea Mustaţă
Abstract:We show that given an ideal $\mathfrak {a}$ generated by regular functions $f_1,\ldots ,f_r$ on $X$, the Bernstein-Sato polynomial of $\mathfrak {a}$ is equal to the reduced Bernstein-Sato polynomial of the function $g=\sum _{i=1}^rf_iy_i$ on $X\times \mathbf {A}^r$. By combining this with results from Budur, Mustaţă, and Saito [Compos. Math. 142 (2006), pp. 779–797], we relate invariants
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Maximal antipodal sets related to 𝐺₂ Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-05-27 Makiko Tanaka, Hiroyuki Tasaki, Osami Yasukura
Abstract:We explicitly describe maximal antipodal sets of Riemannian symmetric spaces related to the compact connected simple Lie group of type $G_{2}$ by realizing it as the automorphism group of the octonions. Using these explicit descriptions we observe a close relation between maximal antipodal sets of the associative Grassmannian of the octonions and the Fano plane.
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Singular limit of mean-square invariant unstable manifolds for SPDEs driven by nonlinear multiplicative white noise in varying phase spaces Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-05-27 Lin Shi
Abstract:In this paper, we consider a family of stochastic partial differential equations with nonlinear multiplicative white noise. The existence of Lipschitz mean-square random invariant unstable manifolds for these equations has been obtained by Wang [Discrete Contin. Dyn. Syst. 41 (2021), pp. 1449–1468]. Based on this result, we investigate the convergence of Lipschitz mean-square random unstable
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Minimal norm Hankel operators Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-05-27 Ole Brevig
Abstract:Let $\varphi$ be a function in the Hardy space $H^2(\mathbb {T}^d)$. The associated (small) Hankel operator $\mathbf {H}_\varphi$ is said to have minimal norm if the general lower norm bound $\|\mathbf {H}_\varphi \| \geq \|\varphi \|_{H^2(\mathbb {T}^d)}$ is attained. Minimal norm Hankel operators are natural extremal candidates for the Nehari problem. If $d=1$, then $\mathbf {H}_\varphi$
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Bernoulli convolutions with Garsia parameters in (1,√2] have continuous density functions Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-05-27 Han Yu
Abstract:Let $\lambda \in (1,\sqrt {2}]$ be an algebraic integer with Mahler measure $2$. A classical result of Garsia shows that the Bernoulli convolution $\mu _\lambda$ is absolutely continuous with respect to the Lebesgue measure with a density function in $L^\infty$. In this paper, we show that the density function is continuous.
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Wavefront’s stability with asymptotic phase in the delayed monostable equations Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-05-27 Abraham Solar, Sergei Trofimchuk
Abstract:We extend the class of initial conditions for scalar delayed reaction-diffusion equations $u_t (t,x)=u_{xx}(t,x)+f(u(t, x), u(t-h, x))$ which evolve in solutions converging to monostable traveling waves. Our approach allows to compute, in the moving reference frame, the phase distortion $\alpha$ of the limiting travelling wave with respect to the position of solution at the initial moment
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A determination theorem in terms of the metric slope Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-05-27 Aris Daniilidis, David Salas
Abstract:We show that in a metric space, any continuous function with compact sublevel sets and finite metric slope is uniquely determined by the slope and its critical values.
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Quadratic residue pattern and the Galois group of ℚ(√𝕒₁,√𝕒₂,…,√𝕒_{𝕟}) Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-05-27 C. Babu, Anirban Mukhopadhyay
Abstract:Let $S= \{ a_{1}, a_{2}, \dots , a_{n} \}$ be a finite set of non-zero integers. R. Balasubramanian, F. Luca and R. Thangadurai [Proc. Amer. Math. Soc. 138 (2010), pp. 2283–2288] gave an exact formula for the degree of the multi-quadratic field $\mathbb {K}= \mathbb {Q}(\sqrt {a_{1}}, \sqrt {a_{2}}, \dots , \sqrt {a_{n}})$ over $\mathbb {Q}$. In this paper, we calculate the explicit structure
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Infinitely many quasi–arithmetic maximal reflection groups Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-05-27 Edoardo Dotti, Alexander Kolpakov
Abstract:In contrast to the fact that there are only finitely many maximal arithmetic reflection groups acting on the hyperbolic space $\mathbb {H}^n$, $n\geq 2$, we show that: one can produce infinitely many maximal quasi–arithmetic reflection groups acting on $\mathbb {H}^2$; they admit infinitely many different fields of definition; the degrees of their fields of definition are unbounded. However
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The 𝑝-primary subgroups of the cohomology of 𝐵𝑃𝑈_{𝑛} in dimensions less than 2𝑝+5 Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-05-27 Xing Gu, Yu Zhang, Zhilei Zhang, Linan Zhong
Abstract:Let $PU_n$ denote the projective unitary group of rank $n$ and $BPU_n$ be its classifying space. For an odd prime $p$, we extend previous results to a complete description of $H^s(BPU_n;\mathbb {Z})_{(p)}$ for $s<2p+5$ by showing that the $p$-primary subgroups of $H^s(BPU_n;\mathbb {Z})$ are trivial for $s = 2p+3$ and $s = 2p+4$.
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Maximal operators and Fourier restriction on the moment curve Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-05-27 Michael Jesurum
Abstract:We bound certain $r$-maximal restriction operators on the moment curve.
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𝐴_{∞} condition for general bases revisited: Complete classification of definitions Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-05-27 Dariusz Kosz
Abstract:We refer to the discussion on different characterizations of the $A_\infty$ class of weights, initiated by Duoandikoetxea, Martín-Reyes, and Ombrosi [Math. Z. 282 (2016), pp. 955–972]. Twelve definitions of the $A_\infty$ condition are considered. For cubes in $\mathbb {R}^d$ every two conditions are known to be equivalent, while for general bases we have a trichotomy: equivalence, one-way
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Improvements of 𝑝-adic estimates of exponential sums Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-05-27 Yulu Feng, Shaofang Hong
Abstract:Let $n, r$ and $f$ be positive integers. Let $p$ be a prime number and $\psi$ be an arbitrary fixed nontrivial additive character of the finite field $\mathbb F_q$ with $q=p^f$ elements. Let $F$ be a polynomial in $\mathbb F_q[x_1,\dots ,x_n]$ and $V$ be the affine algebraic variety defined over $\mathbb {F}_q$ by the simultaneous vanishing of the polynomials $\{F_i\}_{i=1}^r\subseteq \mathbb
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Adjoint Reidemeister torsions of two-bridge knots Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-05-20 Seokbeom Yoon
Abstract:We give an explicit formula for the adjoint Reidemeister torsion of two-bridge knots and prove that the adjoint Reidemeister torsion satisfies a certain type of vanishing identities.
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Critical central sections of the cube Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-05-20 Gergely Ambrus
Abstract:We study the volume of central hyperplane sections of the cube. Using Fourier analytic and variational methods, we retrieve a geometric condition characterizing critical sections which, by entirely different methods, was recently proven by Ivanov and Tsiutsiurupa [Anal. Geom. Metr. Spaces 9 (2021), pp. 1-18]. Using this characterization result, we prove that critical central hyperplane sections
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A short note on relative entropy for a pair of intermediate subfactors Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-05-20 Keshab Bakshi
Abstract:Given a quadruple of finite index subfactors we explicitly compute the Pimsner-Popa probabilistic constant for the pair of intermediate subfactors and relate it with the corresponding Connes-Størmer relative entropy between them. This generalizes an old result of Pimsner and Popa [Ann. Sci. École Norm. Sup. (4) 19 (1986), pp. 57–106].
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Stability and measurability of the modified lower dimension Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-05-20 Richárd Balka, Márton Elekes, Viktor Kiss
Abstract:The lower dimension $\dim _L$ is the dual concept of the Assouad dimension. As it fails to be monotonic, Fraser and Yu [Adv. Math. 329 (2018), pp. 273–328] introduced the modified lower dimension $dim_\textit {{ML}}$ by making the lower dimension monotonic with the simple formula $dim_\textit {{ML}}X=\sup \{\dim _L E: E\subset X\}$. As our first result we prove that the modified lower dimension
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A Łojasiewicz inequality in hypocomplex structures of ℝ² Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-05-20 Abdelhamid Meziani
Abstract:For a real analytic complex vector field $L$, in an open set of $\mathbb {R}^2$, with local first integrals that are open maps, we attach a number $\mu \ge 1$ (obtained through Łojasiewicz inequalities) and show that the equation $Lu=f$ has bounded solution when $f\in L^p$ with $p>1+\mu$. We also establish a similarity principle between the bounded solutions of the equation $Lu=Au+B\overline
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Sequence space representations for spaces of smooth functions and distributions via Wilson bases Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-05-20 C. Bargetz, A. Debrouwere, E. Nigsch
Abstract:We provide explicit sequence space representations for the test function and distribution spaces occurring in the Valdivia-Vogt structure tables by making use of Wilson bases generated by compactly supported smooth windows. Furthermore, we show that these kind of bases are common unconditional Schauder bases for all separable spaces occurring in these tables. Our work implies that the Valdivia-Vogt
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Congruences concerning generalized central trinomial coefficients Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-05-20 Jia-Yu Chen, Chen Wang
Abstract:For any $n\in \mathbb {N}=\{0,1,2,\ldots \}$ and $b,c\in \mathbb {Z}$, the generalized central trinomial coefficient $T_n(b,c)$ denotes the coefficient of $x^n$ in the expansion of $(x^2+bx+c)^n$. Let $p$ be an odd prime. In this paper, we determine the summations $\sum _{k=0}^{p-1}T_k(b,c)^2/m^k$ modulo $p^2$ for integers $m$ with certain restrictions. As applications, we confirm some conjectural
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A note on the Erdős-Hajnal hypergraph Ramsey problem Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-05-20 Dhruv Mubayi, Andrew Suk, Emily Zhu
Abstract:We show that there is an absolute constant $c>0$ such that the following holds. For every $n > 1$, there is a 5-uniform hypergraph on at least $2^{2^{cn^{1/4}}}$ vertices with independence number at most $n$, where every set of 6 vertices induces at most 3 edges. The double exponential growth rate for the number of vertices is sharp. By applying a stepping-up lemma established by the first
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Stability of closedness of semi-algebraic sets under continuous semi-algebraic mappings Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-05-20 Sĩ Đinh, Zbigniew Jelonek, Tiến Phạm
Abstract:Given a closed semi-algebraic set $X \subset \mathbb {R}^n$ and a continuous semi-algebraic mapping $G \colon X \to \mathbb {R}^m$, it will be shown that there exists an open dense semi-algebraic subset $\mathscr {U}$ of $L(\mathbb {R}^n, \mathbb {R}^m)$, the space of all linear mappings from $\mathbb {R}^n$ to $\mathbb {R}^m$, such that for all $F \in \mathscr {U}$, the image $(F + G)(X)$
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The Riemann and Lindelöf hypotheses are determined by thin sets of primes Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-05-13 William Banks
Abstract:Gonek, Graham and Lee have recently formulated an extension of the classical Lindelöf hypothesis. For various sets $\mathcal {N}$, their hypothesis $\operatorname {LH}[\,\mathcal {N}\,]$ asserts the existence of a smooth approximation $M(x)$ to the counting function of $\mathcal {N}$ that satisfies a specific set of properties. Let $\operatorname {LH}[\,\mathcal {N},M(x)\,]$ be the statement
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Properties of solutions to Pell’s equation over the polynomial ring Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-05-13 Nikoleta Kalaydzhieva
Abstract:In the classical theory, a famous by-product of the continued fraction expansion of quadratic irrational numbers $\sqrt {D}$ is the solution to Pell’s equation for $D$. It is well-known that, once an integer solution to Pell’s equation exists, we can use it to generate all other solutions $(u_n,v_n)_{n\in \mathbb {Z}}$. Our object of interest is the polynomial version of Pell’s equation, where
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On cubic fourfolds with an inductive structure Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-05-13 Kenji Koike
Abstract:We study the number of planes in four dimensional projective hypersurfaces which have so-called inductive structure. We also determine transcendental lattices of cubic fourfolds of this type.
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Corrigenda to “Two-point boundary value problems for ordinary differential equations, uniqueness implies existence” Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-05-13 Paul Eloe, Johnny Henderson
Abstract:This paper serves as a corrigenda for the article P. W. Eloe and J. Henderson, “Two-point boundary value problems for ordinary differential equations, uniqueness implies existence”, Proc. Amer. Math. Soc. 148 (2020), 4377–4387. In particular, the proof the authors give in that paper of Theorem 3.3 is incorrect, and so, that alleged theorem remains a conjecture. In this corrigenda, the authors
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A note on convergence of noncompact nonsingular solutions of the Ricci flow Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-05-13 Qi Zhang
Abstract:We extend some convergence results on nonsingular compact Ricci flows in the papers by Hamilton [Comm. Anal. Geom. 7 (1999), pp. 695–729], Sesum [Math. Res. Lett. 12 (2005), pp. 623–632] and Fang, Zhang, and Zhang [J. Geom. Anal. 20 (2010), pp. 592–608] to certain infinite volume noncompact cases which are “partially” nonsingular. As an application, for a finite time singularity which is partially
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Quantitative form of Ball’s cube slicing in ℝⁿ and equality cases in the min-entropy power inequality Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-05-13 James Melbourne, Cyril Roberto
Abstract:We prove a quantitative form of the celebrated Ball’s theorem on cube slicing in $\mathbb {R}^n$ and obtain, as a consequence, equality cases in the min-entropy power inequality. Independently, we also give a quantitative form of Khintchine’s inequality in the special case $p=1$.
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Diameters of the level sets for reaction-diffusion equations in nonperiodic slowly varying media Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-05-13 François Hamel, Grégoire Nadin
Abstract:We consider in this article reaction-diffusion equations of the Fisher-KPP type with a nonlinearity depending on the space variable $x$, oscillating slowly and non-periodically. We are interested in the width of the interface between the unstable steady state $0$ and the stable steady state $1$ of the solutions of the Cauchy problem. We prove that, if the heterogeneity has large enough oscillations
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A Gaussian version of Littlewood’s theorem for random power series Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-05-13 Guozheng Cheng, Xiang Fang, Kunyu Guo, Chao Liu
Abstract:We prove a Littlewood-type theorem for random analytic functions associated with not necessarily independent Gaussian processes. We show that if we randomize a function in the Hardy space $H^2(\mathbb {D})$ by a Gaussian process whose covariance matrix $K$ induces a bounded operator on $l^2$, then the resulting random function is almost surely in $H^p(\mathbb {D})$ for any $p>0$. The case
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The Gelfand problem on annular domains of double revolution with monotonicity Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-05-13 A. Aghajani, C. Cowan, A. Moameni
Abstract:We consider the following Gelfand problem \begin{equation*} (P)_\lambda \qquad \left \{\begin {array}{ll} -\Delta u = \lambda a(x) f(u) & \text { in } \Omega , \\ u>0 & \text { in } \Omega , \\ u= 0 & \text { on } \partial \Omega , \end{array}\right . \end{equation*} where $\lambda >0$ is a parameter and $f(u)=e^u$ or $f(u)=(u+1)^p$ where $p>1$ and $a(x)$ is a nonnegative function with certain
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Precise dispersive estimates for the wave equation inside cylindrical convex domains Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-05-13 Meas Len
Abstract:In this work, we establish precise local in time dispersive estimates for solutions of the model case Dirichlet wave equation inside cylindrical convex domains $\Omega \subset \mathbb {R}^3$ with smooth boundary $\partial \Omega \neq \emptyset$. This result is the improved estimates established by Len Meas [C. R. Math. Acad. Sci. Paris 355 (2017), pp. 161–165]. Let us recall that dispersive
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Asymptotic free independence and entry permutations for Gaussian random matrices Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-05-13 Mihai Popa
Abstract:The paper presents conditions on entry permutations that induce asymptotic freeness when acting on Gaussian random matrices. The class of permutations described includes the matrix transpose, as well as entry permutations relevant in Quantum Information Theory and Quantum Physics.
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Higher order Turán inequalities for Boros-Moll sequences Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-05-13 Jeremy Guo
Abstract:We prove that for the Boros-Moll sequences $\{d_i(m)\}_{i=0}^m$, the higher order Turán inequalities $4(d_i(m)^2 -d_{i-1}(m)d_{i+1}(m))(d_{i+1}(m)^2-d_i(m)d_{i+2}(m)) -(d_i(m)d_{i+1}(m)-d_{i-1}(m)d_{i+1}(m))^2\geq 0$ hold for $m\geq 3$ and $1\leq i\leq m-2$. As a consequence, the 3rd associated Jensen polynomials $d_i(m)+3d_{i+1}(m)x+3d_{i+2}(m)x^2+d_{i+3}(m)x^3$ have only real zeros.
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On a variant of the Beckmann–Black problem Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-05-13 François Legrand
Abstract:Given a field $k$ and a finite group $G$, the Beckmann–Black problem asks whether every Galois field extension $F/k$ with group $G$ is the specialization at some $t_0 \in k$ of some Galois field extension $E/k(T)$ with group $G$ and $E \cap \overline {k} = k$. We show that the answer is positive for arbitrary $k$ and $G$, if one waives the requirement that $E/k(T)$ is normal. In fact, our
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Countably and entropy expansive homeomorphisms with the shadowing property Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-05-13 Alfonso Artigue, Bernardo Carvalho, Welington Cordeiro, José Vieitez
Abstract:We discuss the dynamics beyond topological hyperbolicity considering homeomorphisms satisfying the shadowing property and generalizations of expansivity. It is proved that transitive countably expansive homeomorphisms satisfying the shadowing property are expansive in the set of transitive points. This is in contrast with pseudo-Anosov diffeomorphisms of the two-dimensional sphere that are
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On the 𝐶_{𝑝}-equivariant dual Steenrod algebra Proc. Am. Math. Soc. (IF 1.0) Pub Date : 2022-05-06 Krishanu Sankar, Dylan Wilson
Abstract:We compute the $C_p$-equivariant dual Steenrod algebras associated to the constant Mackey functors $\underline {\mathbb {F}}_p$ and $\underline {\mathbb {Z}}_{(p)}$, as $\mathrm {H}\underline {\mathbb {Z}}_{(p)}$-modules. The $C_p$-spectrum $\mathrm {H}\underline {\mathbb {F}}_p \wedge \mathrm {H}\underline {\mathbb {F}}_p$ is not a direct sum of $RO(C_p)$-graded suspensions of $\mathrm {H}\underline