{"title": "Rational approximation to surfaces defined by polynomials in one\n  variable", "year": 2016, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Johannes Schleischitz"], "abstract": "  We study the rational approximation properties of special manifolds defined\nby a set of polynomials with rational coefficients. Mostly we will assume the\ncase of all polynomials to depend on only one variable. In this case the\nmanifold can be viewed as a Cartesian product of polynomial curves and it is\npossible to generalize recent results concerning such curves with similar\nconcepts. There is hope that the method leads to insights on how to treat more\ngeneral manifolds defined by arbitrary polynomials with rational coefficients.\n", "doi": null, "arxiv_id": "1601.02810", "pdf_urls": ["https://arxiv.org/pdf/1601.02810"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Hungar. 155 (2018), no. 2, 362-375", "categories": "math.NT"}
{"title": "Maximal Non-commuting Sets in Certain Unipotent Upper-triangular Linear\n  Groups", "year": 2016, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["C.P. Anil Kumar and S.K. Prajapati"], "abstract": "  We find the exact size of a maximal non-commuting set in unipotent\nuppertriangular linear group $UU_4(\\mathbb{F}_q)$ in terms of a non-commuting\ngeometric structure (Refer Definition [10]), where $\\mathbb{F}_q$ is the finite\nfield with $q$ elements. Then we get bounds on the size of such a set by\nexplicitly finding certain non-commuting sets in the non-commuting structure.\n", "doi": "10.1007/s10474-016-0675-1", "arxiv_id": "1601.04133", "pdf_urls": ["https://arxiv.org/pdf/1601.04133"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Hungarica, Feb. 2017, Vol. 151, Issue 1, pp.\n  82-116, 35 pages", "categories": "math.NT"}
{"title": "Derivatives of Frobenius and Derivatives of Hodge weights", "year": 2016, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Bingyong Xie"], "abstract": "  In this paper we study the derivatives of Frobenius and the derivatives of\nHodge weights for families of Galois representations with triangulations. We\ngeneralize the Fontaine-Mazur L-invariant and use it to build a formula which\nis a generalization of the Greenberg-Stevens-Colmez formula. For the purpose of\nproving this formula we show two auxiliary results called projection vanishing\nproperty and \"projection vanishing implying L-invariants\" property.\n", "doi": null, "arxiv_id": "1601.04904", "pdf_urls": ["https://arxiv.org/pdf/1601.04904"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematics Sinica, Vol.37 No.1(2021), 1-34", "categories": "math.NT"}
{"title": "Polynomials with palindromic and unimodal coefficients", "year": 2016, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Hua Sun", "Yi Wang and Hai-Xia Zhang"], "abstract": "  Let $f(q)=a_rq^r+\\cdots+a_sq^s$, with $a_r\\neq 0$ and $a_s\\neq 0$, be a real\npolynomial. It is a palindromic polynomial of darga $n$ if $r+s=n$ and\n$a_{r+i}=a_{s-i}$ for all $i$. Polynomials of darga $n$ form a linear subspace\n$\\mathcal{P}_n(q)$ of $\\mathbb{R}(q)_{n+1}$ of dimension\n$\\lfloor{n/2}\\rfloor+1$. We give transition matrices between two bases\n$\\left\\{q^j(1+q+\\cdots+q^{n-2j})\\right\\}, \\left\\{q^j(1+q)^{n-2j}\\right\\}$ and\nthe standard basis $\\left\\{q^j(1+q^{n-2j})\\right\\}$ of $\\mathcal{P}_n(q)$. We\npresent some characterizations and sufficient conditions for palindromic\npolynomials that can be expressed in terms of these two bases with nonnegative\ncoefficients. We also point out the link between such polynomials and\nrank-generating functions of posets.\n", "doi": "10.1007/s10114-015-4331-4", "arxiv_id": "1601.05629", "pdf_urls": ["https://arxiv.org/pdf/1601.05629"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Sinica, English Series, 31 (2015), 565--575", "categories": "math.CO"}
{"title": "Global solutions of the gravity-capillary water-wave system in three\n  dimensions", "year": 2016, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Y. Deng", "A. D. Ionescu", "B. Pausader", "and F. Pusateri"], "abstract": "  In this paper we prove global regularity for the full water waves system in 3\ndimensions for small data, under the influence of both gravity and surface\ntension. This problem presents essential difficulties which were absent in all\nof the earlier global regularity results for other water wave models. To\nconstruct global solutions we use a combination of energy estimates and\nmatching dispersive estimates. There is a significant new difficulty in proving\nenergy estimates in our problem, namely the combination of slow pointwise decay\nof solutions (no better than $|t|^{-5/6}$) and the presence of a large,\ncodimension 1, set of quadratic time-resonances. To deal with such a situation\nwe propose here a new mechanism, which exploits a non-degeneracy property of\nthe time-resonant hypersurfaces and some special structure of the quadratic\npart of the nonlinearity, connected to the conserved energy of the system. The\ndispersive estimates rely on analysis of the Duhamel formula in the Fourier\nspace. The main contributions come from the set of space-time resonances, which\nis a large set of dimension 1. To control the corresponding bilinear\ninteractions we use Harmonic Analysis techniques, such as orthogonality\narguments in the Fourier space and atomic decompositions of functions. Most\nimportantly, we construct and use a refined norm which is well adapted to the\ngeometry of the problem.\n", "doi": null, "arxiv_id": "1601.05685", "pdf_urls": ["https://arxiv.org/pdf/1601.05685"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. 219 (2017), no. 2, 213-402", "categories": "math.AP math-ph math.MP"}
{"title": "The linear stability of the Schwarzschild solution to gravitational\n  perturbations", "year": 2016, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Mihalis Dafermos", "Gustav Holzegel and Igor Rodnianski"], "abstract": "  We prove in this paper the linear stability of the celebrated Schwarzschild\nfamily of black holes in general relativity: Solutions to the linearisation of\nthe Einstein vacuum equations around a Schwarzschild metric arising from\nregular initial data remain globally bounded on the black hole exterior and in\nfact decay to a linearised Kerr metric. We express the equations in a suitable\ndouble null gauge. To obtain decay, one must in fact add a residual pure gauge\nsolution which we prove to be itself quantitatively controlled from initial\ndata. Our result a fortiori includes decay statements for general solutions of\nthe Teukolsky equation (satisfied by gauge-invariant null-decomposed curvature\ncomponents). These latter statements are in fact deduced in the course of the\nproof by exploiting associated quantities shown to satisfy the Regge--Wheeler\nequation, for which appropriate decay can be obtained easily by adapting\nprevious work on the linear scalar wave equation. The bounds on the rate of\ndecay to linearised Kerr are inverse polynomial, suggesting that dispersion is\nsufficient to control the non-linearities of the Einstein equations in a\npotential future proof of nonlinear stability. This paper is self-contained and\nincludes a physical-space derivation of the equations of linearised gravity\naround Schwarzschild from the full non-linear Einstein vacuum equations\nexpressed in a double null gauge.\n", "doi": "10.4310/acta.2019.v222.n1.a1", "arxiv_id": "1601.06467", "pdf_urls": ["https://arxiv.org/pdf/1601.06467"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math., 222 (2019), 1-214", "categories": "gr-qc math-ph math.AP math.DG math.MP"}
{"title": "Asymptotic stability of the Cauchy and Jensen functional equations", "year": 2016, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Anna Bahyrycz and Zsolt P\\'ales and Magdalena Piszczek"], "abstract": "  The aim of this note is to investigate the asymptotic stability behaviour of\nthe Cauchy and Jensen functional equations. Our main results show that if these\nequations hold for large arguments with small error, then they are also valid\neverywhere with a new error term which is a constant multiple of the original\nerror term. As consequences, we also obtain results of hyperstability character\nfor these two functional equations.\n", "doi": "10.1007/s10474-016-0629-7", "arxiv_id": "1602.00300", "pdf_urls": ["https://arxiv.org/pdf/1602.00300"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Hungar. 150(1) (2016), 131-141", "categories": "math.CA"}
{"title": "Weak law of large numbers for linear processes", "year": 2016, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Vaidotas Characiejus and Alfredas Ra\\v{c}kauskas"], "abstract": "  We establish sufficient conditions for the Marcinkiewicz-Zygmund type weak\nlaw of large numbers for a linear process $\\{X_k:k\\in\\mathbb Z\\}$ defined by\n$X_k=\\sum_{j=0}^\\infty\\psi_j\\varepsilon_{k-j}$ for $k\\in\\mathbb Z$, where\n$\\{\\psi_j:j\\in\\mathbb Z\\}\\subset\\mathbb R$ and $\\{\\varepsilon_k:k\\in\\mathbb\nZ\\}$ are independent and identically distributed random variables such that\n$x^p\\Pr\\{|\\varepsilon_0|>x\\}\\to0$ as $x\\to\\infty$ with $1<p<2$ and\n$\\operatorname E\\varepsilon_0=0$. We use an abstract norming sequence that does\nnot grow faster than $n^{1/p}$ if $\\sum|\\psi_j|<\\infty$. If\n$\\sum|\\psi_j|=\\infty$, the abstract norming sequence might grow faster than\n$n^{1/p}$ as we illustrate with an example. Also, we investigate the rate of\nconvergence in the Marcinkiewicz-Zygmund type weak law of large numbers for the\nlinear process.\n", "doi": "10.1007/s10474-016-0603-4", "arxiv_id": "1602.00461", "pdf_urls": ["https://arxiv.org/pdf/1602.00461"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Hungarica, June 2016, Volume 149, Issue 1, pp\n  215-232", "categories": "math.PR"}
{"title": "Eigenvalues under the Ricci flow of model geometries", "year": 2016, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Songbo Hou"], "abstract": "  In this paper, we study the evolving behaviors of the first eigenvalue of\nLaplace-Beltrami operator under the normalized Ricci flow of model geometries.\nIn every Bianchi class, we estimate the derivative of the eigenvalue. Then we\nconstruct monotonic quantities under the Ricci flow and obtain upper and lower\nbounds for the eigenvalue.\n", "doi": null, "arxiv_id": "1602.04597", "pdf_urls": ["https://arxiv.org/pdf/1602.04597"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Sinica (Chin. Ser.) 60 (2017), no. 4, 583-594", "categories": "math.DG"}
{"title": "A hyper-K\\\"ahler compactification of the Intermediate Jacobian fibration\n  associated to a cubic fourfold", "year": 2016, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Radu Laza", "Giulia Sacc\\`a", "Claire Voisin"], "abstract": "  For a general cubic fourfold, it was observed by Donagi and Markman that the\nrelative intermediate Jacobian fibration associated to the family of its\nhyperplane sections carries a natural holomorphic symplectic form making the\nfibration Lagrangian. In this paper, we obtain a smooth projective\ncompactification of the intermediate Jacobian fibration giving a\nten-dimensional compact hyper-K\\\"ahler manifold, which we then show to be\ndeformation equivalent to the exceptional example of O'Grady. This proves a\nconjecture by Markushevich.\n", "doi": null, "arxiv_id": "1602.05534", "pdf_urls": ["https://arxiv.org/pdf/1602.05534"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. 218 (2017), no. 1, 55-135", "categories": "math.AG"}
{"title": "On small univoque bases of real numbers", "year": 2016, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Derong Kong"], "abstract": "  Given a positive real number $x$, we consider the smallest base\n$q_s(x)\\in(1,2)$ for which there exists a unique sequence $(d_i)$ of zeros and\nones such that \\[ x=\\sum_{i=1}^\\infty\\frac{d_i}{(q_s(x))^i}. \\] In this paper\nwe give complete characterizations of those $x$'s for which $q_s(x)\\le q_{KL}$,\nwhere $q_{KL}$ is the Komornik-Loreti constant. Furthermore, we show that\n$q_s(x)=q_{KL}$ if and only if \\[ x\\in\\left\\{1, ~\\frac{q_{KL}}{q_{KL}^2-1},~\n\\frac{1}{q_{KL}^2-1}, ~\\frac{1}{q_{KL}(q_{KL}^2-1)}\\right\\}. \\]\n  Finally, we determine the explicit value of $q_s(x)$ if $q_s(x)<q_{KL}$.\n", "doi": "10.1007/s10474-016-0637-7", "arxiv_id": "1602.06173", "pdf_urls": ["https://arxiv.org/pdf/1602.06173"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math Hungar 150 (1) (2016) 194--208", "categories": "math.NT"}
{"title": "Eigenvalues under the backward Ricci flow on locally homogeneous closed\n  3-manifolds", "year": 2016, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Songbo Hou"], "abstract": "  In this paper, we study the evolving behaviors of the first eigenvalue of\nLaplace-Beltrami operator under the normalized backward Ricci flow, construct\nvarious quantities which are monotonic under the backward Ricci flow and get\nupper and lower bounds. We prove that in cases where the backward Ricci flow\nconverges to a sub-Riemannian geometry after a proper rescaling, the eigenvalue\nevolves toward zero.\n", "doi": null, "arxiv_id": "1602.07824", "pdf_urls": ["https://arxiv.org/pdf/1602.07824"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math.Sin.(Engl.Ser.) 34 (2018), no. 7, 1179-1194", "categories": "math.DG"}
{"title": "Conditionally expectations and martingales in noncommutative\n  $L_p$-spaces associated with center-valued traces", "year": 2016, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Inomjon Ganiev", "Farrukh Mukhamedov"], "abstract": "  In this paper we prove the existence of conditional expectations in the\nnoncommutative $L_p(M,\\Phi)$ spaces associated with center-valued traces.\nMoreover, their description is also provided. As an application of the obtained\nresults, we establish the norm convergence of the martingales in noncommutative\n$L_p(M,\\Phi)$ spaces.\n", "doi": "10.1016/s0252-9602(17)30055-3", "arxiv_id": "1603.08621", "pdf_urls": ["https://arxiv.org/pdf/1603.08621"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Scientia, 37(2017,) 1019-1032", "categories": "math.OA math.FA"}
{"title": "Computing the Thurston-Bennequin invariant in open books", "year": 2016, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Sebastian Durst", "Marc Kegel", "and Mirko Klukas"], "abstract": "We give explicit formulas and algorithms for the computation of the Thurston-Bennequin invariant of a nullhomologous Legendrian knot on a page of a contact open book and on contact Heegaard surfaces. Furthermore, we extend the results to rationally nullhomologous knots in arbitrary 3-manifolds.", "doi": "10.1007/s10474-016-0648-4", "arxiv_id": "1605.00794", "pdf_urls": ["https://arxiv.org/pdf/1605.00794"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Hungar. 150 (2016), 441-455", "categories": "math.GT math.SG"}
{"title": "Computing rotation and self-linking numbers in contact surgery diagrams", "year": 2016, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Sebastian Durst and Marc Kegel"], "abstract": "  We give an explicit formula to compute the rotation number of a\nnullhomologous Legendrian knot in contact (1/n)-surgery diagrams along\nLegendrian links and obtain a corresponding result for the self-linking number\nof transverse knots. Moreover, we extend the formula by Ding-Geiges-Stipsicz\nfor computing the d3-invariant to (1/n)-surgeries.\n", "doi": "10.1007/s10474-016-0660-8", "arxiv_id": "1605.00795", "pdf_urls": ["https://arxiv.org/pdf/1605.00795"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Hungar. 150 (2016), 524-540", "categories": "math.GT math.SG"}
{"title": "On the p-adic valuation of Stirling numbers of the first kind", "year": 2016, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Paolo Leonetti and Carlo Sanna"], "abstract": "  For all integers $n \\geq k \\geq 1$, define $H(n,k) := \\sum 1 / (i_1 \\cdots\ni_k)$, where the sum is extended over all positive integers $i_1 < \\cdots < i_k\n\\leq n$. These quantities are closely related to the Stirling numbers of the\nfirst kind by the identity $H(n,k) = s(n + 1, k + 1) / n!$. Motivated by the\nworks of Erd\\H{o}s-Niven and Chen-Tang, we study the $p$-adic valuation of\n$H(n,k)$. In particular, for any prime number $p$, integer $k \\geq 2$, and $x\n\\geq (k-1)p$, we prove that $\\nu_p(H(n,k)) < -(k - 1)(\\log_p(n/(k - 1)) - 1)$\nfor all positive integers $n \\in [(k-1)p, x]$ whose base $p$ representations\nstart with the base $p$ representation of $k - 1$, but at most $3x^{0.835}$\nexceptions. We also generalize a result of Lengyel by giving a description of\n$\\nu_2(H(n,2))$ in terms of an infinite binary sequence.\n", "doi": "10.1007/s10474-016-0680-4", "arxiv_id": "1605.07424", "pdf_urls": ["https://arxiv.org/pdf/1605.07424"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Hungarica 151 (2017) 217-231", "categories": "math.NT math.CO"}
{"title": "The global non-linear stability of the Kerr-de Sitter family of black\n  holes", "year": 2016, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Peter Hintz", "Andr\\'as Vasy"], "abstract": "  We establish the full global non-linear stability of the Kerr-de Sitter\nfamily of black holes, as solutions of the initial value problem for the\nEinstein vacuum equations with positive cosmological constant, for small\nangular momenta, and without any symmetry assumptions on the initial data. We\nachieve this by extending the linear and non-linear analysis on black hole\nspacetimes described in a sequence of earlier papers by the authors: We develop\na general framework which enables us to deal systematically with the\ndiffeomorphism invariance of Einstein's equations. In particular, the iteration\nscheme used to solve Einstein's equations automatically finds the parameters of\nthe Kerr-de Sitter black hole that the solution is asymptotic to, the\nexponentially decaying tail of the solution, and the gauge in which we are able\nto find the solution; the gauge here is a wave map/DeTurck type gauge, modified\nby source terms which are treated as unknowns, lying in a suitable\nfinite-dimensional space.\n", "doi": "10.4310/acta.2018.v220.n1.a1", "arxiv_id": "1606.04014", "pdf_urls": ["https://arxiv.org/pdf/1606.04014"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica, 220:1-206, 2018", "categories": "math.DG gr-qc math-ph math.AP math.MP"}
{"title": "Sharp constant for Poincar\\'e-type inequalities in the hyperbolic space", "year": 2016, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Qu\\^oc-Anh Ng\\^o and Van Hoang Nguyen"], "abstract": "  In this note, we establish a Poincar\\'e-type inequality on the hyperbolic\nspace $\\mathbb H^n$, namely \\[ \\|u\\|_{p} \\leqslant C(n,m,p) \\|\\nabla^m_g\nu\\|_{p} \\] for any $u \\in W^{m,p}(\\mathbb H^n)$. We prove that the sharp\nconstant $C(n,m,p)$ for the above inequality is \\[ C(n,m,p) = \\begin{cases}\n\\left( p p'/(n-1)^2 \\right)^{m/2}&\\mbox{if $m$ is even},\\\\ (p/(n-1))\\left( p\np'/(n-1)^2\\right)^{(m-1)/2} &\\mbox{if $m$ is odd}, \\end{cases} \\] with $p' =\np/(p-1)$ and this sharp constant is never achieved in $W^{m,p}(\\mathbb H^n)$.\nOur proofs rely on the symmetrization method extended to hyperbolic spaces.\n", "doi": "10.1007/s40306-018-0269-9", "arxiv_id": "1607.00154", "pdf_urls": ["https://arxiv.org/pdf/1607.00154"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Vietnamica 44 (2019) 781-795", "categories": "math.FA math.CA"}
{"title": "Homogeneous ideals on countable sets", "year": 2016, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Adam Kwela and Jacek Tryba"], "abstract": "  We say that an ideal I is homogeneous, if its restriction to any I-positive\nsubset is isomorphic to I. The paper investigates basic properties of this\nnotion -- we give examples of homogeneous ideals and present some applications\nto topology and ideal convergence. Moreover, we answer questions related to our\nresearch.\n", "doi": "10.1007/s10474-016-0669-z", "arxiv_id": "1607.05610", "pdf_urls": ["https://arxiv.org/pdf/1607.05610"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Hungar., 151, No. 1, (2017), pp. 139-161", "categories": "math.LO"}
{"title": "On the equation $ \\boldsymbol{n_1n_2=n_3n_4}$ restricted to factor\n  closed sets", "year": 2016, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Sanying Shi", "Michel Weber"], "abstract": "  We study the number of solutions $N(B,F)$ of the diophantine equation\n$n_1n_2=n_3n_4$, where $1\\le n_1\\le B$, $1\\le n_3\\le B$, $n_2, n_4\\in F$ and\n$F\\subset [1,B]$ is a factor closed set. We study more particularly the case\nwhen $F= \\big\\{m=p_1^{\\e_1}\\ldots p_k^{\\e_k}, \\e_j\\in \\{0,1\\}, 1\\le j\\le\nk\\big\\}$,\n  $p_1,\\ldots,p_k$ being distinct prime numbers.\n", "doi": null, "arxiv_id": "1607.06366", "pdf_urls": ["https://arxiv.org/pdf/1607.06366"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Sinica , 2018 , vol. 34 No. 10, pp. 1517--1530", "categories": "math.NT"}
{"title": "Harmonic oscillators at resonance, perturbed by a non-linear friction\n  force", "year": 2016, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Philip Korman and Yi Li"], "abstract": "  This note is an addendum to the results of P.O. Frederickson and A.C. Lazer\n[1], and A.C. Lazer [4] on periodic oscillations, with linear part at\nresonance. We show that a small modification of the argument in [4] provides a\nmore general result. It turns out that things are different for the\ncorresponding Dirichlet boundary value problem.\n", "doi": null, "arxiv_id": "1609.00369", "pdf_urls": ["https://arxiv.org/pdf/1609.00369"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Scientia Ser. B Engl. Ed. 34 (2014), no. 4,\n  1025-1028", "categories": "math.CA math.AP"}
{"title": "Enumeration of cubic Cayley graphs on dihedral groups", "year": 2016, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Xueyi Huang", "Qiongxiang Huang", "Lu Lu"], "abstract": "  Let $p$ be an odd prime, and $D_{2p}=\\langle a,b\\mid\na^p=b^2=1,bab=a^{-1}\\rangle$ the dihedral group of order $2p$. In this paper,\nwe completely classify the cubic Cayley graphs on $D_{2p}$ up to isomorphism by\nmeans of spectral method. By the way, we show that two cubic Cayley graphs on\n$D_{2p}$ are isomorphic if and only if they are cospectral. Moreover, we obtain\nthe number of isomorphic classes of cubic Cayley graphs on $D_{2p}$ by using\nGauss' celebrated law of quadratic reciprocity.\n", "doi": "10.1007/s10114-017-6241-0", "arxiv_id": "1609.05419", "pdf_urls": ["https://arxiv.org/pdf/1609.05419"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Sinica, English Series, 2017, 33(7): 996-1010", "categories": "math.CO"}
{"title": "Arithmetic properties for cubic partition pairs modulo powers of 3", "year": 2016, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Shane Chern"], "abstract": "  Let $b(n)$ denote the number of cubic partition pairs of $n$. In this paper,\nwe aim to provide a strategy to obtain arithmetic properties of $b(n)$. This\ngives affirmative answers to two of Lin's conjectures.\n", "doi": "10.1007/s10114-017-7052-z", "arxiv_id": "1609.08578", "pdf_urls": ["https://arxiv.org/pdf/1609.08578"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Sin. (Engl. Ser.) 33 (2017), no. 11, 1504--1512", "categories": "math.NT math.CO"}
{"title": "Improved bounds on the diameter of lattice polytopes", "year": 2016, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Antoine Deza", "Lionel Pournin"], "abstract": "  We show that the largest possible diameter $\\delta(d,k)$ of a $d$-dimensional\npolytope whose vertices have integer coordinates ranging between $0$ and $k$ is\nat most $kd-\\lceil2d/3\\rceil$ when $k\\geq3$. In addition, we show that\n$\\delta(4,3)=8$. This substantiates the conjecture whereby $\\delta(d,k)$ is at\nmost $\\lfloor(k+1)d/2\\rfloor$ and is achieved by a Minkowski sum of lattice\nvectors.\n", "doi": "10.1007/s10474-017-0777-4", "arxiv_id": "1610.00341", "pdf_urls": ["https://arxiv.org/pdf/1610.00341"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Hung. 154(2), 457-469 (2018)", "categories": "math.MG math.CO math.OC"}
{"title": "Coloring decompositions of complete geometric graphs", "year": 2016, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Clemens Huemer", "Dolores Lara", "and Christian Rubio-Montiel"], "abstract": "  A decomposition of a non-empty simple graph $G$ is a pair $[G,P]$, such that\n$P$ is a set of non-empty induced subgraphs of $G$, and every edge of $G$\nbelongs to exactly one subgraph in $P$. The chromatic index $\\chi'([G,P])$ of a\ndecomposition $[G,P]$ is the smallest number $k$ for which there exists a\n$k$-coloring of the elements of $P$ in such a way that: for every element of\n$P$ all of its edges have the same color, and if two members of $P$ share at\nleast one vertex, then they have different colors. A long standing conjecture\nof Erd\\H{o}s-Faber-Lov\\'asz states that every decomposition $[K_n,P]$ of the\ncomplete graph $K_n$ satisfies $\\chi'([K_n,P])\\leq n$. In this paper we work\nwith geometric graphs, and inspired by this formulation of the conjecture, we\nintroduce the concept of chromatic index of a decomposition of the complete\ngeometric graph. We present bounds for the chromatic index of several types of\ndecompositions when the vertices of the graph are in general position. We also\nconsider the particular case in which the vertices are in convex position and\npresent bounds for the chromatic index of a few types of decompositions.\n", "doi": "10.1007/s10474-019-00963-0", "arxiv_id": "1610.01676", "pdf_urls": ["https://arxiv.org/pdf/1610.01676"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Hungarica-2019", "categories": "math.CO"}
{"title": "Fodor's lemma can fail everywhere", "year": 2016, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Asaf Karagila"], "abstract": "  We show that it is equiconsistent with $\\mathsf{ZF}$ that Fodor's lemma fails\neverywhere, and furthermore that the club filter on every regular cardinal is\nnot even $\\sigma$-complete. Moreover, these failures can be controlled in a\nvery precise manner.\n", "doi": "10.1007/s10474-017-0768-5", "arxiv_id": "1610.03985", "pdf_urls": ["https://arxiv.org/pdf/1610.03985"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Hungar. (2018) 154: 231", "categories": "math.LO"}
{"title": "A Dirichlet type problem for complex polyharmonic functions", "year": 2016, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Hubert Grzebu{\\l}a", "S{\\l}awomir Michalik"], "abstract": "  We extend holomorphically polyharmonic functions on a real ball to a complex\nset being the union of rotated balls. We solve a Dirichlet type problem for\ncomplex polyharmonic functions with the boundary condition given on the union\nof rotated spheres.\n", "doi": "10.1007/s10474-017-0740-4", "arxiv_id": "1610.04928", "pdf_urls": ["https://arxiv.org/pdf/1610.04928"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Hungar. 153 (2017), 216-229", "categories": "math.AP math.CV"}
{"title": "Approximate derivations of order $n$", "year": 2016, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Eszter Gselmann"], "abstract": "  The aim of this paper is to prove characterization theorems for higher order\nderivations. Among others we prove that the system defining higher order\nderivations is stable. Further characterization theorems in the spirit of\nN.~G.~de Bruijn will also be presented.\n", "doi": "10.1007/s10474-014-0422-4", "arxiv_id": "1612.01365", "pdf_urls": ["https://arxiv.org/pdf/1612.01365"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Hungarica, vol. 144, no. 1 (2014), 217-226", "categories": "math.CA math.FA"}
{"title": "Harmonic analysis for real spherical spaces", "year": 2016, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Bernhard Kr\\\"otz", "Henrik Schlichtkrull"], "abstract": "  We give an introduction to basic harmonic analysis and representation theory\nfor homogeneous spaces $Z=G/H$ attached to a real reductive Lie group $G$. A\nspecial emphasis is made to the case where $Z$ is real spherical.\n", "doi": null, "arxiv_id": "1612.01841", "pdf_urls": ["https://arxiv.org/pdf/1612.01841"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Sinica 34(3) (2018), 341-370", "categories": "math.RT"}
{"title": "Non-normal affine monoids, modules and Poincar\\'e series of plumbed\n  3-manifolds", "year": 2016, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Tam\\'as L\\'aszl\\'o and Zsolt Szil\\'agyi"], "abstract": "  We construct a non-normal affine monoid together with its modules associated\nwith a negative definite plumbed $3$-manifold $M$. In terms of their structure,\nwe describe the $H_1(M,\\mathbb{Z})$-equivariant parts of the topological\nPoincar\\'e series. In particular, we give combinatorial formulas for the\nSeiberg--Witten invariants of $M$ and for polynomial generalizations defined in\na previous paper of the authors.\n", "doi": "10.1007/s10474-017-0726-2", "arxiv_id": "1612.07537", "pdf_urls": ["https://arxiv.org/pdf/1612.07537"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Hungarica 152 (2017), no. 2, 421-452", "categories": "math.GT math.AG math.CO"}
{"title": "The KPZ fixed point", "year": 2017, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Konstantin Matetski", "Jeremy Quastel", "Daniel Remenik"], "abstract": "  An explicit Fredholm determinant formula is derived for the multipoint\ndistribution of the height function of the totally asymmetric simple exclusion\nprocess (TASEP) with arbitrary right-finite initial condition. The method is by\nsolving the biorthogonal ensemble/non-intersecting path representation found by\n[Sas05; BFPS07]. The resulting kernel involves transition probabilities of a\nrandom walk forced to hit a curve defined by the initial data.\n  In the KPZ 1:2:3 scaling limit the formula leads in a transparent way to a\nFredholm determinant formula, in terms of analogous kernels based on Brownian\nmotion, for the transition probabilities of the scaling invariant Markov\nprocess at the centre of the KPZ universality class. The formula readily\nreproduces known special self-similar solutions such as the Airy$_1$ and\nAiry$_2$ processes. The process takes values in real valued functions which\nlook locally like Brownian motion, and is H\\\"older $1/3-$ in time.\n  Both the KPZ fixed point and TASEP are shown to be stochastic integrable\nsystems in the sense that the time evolution of their transition probabilities\ncan be linearized through a new Brownian scattering transform and its discrete\nanalogue.\n", "doi": "10.4310/acta.2021.v227.n1.a3", "arxiv_id": "1701.00018", "pdf_urls": ["https://arxiv.org/pdf/1701.00018"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. 227, 115-203 (2021)", "categories": "math.PR math-ph math.MP"}
{"title": "Commutativity of integral quasi-arithmetic means on measure spaces", "year": 2017, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Dorota G{\\l}azowska", "Paolo Leonetti", "Janusz Matkowski", "and Salvatore\n  Tringali"], "abstract": "  Let $(X, \\mathscr{L}, \\lambda)$ and $(Y, \\mathscr{M}, \\mu)$ be finite measure\nspaces for which there exist $A \\in \\mathscr{L}$ and $B \\in \\mathscr{M}$ with\n$0 < \\lambda(A) < \\lambda(X)$ and $0 < \\mu(B) < \\mu(Y)$, and let $I\\subseteq\n\\mathbf{R}$ be a non-empty interval. We prove that, if $f$ and $g$ are\ncontinuous bijections $I \\to \\mathbf{R}^+$, then the equation $$\nf^{-1}\\!\\left(\\int_X f\\!\\left(g^{-1}\\!\\left(\\int_Y g \\circ\nh\\;d\\mu\\right)\\right)d \\lambda\\right)\\! = g^{-1}\\!\\left(\\int_Y\ng\\!\\left(f^{-1}\\!\\left(\\int_X f \\circ h\\;d\\lambda\\right)\\right)d \\mu\\right)$$\nis satisfied by every $\\mathscr{L} \\otimes \\mathscr{M}$-measurable simple\nfunction $h: X \\times Y \\to I$ if and only if $f=c g$ for some $c \\in\n\\mathbf{R}^+$ (it is easy to see that the equation is well posed). An\nanalogous, but essentially different, result, with $f$ and $g$ replaced by\ncontinuous injections $I \\to \\mathbf R$ and $\\lambda(X)=\\mu(Y)=1$, was recently\nobtained in [Indag. Math. 27 (2016), 945-953].\n", "doi": "10.1007/s10474-017-0734-2", "arxiv_id": "1703.03938", "pdf_urls": ["https://arxiv.org/pdf/1703.03938"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Hungar., Vol. 153, No. 2 (2017), 350-355", "categories": "math.CA"}
{"title": "Geometric counting on wavefront real spherical spaces", "year": 2017, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Bernhard Kr\\\"otz", "Eitan Sayag", "Henrik Schlichtkrull"], "abstract": "  We provide $L^p$-versus $L^\\infty$-bounds for eigenfunctions on a real\nspherical space $Z$ of wavefront type. It is shown that these bounds imply a\nnon-trivial error term estimate for lattice counting on $Z$. The paper also\nserves as an introduction to geometric counting on spaces of the mentioned\ntype. Section 7 on higher rank is new and extends the result from v1 to higher\nrank. Final version. To appear in Acta Math. Sinica.\n", "doi": null, "arxiv_id": "1703.10947", "pdf_urls": ["https://arxiv.org/pdf/1703.10947"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Sinica 34(3) (2018), 488-531", "categories": "math.RT math.NT"}
{"title": "Unions of admissible relations", "year": 2017, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Paolo Lipparini"], "abstract": "  We show that a variety $\\mathcal V$ is congruence distributive if and only if\nthere is some $h$ such that the inclusion\n  (1) $\\Theta \\cap ( \\sigma \\circ \\sigma ) \\subseteq ( \\Theta \\cap \\sigma )\n\\circ ( \\Theta \\cap \\sigma ) \\circ \\dots $ ($h$ factors)\n  holds in every algebra in $\\mathcal V$, for every tolerance $\\Theta$ and\nevery U-admissible relation $\\sigma$. By a U-admissible relation we mean a\nbinary relation which is the set-theoretical union of a set of reflexive and\nadmissible relations. For any fixed $h$, a Maltsev-type characterization is\ngiven for the inclusion (1). It is an open problem whether (1) is still\nequivalent to congruence distributivity when $\\Theta$ is assumed to be a\n$U$-admissible relation, rather than a tolerance. In both cases many equivalent\nformulations for (1) are presented. The results suggest that it might be\ninteresting to study the structure of the set of U-admissible relations on an\nalgebra, as well as identities dealing with such relations.\n", "doi": null, "arxiv_id": "1704.02476", "pdf_urls": ["https://arxiv.org/pdf/1704.02476"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Universitatis Comenianae Vol 87 No 2 (2018)\n  251-266\n  http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/681/625", "categories": "math.RA"}
{"title": "Standard Embeddings of Smooth Schubert Varieties in Rational Homogeneous\n  Manifolds of Picard Number 1", "year": 2017, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Shin-Young Kim and Kyeong-Dong Park"], "abstract": "  Smooth Schubert varieties in rational homogeneous manifolds of Picard number\n1 are horospherical varieties. We characterize standard embeddings of smooth\nSchubert varieties in rational homogeneous manifolds of Picard number 1 by\nmeans of varieties of minimal rational tangents. In particular, we mainly\nconsider nonhomogeneous smooth Schubert varieties in symplectic Grassmannians\nand in the 20-dimensional $F_4$-homogeneous manifold associated to a short\nsimple root.\n", "doi": "10.1007/s10114-018-7165-z", "arxiv_id": "1704.05206", "pdf_urls": ["https://arxiv.org/pdf/1704.05206"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Sinica, English Series (2018) 34: 466", "categories": "math.AG math.DG"}
{"title": "Sums of four prime cubes in short intervals", "year": 2017, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Alessandro Languasco and Alessandro Zaccagnini"], "abstract": "  We prove that a suitable asymptotic formula for the average number of\nrepresentations of integers $n=p_{1}^{3}+p_{2}^{3}+p_{3}^{3}+p_{4}^{3}$, where\n$p_1,p_2,p_3,p_4$ are prime numbers, holds in intervals shorter than the the\nones previously known.\n", "doi": "10.1007/s10474-019-00973-y", "arxiv_id": "1705.04457", "pdf_urls": ["https://arxiv.org/pdf/1705.04457"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Hungarica 159 (2019), 150--163", "categories": "math.NT"}
{"title": "Pencilled regular parallelisms", "year": 2017, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Hans Havlicek and Rolf Riesinger"], "abstract": "  Over any field $\\mathbb K$, there is a bijection between regular spreads of\nthe projective space ${\\rm PG}(3,{\\mathbb K})$ and $0$-secant lines of the\nKlein quadric in ${\\rm PG}(5,{\\mathbb K})$. Under this bijection, regular\nparallelisms of ${\\rm PG}(3,{\\mathbb K})$ correspond to hyperflock determining\nline sets (hfd line sets) with respect to the Klein quadric. An hfd line set is\ndefined to be \\emph{pencilled} if it is composed of pencils of lines. We\npresent a construction of pencilled hfd line sets, which is then shown to\ndetermine all such sets. Based on these results, we describe the corresponding\nregular parallelisms. These are also termed as being \\emph{pencilled}. Any\nClifford parallelism is regular and pencilled. From this, we derive necessary\nand sufficient algebraic conditions for the existence of pencilled hfd line\nsets.\n", "doi": "10.1007/s10474-017-0742-2", "arxiv_id": "1705.07276", "pdf_urls": ["https://arxiv.org/pdf/1705.07276"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Hungar. 153 (2017), 249-264", "categories": "math.AG math.RA"}
{"title": "Metric Mahler measures over number fields", "year": 2017, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Charles L. Samuels"], "abstract": "  For an algebraic number $\\alpha$, the metric Mahler measure $m_1(\\alpha)$ was\nfirst studied by Dubickas and Smyth in 2001 and was later generalized to the\n$t$-metric Mahler measure $m_t(\\alpha)$ by the author in 2010. The definition\nof $m_t(\\alpha)$ involves taking an infimum over a certain collection\n$N$-tuples of points in $\\overline{\\mathbb Q}$, and from previous work of\nJankauskas and the author, the infimum in the definition of $m_t(\\alpha)$ is\nattained by rational points when $\\alpha\\in \\mathbb Q$. As a consequence of our\nmain theorem in this article, we obtain an analog of this result when $\\mathbb\nQ$ is replaced with any imaginary quadratic number field of class number equal\nto $1$. Further, we study examples of other number fields to which our methods\nmay be applied, and we establish various partial results in those cases.\n", "doi": "10.1007/s10474-017-0770-y", "arxiv_id": "1705.07932", "pdf_urls": ["https://arxiv.org/pdf/1705.07932"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Hungar. 154 (2018), no. 1, 105--123", "categories": "math.NT"}
{"title": "Minimal complex surfaces with Levi-Civita Ricci-flat metrics", "year": 2017, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Kefeng Liu", "Xiaokui Yang"], "abstract": "  This is a continuation of our previous paper [14]. In [14], we introduced the\nfirst Aeppli-Chern class on compact complex manifolds, and proved that the\n$(1,1)$ curvature form of the Levi-Civita connection represents the first\nAeppli-Chern class which is a natural link between Riemannian geometry and\ncomplex geometry. In this paper, we study the geometry of compact complex\nmanifolds with Levi-Civita Ricci-flat metrics and classify minimal complex\nsurfaces with Levi-Civita Ricci-flat metrics. More precisely, we show that\nminimal complex surfaces admitting Levi-Civita Ricci-flat metrics are K\\\"ahler\nCalabi-Yau surfaces and Hopf surfaces.\n", "doi": null, "arxiv_id": "1706.01219", "pdf_urls": ["https://arxiv.org/pdf/1706.01219"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Sinica. 34(2018), 1195-1207", "categories": "math.DG"}
{"title": "Stability of Depth and Cohen-Macaulayness of Integral Closures of Powers\n  of Monomial Ideals", "year": 2017, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Le Tuan Hoa and Tran Nam Trung"], "abstract": "  Let $I$ be a monomial ideal $I$ in a polynomial ring $R = k[x_1,...,x_r]$. In\nthis paper we give an upper bound on $\\overline{\\dstab} (I)$ in terms of $r$\nand the maximal generating degree $d(I)$ of $I$ such that $\\depth\nR/\\overline{I^n}$ is constant for all $n\\geqslant \\overline{\\dstab}(I)$. As an\napplication, we classify the class of monomial ideals $I$ such that\n$\\overline{I^n}$ is Cohen-Macaulay for some integer $n\\gg 0$.\n", "doi": "10.1007/s40306-017-0225-0", "arxiv_id": "1706.07603", "pdf_urls": ["https://arxiv.org/pdf/1706.07603"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math Vietnam. 43 (2018), 67 - 81", "categories": "math.AC"}
{"title": "An explicit formula for Szego kernels on the Heisenberg group", "year": 2017, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Hendrik Herrmann", "Chin-Yu Hsiao and Xiaoshan Li"], "abstract": "  In this paper, we give an explicit formula for the Szego kernel for $(0, q)$\nforms on the Heisenberg group $H_{n+1}$.\n", "doi": null, "arxiv_id": "1706.09762", "pdf_urls": ["https://arxiv.org/pdf/1706.09762"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Sinica, English Series, 34 (8), 1225-1247, 2018", "categories": "math.CV"}
{"title": "Mirror symmetry for very affine hypersurfaces", "year": 2017, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Benjamin Gammage and Vivek Shende"], "abstract": "  We show that the category of coherent sheaves on the toric boundary divisor\nof a smooth quasiprojective toric DM stack is equivalent to the wrapped Fukaya\ncategory of a hypersurface in a complex torus. Hypersurfaces with every Newton\npolytope can be obtained.\n  Our proof has the following ingredients. Using recent results on\nlocalization, we may trade wrapped Fukaya categories for microlocal sheaf\ntheory along the skeleton of the hypersurface. Using Mikhalkin-Viro\npatchworking, we identify the skeleton of the hypersurface with the boundary of\nthe Fang-Liu-Treumann-Zaslow skeleton. By proving a new functoriality result\nfor Bondal's coherent-constructible correspondence, we reduce the sheaf\ncalculation to Kuwagaki's recent theorem on mirror symmetry for toric\nvarieties.\n", "doi": "10.4310/acta.2022.v229.n2.a2", "arxiv_id": "1707.02959", "pdf_urls": ["https://arxiv.org/pdf/1707.02959"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. 229:2 (2022), 287-346", "categories": "math.SG math.AG"}
{"title": "Assassins and torsion functors", "year": 2017, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Fred Rohrer"], "abstract": "  Let $R$ be a ring, let $\\mathfrak{a}\\subseteq R$ be an ideal, and let $M$ be\nan $R$-module. Let $\\Gamma_{\\mathfrak{a}}$ denote the $\\mathfrak{a}$-torsion\nfunctor. Conditions are given for the (weakly) associated primes of\n$\\Gamma_{\\mathfrak{a}}(M)$ to be the (weakly) associated primes of $M$\ncontaining $\\mathfrak{a}$, and for the (weakly) associated primes of\n$M/\\Gamma_{\\mathfrak{a}}(M)$ to be the (weakly) associated primes of $M$ not\ncontaining $\\mathfrak{a}$.\n", "doi": "10.1007/s40306-017-0233-0", "arxiv_id": "1708.09008", "pdf_urls": ["https://arxiv.org/pdf/1708.09008"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Vietnam. 43 (2018), 125-136", "categories": "math.AC"}
{"title": "On compact Hermitian manifolds with flat Gauduchon connections", "year": 2017, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Bo Yang and Fangyang Zheng"], "abstract": "  Given a Hermitian manifold $(M^n,g)$, the Gauduchon connections are the one\nparameter family of Hermitian connections joining the Chern connection and the\nBismut connection. We will call $\\nabla^s = (1-\\frac{s}{2})\\nabla^c +\n\\frac{s}{2}\\nabla^b$ the $s$-Gauduchon connection of $M$, where $\\nabla^c$ and\n$\\nabla^b$ are respectively the Chern and Bismut connections. It is natural to\nask when a compact Hermitian manifold could admit a flat $s$-Gauduchon\nconnection. This is related to a question asked by Yau \\cite{Yau}. The cases\nwith $s=0$ (a flat Chern connection) or $s=2$ (a flat Bismut connection) are\nclassified respectively by Boothby \\cite{Boothby} in the 1950s or by Q. Wang\nand the authors recently \\cite{WYZ}. In this article, we observe that if either\n$s\\geq 4+2\\sqrt{3} \\approx 7.46$ or $s\\leq 4-2\\sqrt{3}\\approx 0.54$ and $s\\neq\n0$, then $g$ is K\\\"ahler. We also show that, when $n=2$, $g$ is always K\\\"ahler\nunless $s=2$. Note that non-K\\\"ahler compact Bismut flat surfaces are exactly\nthose isosceles Hopf surfaces by \\cite{WYZ}.\n", "doi": null, "arxiv_id": "1709.02530", "pdf_urls": ["https://arxiv.org/pdf/1709.02530"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta. Math. Sinica (English Series), 34 (2018), no.8, 1259-1268", "categories": "math.DG"}
{"title": "Hyperfinite graphings and combinatorial optimization", "year": 2017, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["L\\'aszl\\'o Lov\\'asz"], "abstract": "  We exhibit an analogy between the problem of pushing forward measurable sets\nunder measure preserving maps and linear relaxations in\ncombinatorialoptimization. We show how invariance of hyperfiniteness of\ngraphings under local isomorphism can be reformulated as an infinite version of\na natural combinatorial optimization problem, and how one can prove it by\nextending well-known proof techniques (linear relaxation, greedy algorithm,\nlinear programming duality) from the finite case to the infinite.\n", "doi": null, "arxiv_id": "1709.03179", "pdf_urls": ["https://arxiv.org/pdf/1709.03179"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Hung. 161 (2020), 516--539", "categories": "math.CO"}
{"title": "Some integrals of hypergeometric functions", "year": 2017, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Andr\\'as Bir\\'o"], "abstract": "  We consider a certain definite integral involving the product of two\nclassical hypergeometric functions having complicated arguments. We show in\nthis paper the surprising fact that this integral does not depend on the\nparameters of the hypergeometric functions.\n", "doi": null, "arxiv_id": "1709.03475", "pdf_urls": ["https://arxiv.org/pdf/1709.03475"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Hung., 152 (2017), 1, 58-71", "categories": "math.CA"}
{"title": "On a conformally invariant integral equation involving Poisson kernel", "year": 2017, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Jingang Xiong"], "abstract": "  We study a prescribing functions problem of a conformally invariant integral\nequation involving Poisson kernel on the unit ball. This integral equation is\nnot the dual of any standard type of PDE. As in Nirenberg problem, there exists\na Kazdan-Warner type obstruction to existence of solutions. We prove existence\nin the antipodal symmetry functions class.\n", "doi": null, "arxiv_id": "1709.04124", "pdf_urls": ["https://arxiv.org/pdf/1709.04124"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Sin. (Engl. Ser.) 34 (2018), no. 4, 681-690", "categories": "math.AP"}
{"title": "Graphs, Skeleta and Reconstruction of Polytopes", "year": 2017, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Margaret M. Bayer (University of Kansas)"], "abstract": "  A renowned theorem of Blind and Mani, with a constructive proof by Kalai and\nan efficiency proof by Friedman, shows that the whole face lattice of a simple\npolytope can be determined from its graph. This is part of a broader story of\nreconstructing face lattices from partial information, first considered\ncomprehensively in Gr\\\"unbaum's 1967 book. This survey paper includes varied\nresults and open questions by many researchers on simplicial polytopes, nearly\nsimple polytopes, cubical polytopes, zonotopes, crosspolytopes, and Eulerian\nposets.\n", "doi": null, "arxiv_id": "1710.00118", "pdf_urls": ["https://arxiv.org/pdf/1710.00118"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Hungar. 155 (2018), no. 1, 61-73", "categories": "math.CO"}
{"title": "Covering compact metric spaces greedily", "year": 2017, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Jan Hendrik Rolfes and Frank Vallentin"], "abstract": "  A general greedy approach to construct coverings of compact metric spaces by\nmetric balls is given and analyzed. The analysis is a continuous version of\nChvatal's analysis of the greedy algorithm for the weighted set cover problem.\nThe approach is demonstrated in an exemplary manner to construct efficient\ncoverings of the n-dimensional sphere and n-dimensional Euclidean space to give\nshort and transparent proofs of several best known bounds obtained from\ndeterministic constructions in the literature on sphere coverings.\n", "doi": "10.1007/s10474-018-0829-4", "arxiv_id": "1710.06002", "pdf_urls": ["https://arxiv.org/pdf/1710.06002"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Hungar. 155 (2018), no. 1, 130-140", "categories": "math.MG cs.CG"}
{"title": "On the action of the Steenrod algebra on the modular invariants of\n  special linear group", "year": 2017, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Nguyen Sum"], "abstract": "  We compute the action of the Steenrod algebra on generators of algebras of\ninvariants of special linear group ${SL_n=SL(n,\\mathbb Z/p)}$ in the polynomial\nalgebra with $ p$ an odd prime number.\n", "doi": null, "arxiv_id": "1710.06556", "pdf_urls": ["https://arxiv.org/pdf/1710.06556"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Vietnamica, Vol.18, No. 2 (1993), 203-213", "categories": "math.AT"}
{"title": "Strong property (T) for higher rank lattices", "year": 2017, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Mikael de la Salle"], "abstract": "  We prove that every lattice in a product of higher rank simple Lie groups or\nhigher rank simple algebraic groups over local fields has Vincent Lafforgue's\nstrong property (T). Over non-archimedean local fields, we also prove that they\nhave strong Banach proerty (T) with respect to all Banach spaces with\nnontrivial type, whereas in general we obtain such a result with additional\nhypotheses on the Banach spaces. The novelty is that we deal with non-cocompact\nlattices, such as $\\mathrm{SL}_n(\\mathbf{Z})$ for $n \\geq 3$. To do so, we\nintroduce a stronger form of strong property (T) which allows us to deal with\nmore general objects than group representations on Banach spaces that we call\ntwo-step representations, namely families indexed by a group of operators\nbetween different Banach spaces that we can compose only once. We prove that\nhigher rank groups have this property and that this property passes to\nundistorted lattices.\n", "doi": "10.4310/acta.2019.v223.n1.a3", "arxiv_id": "1711.01900", "pdf_urls": ["https://arxiv.org/pdf/1711.01900"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Volume 223 (2019) 1 151 - 193", "categories": "math.FA math.GR math.OA"}
{"title": "A Unified Convergence Theorem", "year": 2017, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Junde Wu", "Jianwen Luo", "Shijie Lu"], "abstract": "  We prove a unified convergence theorem, which presents in four equivalent\nforms of the famous Antosik-Mikusinski Theorems. In particular, we show that\nSwartz' three uniform convergence principles are all equivalent to the\nAntosik-Mikusinski Theorems.\n", "doi": null, "arxiv_id": "1711.06817", "pdf_urls": ["https://arxiv.org/pdf/1711.06817"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Sin. (Eng. Ser.), 21(2005), 315-322", "categories": "quant-ph"}
{"title": "On Vortex Alignment and Boundedness of $L^q$ Norm of Vorticity", "year": 2017, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Siran Li"], "abstract": "  We show that the spatial $L^q$ ($q > 5/3$) norm of the vorticity of an\nincompressible viscous fluid in $\\mathbb{R}^3$ or $\\mathbb{T}^3$ remains\nbounded uniformly in time, provided that the direction of vorticity is H\\\"older\ncontinuous in the space variable, and that the space--time $L^q$ norm of the\nvorticity is finite. The H\\\"older index depends only on $q$. This serves as a\nvariant of the classical result by P. Constantin and Ch. Fefferman (Direction\nof vorticity and the problem of global regularity for the Navier--Stokes\nequations, Indiana Univ. J. Math., 42 (1993), 775--789).\n", "doi": null, "arxiv_id": "1712.00551", "pdf_urls": ["https://arxiv.org/pdf/1712.00551"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Sci. Ser. B (Engl. Ed.) 40 (2020), no. 6, 1700--1708", "categories": "math.AP"}
{"title": "On derivations with respect to finite sets of smooth functions", "year": 2017, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Rich\\'ard Gr\\\"unwald and Zsolt P\\'ales"], "abstract": "  The purpose of this paper is to show that functions that derivate the\ntwo-variable product function and one of the exponential, trigonometric or\nhyperbolic functions are also standard derivations. The more general problem\nconsidered is to describe finite sets of differentiable functions such that\nderivations with respect to this set are automatically standard derivations.\n", "doi": "10.1007/s10474-018-0790-2", "arxiv_id": "1712.02171", "pdf_urls": ["https://arxiv.org/pdf/1712.02171"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Hungar. 154(2) 2018, 530--544", "categories": "math.CA"}
{"title": "Towards a proof of the 24-cell conjecture", "year": 2017, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Oleg R. Musin"], "abstract": "  This review paper is devoted to the problems of sphere packings in 4\ndimensions. The main goal is to find reasonable approaches for solutions to\nproblems related to densest sphere packings in 4-dimensional Euclidean space.\nWe consider two long-standing open problems: the uniqueness of maximum kissing\narrangements in 4 dimensions and the 24-cell conjecture. Note that a proof of\nthe 24-cell conjecture also proves that the checkerboard lattice packing D4 is\nthe densest sphere packing in 4 dimensions.\n", "doi": null, "arxiv_id": "1712.04099", "pdf_urls": ["https://arxiv.org/pdf/1712.04099"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Hungar., 155:1 (2018), 184-199", "categories": "math.MG math.CO"}
{"title": "Purely unrectifiable metric spaces and perturbations of Lipschitz\n  functions", "year": 2017, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["David Bate"], "abstract": "  We characterise purely $n$-unrectifiable subsets $S$ of a complete metric\nspace $X$ with finite Hausdorff $n$-measure by studying arbitrarily small\nperturbations of elements of the set of all bounded 1-Lipschitz functions\n$f\\colon X \\to \\mathbb R^m$ with respect to the supremum norm. In one such\ncharacterisation it is shown that, if $S$ has positive lower density almost\neverywhere, then the set of all $f$ with $\\mathcal H^n(f(S))=0$ is residual.\nConversely, if $E\\subset X$ is $n$-rectifiable with $\\mathcal H^n(E)>0$, the\nset of all $f$ with $\\mathcal H^n(f(E))>0$ is residual.\n  These results provide a replacement for the Besicovitch-Federer projection\ntheorem in arbitrary metric spaces, which is known to be false outside of\nEuclidean spaces.\n", "doi": "10.4310/acta.2020.v224.n1.a1", "arxiv_id": "1712.07139", "pdf_urls": ["https://arxiv.org/pdf/1712.07139"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math., Vol. 224, No. 1 (2020), pp. 1-65", "categories": "math.MG math.CA"}
{"title": "On flexible sequences", "year": 2018, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Bruno Dinis", "Tran Van Nam", "Imme van den Berg"], "abstract": "  In the setting of nonstandard analysis we introduce the notion of flexible\nsequence. The terms of flexible sequences are external numbers. These are a\nsort of analogue for the classical \\emph{O$ (\\cdot ) $} and \\emph{o$ (\\cdot )\n$} notation for functions, and have algebraic properties similar to those of\nreal numbers. The flexibility originates from the fact that external numbers\nare stable under some shifts, additions and multiplications. We introduce two\nforms of convergence, and study their relation. We show that the usual\nproperties of convergence of sequences hold or can be adapted to these new\nnotions of convergence and give some applications.\n", "doi": "10.1007/s40306-018-00303-4", "arxiv_id": "1801.02413", "pdf_urls": ["https://arxiv.org/pdf/1801.02413"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Vietnamica 44:4 (2019) 833--87", "categories": "math.LO"}
{"title": "The Kakeya problem for circular arcs", "year": 2018, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Korn\\'elia H\\'era and Mikl\\'os Laczkovich"], "abstract": "  We prove that if a circular arc has angle short enough, then it can be\ncontinuously moved to any prescribed position within a set of arbitrarily small\narea.\n", "doi": "10.1007/s10474-016-0663-5", "arxiv_id": "1802.00290", "pdf_urls": ["https://arxiv.org/pdf/1802.00290"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Hungar. 150, (2016), 479-511", "categories": "math.MG math.CA"}
{"title": "Spectral Characterizations of Solvability and Stability for Delay\n  Differential-Algebraic Equations", "year": 2018, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Phi Ha"], "abstract": "  The solvability and stability analysis of linear time invariant systems of\ndelay differential-algebraic equations (DDAEs) is analyzed. The behavior\napproach is applied to DDAEs in order to establish characterizations of their\nsolvability in terms of spectral conditions. Furthermore, examples are\ndelivered to demonstrate that the eigenvalue-based approach to analyze the\nexponential stability of dynamical system is only valid for a special class of\nDDAEs, namely non-advanced. Then, a new concept of weak stability is proposed\nand studied for DDAEs whose matrix coefficients pairwise commute.\n", "doi": "10.1007/s40306-018-0279-7", "arxiv_id": "1802.01148", "pdf_urls": ["https://arxiv.org/pdf/1802.01148"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Vietnamica, volume 43, pages 715-735(2018)", "categories": "math.DS"}
{"title": "Jacobi-Trudi type formula for character of irreducible representations\n  of $\\frak{gl}(m|1)$", "year": 2018, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Nguyen Luong Thai Binh", "Nguyen Thi Phuong Dung", "Phung Ho Hai"], "abstract": "  We prove a determinantal type formula to compute the irreducible characters\nof the general Lie superalgebra $\\mathfrak{gl}(m|1)$ in terms of the characters\nof the symmetric powers of the fundamental representation and their duals. This\nformula was conjectured by J. van der Jeugt and E. Moens for the Lie\nsuperalgebra $\\frak{gl}(m|n)$ and generalizes the well-known Jacobi-Trudi\nformula.\n", "doi": "10.1007/s40306-018-0280-1", "arxiv_id": "1802.09946", "pdf_urls": ["https://arxiv.org/pdf/1802.09946"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Vietnamica volume 44, pages603-615 (2019)", "categories": "math.RT"}
{"title": "Rough Path Renormalization from Stratonovich to It\\^o for Fractional Brownian Motion", "year": 2018, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Zhongmin Qian and Xingcheng Xu"], "abstract": "This paper develops an It\\^o-type fractional pathwise integration theory for fractional Brownian motion with Hurst parameters \\( H \\in (\\frac{1}{3}, \\frac{1}{2}] \\), using the Lyons' rough path framework. This approach is designed to fill gaps in conventional stochastic calculus models that fail to account for temporal persistence prevalent in dynamic systems such as those found in economics, finance, and engineering. The pathwise-defined method not only meets the zero expectation criterion but also addresses the challenges of integrating non-semimartingale processes, which traditional It\\^o calculus cannot handle. We apply this theory to fractional Black-Scholes models and high-dimensional fractional Ornstein-Uhlenbeck processes, illustrating the advantages of this approach. Additionally, the paper discusses the generalization of It\\^o integrals to rough differential equations (RDE) driven by fBM, emphasizing the necessity of integrand-specific adaptations in the It\\^o rough path lift for stochastic modeling.", "doi": "10.1007/s10114-025-4377-x", "arxiv_id": "1803.00335", "pdf_urls": ["https://arxiv.org/pdf/1803.00335"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Sinica, English Series, Vol. 41, No. 9, 2195-2230 (2025)", "categories": "math.PR"}
{"title": "Depth and regularity of monomial ideals via polarization and\n  combinatorial optimization", "year": 2018, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Jose Mart\\'inez-Bernal", "Susan Morey", "Rafael H. Villarreal", "Carlos E.\n  Vivares"], "abstract": "  In this paper we use polarization to study the behavior of the depth and\nregularity of a monomial ideal $I$, locally at a variable $x_i$, when we lower\nthe degree of all the highest powers of the variable $x_i$ occurring in the\nminimal generating set of $I$, and examine the depth and regularity of powers\nof edge ideals of clutters using combinatorial optimization techniques. If $I$\nis the edge ideal of an unmixed clutter with the max-flow min-cut property, we\nshow that the powers of $I$ have non-increasing depth and non-decreasing\nregularity. In particular edge ideals of unmixed bipartite graphs have\nnon-decreasing regularity. We are able to show that the symbolic powers of the\nideal of covers of the clique clutter of a strongly perfect graph have\nnon-increasing depth. A similar result holds for the ideal of covers of a\nuniform ideal clutter.\n", "doi": null, "arxiv_id": "1803.02017", "pdf_urls": ["https://arxiv.org/pdf/1803.02017"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Vietnam. 44 (2019), no. 1, 243--268", "categories": "math.AC math.CO"}
{"title": "On a problem of Bermond and Bollob\\'as", "year": 2018, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Slobodan Filipovski and Robert Jajcay"], "abstract": "  Let $n(k, d)$ be the order of the largest undirected graphs of maximum degree\n$k$ and diameter $d$, and let $M(k,d)$ be the corresponding Moore bound. In\nthis paper, we give a positive answer to the question of Bermond and Bollob\\'as\nconcerning the Degree/Diameter Problem: Given a positive integer $c>0$, does\nthere exist a pair $k$ and $d$, such that $n(k, d)\\leq M(k,d)-c?$\n", "doi": "10.1007/s10440-021-00429-y", "arxiv_id": "1803.07501", "pdf_urls": ["https://arxiv.org/pdf/1803.07501"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematicae Applicandae 2021", "categories": "math.CO"}
{"title": "The Webster scalar curvature and sharp upper and lower bounds for the\n  first positive eigenvalue of the Kohn-Laplacian on real hypersurfaces", "year": 2018, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Song-Ying Li and Duong Ngoc Son"], "abstract": "  Let $(M,\\theta)$ be a compact strictly pseudoconvex pseudohermitian manifold\nwhich is CR embedded into a complex space. In an earlier paper, Lin and the\nauthors gave several sharp upper bounds for the first positive eigenvalue\n$\\lambda_1$ of the Kohn-Laplacian $\\Box_b$ on $(M,\\theta)$. In the present\npaper, we give a sharp upper bound for $\\lambda_1$, generalizing and extending\nsome previous results. As a corollary, we obtain a Reilly-type estimate when\n$M$ is embedded into the standard sphere. In another direction, using a\nLichnerowicz-type estimate by Chanillo, Chiu, and Yang and an explicit formula\nfor the Webster scalar curvature, we give a lower bound for $\\lambda_1$ when\nthe pseudohermitian structure $\\theta$ is volume-normalized.\n", "doi": "10.1007/s10114-018-7415-0", "arxiv_id": "1803.07653", "pdf_urls": ["https://arxiv.org/pdf/1803.07653"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Sinica, English Series, Volume 34 Issue 8 (2018),\n  Pages 1248-1258", "categories": "math.CV"}
{"title": "Cohen-Macaulay criteria for projective monomial curves via Gr\\\"obner\n  bases", "year": 2018, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["J\\\"urgen Herzog", "Dumitru I. Stamate"], "abstract": "  We prove new characterizations based on Gr\\\"obner bases for the\nCohen-Macaulay property of a projective monomial curve.\n", "doi": "10.1007/s40306-018-00302-5", "arxiv_id": "1803.08961", "pdf_urls": ["https://arxiv.org/pdf/1803.08961"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math Vietnam 44 (2019), 51--64", "categories": "math.AC math.AG"}
{"title": "L\\'evy Area Analysis and Parameter Estimation for fOU Processes via\n  Non-Geometric Rough Path Theory", "year": 2018, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Zhongmin Qian and Xingcheng Xu"], "abstract": "  This paper addresses the estimation problem of an unknown drift parameter\nmatrix for a fractional Ornstein-Uhlenbeck process in a multi-dimensional\nsetting. To tackle this problem, we propose a novel approach based on rough\npath theory that allows us to construct pathwise rough path estimators from\nboth continuous and discrete observations of a single path. Our approach is\nparticularly suitable for high-frequency data. To formulate the parameter\nestimators, we introduce a theory of pathwise It\\^o integrals with respect to\nfractional Brownian motion. By establishing the regularity of fractional\nOrnstein-Uhlenbeck processes and analyzing the long-term behavior of the\nassociated L\\'evy area processes, we demonstrate that our estimators are\nstrongly consistent and pathwise stable. Our findings offer a new perspective\non estimating the drift parameter matrix for fractional Ornstein-Uhlenbeck\nprocesses in multi-dimensional settings, and may have practical implications\nfor fields including finance, economics, and engineering.\n", "doi": "10.1007/s10473-024-0501-8", "arxiv_id": "1803.11039", "pdf_urls": ["https://arxiv.org/pdf/1803.11039"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Sci, 44, 1609-1638 (2024)", "categories": "math.PR math.ST stat.TH"}
{"title": "Strong Comparison Principles for Some Nonlinear Degenerate Elliptic\n  Equations", "year": 2018, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["YanYan Li", "Bo Wang"], "abstract": "  In this paper, we obtain the strong comparison principle and Hopf Lemma for\nlocally Lipschitz viscosity solutions to a class of nonlinear degenerate\nelliptic operators of the form $\\nabla^2 \\psi + L(x,\\nabla \\psi)$, including\nthe conformal hessian operator.\n", "doi": null, "arxiv_id": "1804.01056", "pdf_urls": ["https://arxiv.org/pdf/1804.01056"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Sci. Ser. B (Engl. Ed. ) 38 (2018), no. 5, pp.\n  1583--1590", "categories": "math.AP"}
{"title": "Normal reduction numbers for normal surface singularities with application to elliptic singularities of Brieskorn type", "year": 2018, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Tomohiro Okuma", "Kei-ichi Watanabe", "Ken-ichi Yoshida"], "abstract": "In this paper, we give a formula for normal reduction number of an integrally closed $\\mathfrak m$-primary ideal of a $2$-dimensional normal local ring $(A,\\mathfrak m)$ in terms of the geometric genus $p_g(A)$ of $A$. Also we compute the normal reduction number of the maximal ideal of Brieskorn hypersurfaces. As an application, we give a short proof of a classification of Brieskorn hypersurfaces having elliptic singularities.", "doi": "10.1007/s40306-018-00311-4", "arxiv_id": "1804.03795", "pdf_urls": ["https://arxiv.org/pdf/1804.03795"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Vietnam. 44, No. 1, 87-100 (2019)", "categories": "math.AC"}
{"title": "The orbit method and analysis of automorphic forms", "year": 2018, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Paul D. Nelson and Akshay Venkatesh"], "abstract": "  We develop the orbit method in a quantitative form, along the lines of\nmicrolocal analysis, and apply it to the analytic theory of automorphic forms.\n  Our main global application is an asymptotic formula for averages of\nGan--Gross--Prasad periods in arbitrary rank. The automorphic form on the\nlarger group is held fixed, while that on the smaller group varies over a\nfamily of size roughly the fourth root of the conductors of the corresponding\n$L$-functions. Ratner's results on measure classification provide an important\ninput to the proof.\n  Our local results include asymptotic expansions for certain special functions\narising from representations of higher rank Lie groups, such as the relative\ncharacters defined by matrix coefficient integrals as in the Ichino--Ikeda\nconjecture.\n", "doi": "10.4310/acta.2021.v226.n1.a1", "arxiv_id": "1805.07750", "pdf_urls": ["https://arxiv.org/pdf/1805.07750"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. 226 (2021), no. 1, 1-209", "categories": "math.NT math.AP math.RT"}
{"title": "On crossing families of complete geometric graphs", "year": 2018, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Dolores Lara and Christian Rubio-Montiel"], "abstract": "  A crossing family is a collection of pairwise crossing segments, this concept\nwas introduced by Aronov et. al. (1994). They prove that any set of $n$ points\n(in general position) in the plain contains a crossing family of size\n$\\sqrt{n/12}$. In this paper we present a generalization of the concept and\ngive several results regarding this generalization.\n", "doi": "10.1007/s10474-018-0880-1", "arxiv_id": "1805.09888", "pdf_urls": ["https://arxiv.org/pdf/1805.09888"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Hungarica-2019", "categories": "math.CO"}
{"title": "The permanent functions of tensors", "year": 2018, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Qing-Wen Wang and Fuzhen Zhang"], "abstract": "  By a tensor we mean a multidimensional array (matrix) or hypermatrix over a\nnumber field. This article aims to set an account of the studies on the\npermanent functions of tensors. We formulate the definitions of 1-permanent,\n2-permanent, and $k$-permanent of a tensor in terms of hyperplanes, planes and\n$k$-planes of the tensor; we discuss the polytopes of stochastic tensors; at\nend we present an extension of the generalized matrix function for tensors.\n", "doi": null, "arxiv_id": "1806.00002", "pdf_urls": ["https://arxiv.org/pdf/1806.00002"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Special Issue of Acta Mathematica Vietnamica (Springer, Article\n  268) for ICMAA, 2018", "categories": "math.CO math.FA"}
{"title": "Eakin-Sathaye type theorems for joint reductions and good filtrations of\n  ideals", "year": 2018, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Kriti Goel", "Sudeshna Roy and J. K. Verma"], "abstract": "  Analogues of Eakin-Sathaye theorem for reductions of ideals are proved for\n${\\mathbb N}^s$-graded good filtrations. These analogues yield bounds on joint\nreduction vectors for a family of ideals and reduction numbers for $\\mathbb\nN$-graded filtrations. Several examples related to lex-segment ideals,\ncontracted ideals in $2$-dimensional regular local rings and the filtration of\nintegral and tight closures of powers of ideals in hypersurface rings are\nconstructed to show effectiveness of these bounds.\n", "doi": null, "arxiv_id": "1806.07518", "pdf_urls": ["https://arxiv.org/pdf/1806.07518"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Vietnamica (44)(2019),671-689", "categories": "math.AC"}
{"title": "Normal projective varieties admitting polarized or int-amplified\n  endomorphisms", "year": 2018, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Sheng Meng", "De-Qi Zhang"], "abstract": "  Let $X$ be a normal projective variety admitting a polarized or int-amplified\nendomorphism $f$. We list up characteristic properties of such an endomorphism\nand classify such a variety from the aspects of its singularity, anti-canonical\ndivisor and Kodaira dimension. Then we run the equivariant minimal model\nprogram with respect to not just the single $f$ but also the monoid $SEnd(X)$\nof all surjective endomorphisms of $X$, up to finite-index. Several\napplications are given. We also give both algebraic and geometric\ncharacterizations of toric varieties via polarized endomorphisms.\n", "doi": null, "arxiv_id": "1806.07747", "pdf_urls": ["https://arxiv.org/pdf/1806.07747"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Vietnamica, Volume 45, pages11 - 26 (2020),\n  Special issue on: Nevanlinna theory and Complex Geometry in Honor of Le Van\n  Thiem's Centenary", "categories": "math.AG math.DS"}
{"title": "Prime filter structures of pseudocomplemented Kleene algebras and\n  representation by rough sets", "year": 2018, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Jouni J\\\"arvinen and S\\'andor Radeleczki"], "abstract": "  We introduce Kleene-Varlet spaces as partially ordered sets equipped with a\npolarity satisfying certain additional conditions. By applying Kleene-Varlet\nspaces, we prove that each regular pseudocomplemented Kleene algebra is\nisomorphic to a subalgebra of the rough set regular pseudocomplemented Kleene\nalgebra defined by a tolerance induced by an irredundant covering. We also\ncharacterize the Kleene-Varlet spaces corresponding to the regular\npseudocomplemented Kleene algebras satisfying the Stone identity.\n", "doi": "10.1007/s10474-019-00985-8", "arxiv_id": "1806.09203", "pdf_urls": ["https://arxiv.org/pdf/1806.09203"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Hungarica (online 4 September 2019)", "categories": "math.LO"}
{"title": "A note on asymptotic class number upper bounds in $p$-adic Lie\n  extensions", "year": 2018, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Meng Fai Lim"], "abstract": "  Let $p$ be an odd prime and $F_{\\infty}$ a $p$-adic Lie extension of a number\nfield $F$ with Galois group $G$. Suppose that $G$ is a compact pro-$p$ $p$-adic\nLie group with no torsion and that it contains a closed normal subgroup $H$\nsuch that $G/H\\cong \\mathbb{Z}_p$. Under various assumptions, we establish\nasymptotic upper bounds for the growth of $p$-exponents of the class groups in\nthe said $p$-adic Lie extension. Our results generalize a previous result of\nLei, where he established such an estimate under the assumption that $H\\cong\n\\mathbb{Z}_p$.\n", "doi": "10.1007/s10114-019-8410-9", "arxiv_id": "1807.04916", "pdf_urls": ["https://arxiv.org/pdf/1807.04916"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta. Math. Sin.-English Ser. (2019) Vol. 35 Issue 9, 1481-1490", "categories": "math.NT"}
{"title": "Stability of Steady Multi-Wave Configurations for the Full Euler\n  Equations of Compressible Fluid Flow", "year": 2018, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Gui-Qiang G. Chen and Matthew Rigby"], "abstract": "  We are concerned with the stability of steady multi-wave configurations for\nthe full Euler equations of compressible fluid flow. In this paper, we focus on\nthe stability of steady four-wave configurations that are the solutions of the\nRiemann problem in the flow direction, consisting of two shocks, one vortex\nsheet, and one entropy wave, which is one of the core multi-wave configurations\nfor the two-dimensional Euler equations. It is proved that such steady\nfour-wave configurations in supersonic flow are stable in structure globally,\neven under the BV perturbation of the incoming flow in the flow direction. In\norder to achieve this, we first formulate the problem as the Cauchy problem\n(initial value problem) in the flow direction, and then develop a modified\nGlimm difference scheme and identify a Glimm-type functional to obtain the\nrequired BV estimates by tracing the interactions not only between the strong\nshocks and weak waves, but also between the strong vortex sheet/entropy wave\nand weak waves. The key feature of the Euler equations is that the reflection\ncoefficient is always less than 1, when a weak wave of different family\ninteracts with the strong vortex sheet/entropy wave or the shock wave, which is\ncrucial to guarantee that the Glimm functional is decreasing. Then these\nestimates are employed to establish the convergence of the approximate\nsolutions to a global entropy solution, close to the background solution of\nsteady four-wave configuration.\n", "doi": null, "arxiv_id": "1807.06646", "pdf_urls": ["https://arxiv.org/pdf/1807.06646"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Scientia, 38B(5) (2018), 1485--1514", "categories": "math.AP math-ph math.MP"}
{"title": "Notes On a Borwein and Choi's conjecture of cyclotomic polynomials with\n  coefficients $\\pm1$", "year": 2018, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Shaofang Hong", "Wei Cao"], "abstract": "  Borwein and Choi conjectured that a polynomial $P(x)$ with coefficients\n$\\pm1$ of degree $N-1$ is cyclotomic iff $$P(x)=\\pm \\Phi_{p_1}(\\pm\nx)\\Phi_{p_2}(\\pm x^{p_1})\\cdots \\Phi_{p_r}(\\pm x^{p_1p_2\\cdots p_{r-1}})$$\nwhere $N=p_1p_2\\cdots p_{r}$ and the $p_i$ are primes, not necessarily\ndistinct. Here $\\Phi_p(x):=(x^p-1)/(x-1)$ is the $p-$th cyclotomic polynomial.\nIn \\cite{1}, they also proved the conjecture for $N$ odd or a power of 2. In\nthis paper we introduce a so-called $E-$transformation, by which we prove the\nconjecture for a wider variety of cases and present the key as well as a new\napproach to investigate the conjecture.\n", "doi": "10.1007/s10114-008-6444-5", "arxiv_id": "1807.11693", "pdf_urls": ["https://arxiv.org/pdf/1807.11693"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Sinica (English Series), 25 (2009), 65 -76", "categories": "math.NT"}
{"title": "Syzygies of determinantal thickenings and representations of the general\n  linear Lie superalgebra", "year": 2018, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Claudiu Raicu and Jerzy Weyman"], "abstract": "  We let S denote the ring of polynomial functions on the space of m x n\nmatrices, and consider the action of the group GL = GL_m x GL_n via row and\ncolumn operations on the matrix entries. For a GL-invariant ideal I in S we\nshow that the linear strands of its minimal free resolution translate via the\nBGG correspondence to modules over the general linear Lie superalgebra gl(m|n).\nWhen I is the ideal generated by the GL-orbit of a highest weight vector, we\ngive a conjectural description of the classes of these gl(m|n)-modules in the\nGrothendieck group, and prove that our prediction is correct for the first\nstrand of the minimal free resolution.\n", "doi": "10.1007/s40306-018-0282-z", "arxiv_id": "1808.05649", "pdf_urls": ["https://arxiv.org/pdf/1808.05649"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Vietnam. 44, no. 1, 269-284 (2019)", "categories": "math.AC math.RT"}
{"title": "Membership criteria and containments of powers of monomial ideals", "year": 2018, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Huy Tai Ha and Ngo Viet Trung"], "abstract": "  We present a close relationship between matching number, covering numbers and\ntheir fractional versions in combinatorial optimization and ordinary powers,\nintegral closures of powers, and symbolic powers of monomial ideals. This\nrelationship leads to several new results and problems on the containments\nbetween these powers.\n", "doi": "10.1007/s40306-018-00325-y", "arxiv_id": "1808.05899", "pdf_urls": ["https://arxiv.org/pdf/1808.05899"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Vietnamica 44 (2019), 117-139", "categories": "math.AC math.CO math.OC"}
{"title": "Correspondence scrolls", "year": 2018, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["David Eisenbud and Alessio Sammartano"], "abstract": "  This paper initiates the study of a class of schemes that we call\ncorrespondence scrolls, which includes the rational normal scrolls and linearly\nembedded projective bundle of decomposable bundles, as well as degenerate K3\nsurfaces, Calabi-Yau 3-folds, and many other examples.\n", "doi": "10.1007/s40306-018-0296-6", "arxiv_id": "1809.03059", "pdf_urls": ["https://arxiv.org/pdf/1809.03059"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Vietnamica 44, pp. 101-116 (2019)", "categories": "math.AG math.AC"}
{"title": "Inverse zero-sum problems for certain groups of rank three", "year": 2018, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Benjamin Girard (IMJ-PRG)", "Wolfgang Schmid (LAGA)"], "abstract": "  The inverse problem associated to the Erd\\H{o}s-Ginzburg-Ziv constant and the\n$\\eta$-constant is solved for finite abelian groups of the form $C_2 \\oplus C_2\n\\oplus C_{2n}$ where $n \\ge 2$ is an integer.\n", "doi": "10.1007/s10474-019-00983-w", "arxiv_id": "1809.03178", "pdf_urls": ["https://arxiv.org/pdf/1809.03178"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Hungarica 160, 1 (2020) 229-247", "categories": "math.NT math.CO math.GR"}
{"title": "Nonlinear Schr\\\"odinger equation with Coulomb potential", "year": 2018, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Changxing Miao", "Junyong Zhang", "Jiqiang Zheng"], "abstract": "  In this paper, we study the Cauchy problem for the nonlinear Schr\\\"odinger\nequations with Coulomb potential $i\\partial_tu+\\Delta\nu+\\frac{K}{|x|}u=\\lambda|u|^{p-1}u$ with $1<p\\leq5$ on $\\mathbb{R}^3$. We\nmainly consider the influence of the long range potential $K|x|^{-1}$ on the\nexistence theory and scattering theory for nonlinear Schr\\\"odinger equation. In\nparticular, we prove the global existence when the Coulomb potential is\nattractive, i.e. $K>0$ and scattering theory when the Coulomb potential is\nrepulsive i.e. $K\\leq0$. The argument is based on the interaction Morawetz-type\ninequalities and the equivalence of Sobolev norms.\n", "doi": "10.1007/s10473-022-0606-x", "arxiv_id": "1809.06685", "pdf_urls": ["https://arxiv.org/pdf/1809.06685"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Scientia, 2022, 42B(6): 2230-2256", "categories": "math.AP"}
{"title": "Besov and Triebel-Lizorkin spaces associated with Laguerre expansions of\n  Hermite type", "year": 2018, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Pawe{\\l} Plewa"], "abstract": "  Homogeneous Besov and Triebel-Lizorkin spaces associated with\nmulti-dimensional Laguerre function expansions of Hermite type with index\n$\\alpha \\in [-1/2,\\infty)^d\\backslash (-1/2,1/2)^d$, $d\\geq 1$, are defined and\ninvestigated. To achieve expected goals Schwartz type spaces on $R^d_+$ are\nintroduced and then tempered type distributions are constructed. Also, ideas\nfrom a recent paper of Bui and Duong on Besov and Triebel-Lizorkin spaces\nassociated with Hermite functions expansions are used. This means, in\nparticular, using molecular decomposition and an appropriate form of a\nCalder\\'on reproducing formula.\n", "doi": "10.1007/s10474-017-0747-x", "arxiv_id": "1809.08039", "pdf_urls": ["https://arxiv.org/pdf/1809.08039"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Hung. 153 (2017), 143-176", "categories": "math.CA"}
{"title": "A construction of singular overlapping asymmetric self-similar measures", "year": 2018, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["J\\\"org Neunh\\\"auserer"], "abstract": "  In [8] we found a class of overlapping asymmetric self-similar measures on\nthe real line, which are generically absolutely continuous with respect to the\nLebesgue measure. Here we construct exceptional measures in this class being\nsingular.\n", "doi": null, "arxiv_id": "1810.12622", "pdf_urls": ["https://arxiv.org/pdf/1810.12622"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Hungarica, vol. 113 (4-4),333-343, 2006", "categories": "math.DS"}
{"title": "Irreducibility of random polynomials of large degree", "year": 2018, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Emmanuel Breuillard", "P\\'eter P. Varj\\'u"], "abstract": "  We consider random polynomials with independent identically distributed\ncoefficients with a fixed law. Assuming the Riemann hypothesis for Dedekind\nzeta functions, we prove that such polynomials are irreducible and their Galois\ngroups contain the alternating group with high probability as the degree goes\nto infinity. This settles a conjecture of Odlyzko and Poonen conditionally on\nRH for Dedekind zeta functions.\n", "doi": "10.4310/acta.2019.v223.n2.a1", "arxiv_id": "1810.13360", "pdf_urls": ["https://arxiv.org/pdf/1810.13360"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. 223(2): 195-249 (December 2019)", "categories": "math.NT math.PR"}
{"title": "The directed landscape", "year": 2018, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Duncan Dauvergne", "Janosch Ortmann", "and Balint Virag"], "abstract": "  The conjectured limit of last passage percolation is a scale-invariant,\nindependent, stationary increment process with respect to metric composition.\nWe prove this for Brownian last passage percolation. We construct the Airy\nsheet and characterize it in terms of the Airy line ensemble. We also show that\nlast passage geodesics converge to random functions with Holder-2/3- continuous\npaths. This work completes the construction of the central object in the\nKardar-Parisi-Zhang universality class, the directed landscape.\n", "doi": "10.4310/acta.2022.v229.n2.a1", "arxiv_id": "1812.00309", "pdf_urls": ["https://arxiv.org/pdf/1812.00309"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica, 229, 201-285, 2022", "categories": "math.PR math-ph math.MP"}
{"title": "Cardinal characteristics at aleph omega", "year": 2018, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Shimon Garti", "Moti Gitik", "Saharon Shelah"], "abstract": "  We prove the consistency of the statement\n$\\mathfrak{u}_{\\aleph_\\omega}<2^{\\aleph_\\omega}$. We show that the consistency\nstrength of this statement is exactly a measurable cardinal $\\mu$ so that\n$o(\\mu)=\\mu^{++}$.\n", "doi": "10.1007/s10474-019-00971-0", "arxiv_id": "1812.05291", "pdf_urls": ["https://arxiv.org/pdf/1812.05291"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Hungarica, vol. 160 (2), 2020, pp. 320-336", "categories": "math.LO"}
{"title": "H\\\"older Continuity and Differentiability Almost Everywhere of $(K_1,\n  K_2)$-Quasiregular Mappings", "year": 2018, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Hongya Gao", "Chao Liu", "Junwei Li"], "abstract": "  This paper deals with $(K_1, K_2)$-quasiregular mappings. It is shown, by\nMorrey's Lemma and isoperimetric inequality, that every $(K_1,\nK_2)$-quasiregular mapping satisfies a H\\\"older condition with exponent\n$\\alpha$ on compact subsets of its domain, where \\begin{align}\n\\alpha=\\begin{cases} 1/K_1, & \\text{for } K_1>1, \\\\ \\text{any positive number\nless than } 1, & \\text{for } K_1=1 \\text{ and } K_2>0, \\\\ 1, & \\text{for }\nK_1=1 \\text{ and } K_2=0, \\\\ 1, & \\text{for } K_1<1,\\\\ \\end{cases} \\end{align}\nDifferentiability almost everywhere of $(K_1, K_2)$-quasiregular mappings is\nalso derived.\n", "doi": null, "arxiv_id": "1812.07779", "pdf_urls": ["https://arxiv.org/pdf/1812.07779"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Sinica Chinese Series, 2012,55(4), 721-726", "categories": "math.AP"}
{"title": "Quillen equivalence of singular model categories", "year": 2019, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Wei Ren"], "abstract": "  Let $R$ be a left-Gorenstein ring. We show that there is a Quillen\nequivalence between singular contraderived model category and singular\ncoderived model category. Consequently, an equivalence between the homotopy\ncategory of exact complexes of projective modules and the homotopy category of\nexact complexes of injective modules is given.\n", "doi": null, "arxiv_id": "1901.02137", "pdf_urls": ["https://arxiv.org/pdf/1901.02137"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "An English version of Acta Mathematica Sinica (Chinese Series),\n  62(3) 521-528, 2019", "categories": "math.KT"}
{"title": "Quotients of higher dimensional Cremona groups", "year": 2019, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["J\\'er\\'emy Blanc", "St\\'ephane Lamy", "Susanna Zimmermann"], "abstract": "  We study large groups of birational transformations Bir(X), where X is a\nvariety of dimension at least 3, defined over C or a subfield of C. Two\nprominent cases are when X is the projective space, in which case Bir(X) is the\nCremona group of rank n, or when X is a smooth cubic hypersurface. In both\ncases, and more generally when X is birational to a conic bundle, we produce\ninfinitely many distinct group homomorphisms from Bir(X) to Z/2, showing in\nparticular that the group Bir(X) is not perfect and thus not simple. As a\nconsequence we also obtain that the Cremona group of rank n at least 3 is not\ngenerated by linear and Jonqui\\`eres elements.\n", "doi": "10.4310/acta.2021.v226.n2.a1", "arxiv_id": "1901.04145", "pdf_urls": ["https://arxiv.org/pdf/1901.04145"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica, Vol. 226, No. 2, pp. 211-318, 2021", "categories": "math.AG math.GR"}
{"title": "Examples of homological torsion and volume growth", "year": 2019, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Abhijit Champanerkar and Ilya Kofman"], "abstract": "  We provide examples of towers of covers of cusped hyperbolic 3-manifolds\nwhose exponential homological torsion growth is explicitly computed in terms of\nvolume growth. These examples arise from abelian covers of alternating links in\nthe thickened torus. A corollary is that the spanning tree entropy for each\nregular planar lattice is given by the volume of a hyperbolic polyhedron.\n", "doi": "10.1007/s40306-020-00412-z", "arxiv_id": "1901.07494", "pdf_urls": ["https://arxiv.org/pdf/1901.07494"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math Vietnam (2021)", "categories": "math.GT"}
{"title": "Compact graphings", "year": 2019, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["L\\'aszl\\'o Lov\\'asz"], "abstract": "  Graphings are special bounded-degree graphs on probability spaces,\nrepresenting limits of graph sequences that are convergent in a local or\nlocal-global sense. We describe a procedure for turning the underlying space\ninto a compact metric space, where the edge set is closed and nearby points\nhave nearby graph neighborhoods.\n", "doi": "10.1007/s10474-019-01010-8", "arxiv_id": "1902.09573", "pdf_urls": ["https://arxiv.org/pdf/1902.09573"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta. Math. Hung. 161 (2020), 185--196", "categories": "math.CO"}
{"title": "The convergence of the sums of independent random variables under the\n  sub-linear expectations", "year": 2019, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Li-Xin Zhang"], "abstract": "  Let $\\{X_n;n\\ge 1\\}$ be a sequence of independent random variables on a\nprobability space $(\\Omega, \\mathcal{F}, P)$ and $S_n=\\sum_{k=1}^n X_k$. It is\nwell-known that the almost sure convergence, the convergence in probability and\nthe convergence in distribution of $S_n$ are equivalent. In this paper, we\nprove similar results for the independent random variables under the sub-linear\nexpectations, and give a group of sufficient and necessary conditions for these\nconvergence. For proving the results, the Levy and Kolmogorov maximal\ninequalities for independent random variables under the sub-linear expectation\nare established. As an application of the maximal inequalities, the sufficient\nand necessary conditions for the central limit theorem of independent and\nidentically distributed random variables are also obtained.\n", "doi": "10.1007/s10114-020-8508-0", "arxiv_id": "1902.10872", "pdf_urls": ["https://arxiv.org/pdf/1902.10872"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta mathematica Sinica, English series, volume 36, pages 224-244,\n  2020", "categories": "math.PR"}
{"title": "Symbolic powers of certain cover ideals of graphs", "year": 2019, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Arvind Kumar", "Rajiv Kumar", "Rajib Sarkar", "S. Selvaraja"], "abstract": "  In this paper, we compute the regularity and Hilbert series of symbolic\npowers of the cover ideal of a graph $G$ when $G$ is either a crown graph or a\ncomplete multipartite graph. We also compute the multiplicity of symbolic\npowers of cover ideals in terms of the number of edges.\n", "doi": "10.1007/s40306-020-00409-8", "arxiv_id": "1903.00178", "pdf_urls": ["https://arxiv.org/pdf/1903.00178"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Vietnam. (2021)", "categories": "math.AC"}
{"title": "On the volume of sectional-hyperbolic sets", "year": 2019, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Daofei Zhang and Yuntao Zang"], "abstract": "  For a transitive sectional-hypebolic set $\\Lambda$ with positive volume on a\n$d$-dimensional manifold $M$($d\\ge3$), we show that $\\Lambda=M$ and $\\Lambda$\nis a uniformly hyperbolic set without singularities\n", "doi": "10.1007/s10114-021-0161-8", "arxiv_id": "1903.01089", "pdf_urls": ["https://arxiv.org/pdf/1903.01089"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Sin. (Engl. Ser.) 37 (2021), no. 10, 1507-1512", "categories": "math.DS"}
{"title": "Flexibility of planar graphs without 4-cycles", "year": 2019, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Tom\\'a\\v{s} Masa\\v{r}\\'ik"], "abstract": "  Proper graph coloring assigns different colors to adjacent vertices of the\ngraph. Usually, the number of colors is fixed or as small as possible. Consider\napplications (e.g. variants of scheduling) where colors represent limited\nresources and graph represents conflicts, i.e., two adjacent vertices cannot\nobtain the same resource. In such applications, it is common that some vertices\nhave preferred resource(s). However, unfortunately, it is not usually possible\nto satisfy all such preferences. The notion called flexibility was recently\ndefined in [Dvo\\v{r}\\'ak, Norin, Postle: List coloring with requests, Journal\nof Graph Theory 2019]. There instead of satisfying all the preferences the aim\nis to satisfy at least a constant fraction of the request. Recently, the\nstructural properties of planar graphs in terms of flexibility were\ninvestigated. We continue this line of research. Let G be a planar graph with a\nlist assignment L. Suppose a preferred color is given for some of the vertices.\nWe prove that if G is a planar graph without 4-cycles and all lists have size\nat least five, then there exists an L-coloring respecting at least a constant\nfraction of the preferences.\n", "doi": null, "arxiv_id": "1903.01460", "pdf_urls": ["https://arxiv.org/pdf/1903.01460"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Universitatis Comenianae, 88(3), 935-940, 2019", "categories": "math.CO cs.DM"}
{"title": "Unique continuation property with partial information for\n  two-dimensional anisotropic elasticity systems", "year": 2019, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Jin Cheng", "Yikan Liu", "Yanbo Wang", "Masahiro Yamamoto"], "abstract": "  In this paper, we establish a novel unique continuation property for\ntwo-dimensional anisotropic elasticity systems with partial information. More\nprecisely, given a homogeneous elasticity system in a domain, we investigate\nthe unique continuation by assuming only the vanishing of one component of the\nsolution in a subdomain. Using the corresponding Riemann function, we prove\nthat the solution vanishes in the whole domain provided that the other\ncomponent vanishes at one point up to its second derivatives. Further, we\nconstruct several examples showing the possibility of further reducing the\nadditional information of the other component. This result possesses remarkable\nsignificance in both theoretical and practical aspects because the required\ndata is almost halved for the unique determination of the whole solution.\n", "doi": "10.1007/s10255-020-0910-y", "arxiv_id": "1903.11930", "pdf_urls": ["https://arxiv.org/pdf/1903.11930"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Appl. Sin. Eng. Ser., 36 (2020) 3-17", "categories": "math.AP"}
{"title": "Rational Diophantine sextuples containing two regular quadruples and one\n  regular quintuple", "year": 2019, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Andrej Dujella", "Matija Kazalicki and Vinko Petri\\v{c}evi\\'c"], "abstract": "  A set of $m$ distinct nonzero rationals $\\{a_1,a_2,\\ldots,a_m\\}$ such that\n$a_ia_j+1$ is a perfect square for all $1\\leq i<j\\leq m$, is called a rational\nDiophantine $m$-tuple. It is proved recently that there are infinitely many\nrational Diophantine sextuples. In this paper, we construct infinite families\nof rational Diophantine sextuples with special structure, namely the sextuples\ncontaining quadruples and quintuples of certain type.\n", "doi": "10.32817/ams.1.1.2", "arxiv_id": "1904.00348", "pdf_urls": ["https://arxiv.org/pdf/1904.00348"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Spalatensia 1 (2020), 19-27", "categories": "math.NT"}
{"title": "Lie, associative and commutative quasi-isomorphism", "year": 2019, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Ricardo Campos", "Dan Petersen", "Daniel Robert-Nicoud", "Felix Wierstra"], "abstract": "  Over a field of characteristic zero, we show that two commutative\ndifferential graded (dg) algebras are quasi-isomorphic if and only if they are\nquasi-isomorphic as associative dg algebras. This answers a folklore problem in\nrational homotopy theory, showing that the rational homotopy type of a space is\ndetermined by its associative dg algebra of rational cochains. We also show a\nKoszul dual statement, under an additional completeness hypothesis: two\nhomotopy complete dg Lie algebras whose universal enveloping algebras are\nquasi-isomorphic as associative dg algebras must themselves be\nquasi-isomorphic. The latter result applies in particular to nilpotent Lie\nalgebras (not differential graded), in which case it says that two nilpotent\nLie algebras whose universal enveloping algebras are isomorphic as associative\nalgebras must be isomorphic.\n", "doi": "10.4310/acta.2024.v233.n2.a1", "arxiv_id": "1904.03585", "pdf_urls": ["https://arxiv.org/pdf/1904.03585"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. 233, No. 2, 195-238 (2024)", "categories": "math.RA math.AT math.KT math.QA math.RT"}
{"title": "The Fuglede conjecture for convex domains is true in all dimensions", "year": 2019, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Nir Lev", "M\\'at\\'e Matolcsi"], "abstract": "  A set $\\Omega \\subset \\mathbb{R}^d$ is said to be spectral if the space\n$L^2(\\Omega)$ has an orthogonal basis of exponential functions. A conjecture\ndue to Fuglede (1974) stated that $\\Omega$ is a spectral set if and only if it\ncan tile the space by translations. While this conjecture was disproved for\ngeneral sets, it has long been known that for a convex body $\\Omega \\subset\n\\mathbb{R}^d$ the \"tiling implies spectral\" part of the conjecture is in fact\ntrue.\n  To the contrary, the \"spectral implies tiling\" direction of the conjecture\nfor convex bodies was proved only in $\\mathbb{R}^2$, and also in $\\mathbb{R}^3$\nunder the a priori assumption that $\\Omega$ is a convex polytope. In higher\ndimensions, this direction of the conjecture remained completely open (even in\nthe case when $\\Omega$ is a polytope) and could not be treated using the\npreviously developed techniques.\n  In this paper we fully settle Fuglede's conjecture for convex bodies\naffirmatively in all dimensions, i.e. we prove that if a convex body $\\Omega\n\\subset \\mathbb{R}^d$ is a spectral set then $\\Omega$ is a convex polytope\nwhich can tile the space by translations. To prove this we introduce a new\ntechnique, involving a construction from crystallographic diffraction theory,\nwhich allows us to establish a geometric \"weak tiling\" condition necessary for\na set $\\Omega \\subset \\mathbb{R}^d$ to be spectral.\n", "doi": "10.4310/acta.2022.v228.n2.a3", "arxiv_id": "1904.12262", "pdf_urls": ["https://arxiv.org/pdf/1904.12262"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica 228 (2022), no. 2, 385-420", "categories": "math.CA math.FA math.MG"}
{"title": "Modulus of continuity and Heinz-Schwarz type inequalities of solutions\n  to biharmonic equations", "year": 2019, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Shaolin Chen"], "abstract": "  For positive integers $n\\geq2$ and $m\\geq1$, suppose that function\n$f\\in\\mathcal{C}^{4}(\\mathbb{B}^{n},\\mathbb{R}^{m})$ satisfying the following:\n$(1)$ the inhomogeneous biharmonic equation $\\Delta(\\Delta f)=g$ ($g\\in\n\\mathcal{C}(\\overline{\\mathbb{B}^{n}},\\mathbb{R}^{m})$) in $\\mathbb{B}^{n}$,\n(2) the boundary conditions $f=\\varphi_{1}$ $(\\varphi_{1}\\in\n\\mathcal{C}(\\mathbb{S}^{n-1},\\mathbb{R}^{m}))$ on $\\mathbb{S}^{n-1}$ and\n$\\partial f/\\partial\\mathbf{n}=\\varphi_{2}$ ( $\\varphi_{2}\\in\n\\mathcal{C}(\\mathbb{S}^{n-1},\\mathbb{R}^{m})$) on $\\mathbb{S}^{n-1}$, where\n$\\partial /\\partial\\mathbf{n}$ stands for the inward normal derivative,\n$\\mathbb{B}^{n}$ is the unit ball in $\\mathbb{R}^{n}$ and $\\mathbb{S}^{n-1}$ is\nthe unit sphere of $\\mathbb{B}^{n}$. First, we establish the representation\nformula of solutions to the above inhomogeneous biharmonic Dirichlet problem,\nand then discuss the Heinz-Schwarz type inequalities and the modulus of\ncontinuity of the solutions.\n", "doi": null, "arxiv_id": "1905.01794", "pdf_urls": ["https://arxiv.org/pdf/1905.01794"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Sinica, 2020", "categories": "math.CV"}
{"title": "On the continuous dual of the sequence space $bv$", "year": 2019, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["M. El Azhari"], "abstract": "  Imaninezhad and Miri introduced the sequence space $ d_{\\infty} $ in order to\ncharacterize the continuous dual of the sequence space $ bv. $ We show by a\ncounterexample that this claimed characterization is false.\n", "doi": null, "arxiv_id": "1905.03800", "pdf_urls": ["https://arxiv.org/pdf/1905.03800"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Univ. Comenianae, 89(2)(2020), 295-298", "categories": "math.FA"}
{"title": "Accretivity and form boundedness of second order differential operators", "year": 2019, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["V. G. Maz'ya and I. E. Verbitsky"], "abstract": "  Let $\\mathcal{L}$ be the general second order differential operator with\ncomplex-valued distributional coefficients $A=(a_{jk})_{j, k=1}^n$,\n$\\vec{b}=(b_{j})_{j=1}^n$, and $c$ in an open set $\\Omega \\subseteq\n\\mathbb{R}^n$ ($n \\ge 1$), with principal part either in the divergence form,\n$\\mathcal{L} u= {\\rm div} \\, (A \\nabla u) + \\vec{b} \\cdot\\nabla u + c \\, u$, or\nnon-divergence form, $ \\mathcal L u= \\sum_{j, \\, k=1}^n \\, a_{jk} \\, \\partial_j\n\\partial_k u + \\vec{b} \\cdot\\nabla u + c \\, u $.\n  We give a survey of the results by the authors which characterize the\nfollowing two properties of $\\mathcal{L}$:\n  (1) $-\\mathcal{L}$ is accretive, i.e., ${\\rm Re} \\, \\langle -\\mathcal L u, \\,\nu\\rangle \\ge 0$;\n  (2) $\\mathcal L$ is form bounded, i.e., $\\vert \\langle \\mathcal L u, u\n\\rangle \\vert \\le C \\, \\Vert \\nabla u \\Vert_{L^2(\\Omega)}^2$,\n  for all complex-valued $u \\in C^\\infty_0(\\Omega)$.\n", "doi": "10.1007/s10114-019-8127-9", "arxiv_id": "1905.04306", "pdf_urls": ["https://arxiv.org/pdf/1905.04306"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Sin. (Engl. Ser.) 35 (2019), no. 6, 832-852", "categories": "math.AP"}
{"title": "The $\\partial\\bar{\\partial}$-lemma under surjective maps", "year": 2019, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Lingxu Meng"], "abstract": "  We consider the $\\partial\\bar{\\partial}$-lemma for complex manifolds under\nsurjective holomorphic maps. Furthermore, using\nDeligne-Griffiths-Morgan-Sullivan's theorem, we prove that a product compact\ncomplex manifold satisfies the $\\partial\\bar{\\partial}$-lemma if and only if so\ndo all its components.\n", "doi": "10.1007/s10473-022-0303-9", "arxiv_id": "1905.13585", "pdf_urls": ["https://arxiv.org/pdf/1905.13585"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Sci. Ser. B 42 (2022), no. 3, 865-875", "categories": "math.AG math.CV"}
{"title": "Regularization by noise for the point vortex model of mSQG equations", "year": 2019, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Dejun Luo", "Martin Saal"], "abstract": "  We consider the point vortex model corresponding to the modified Surface\nQuasi-Geostrophic (mSQG) equations on the two dimensional torus. It is known\nthat this model is well posed for almost every initial conditions. We show\nthat, when the system is perturbed by a certain space-dependent noise, it\nadmits a unique global solution for any initial configuration. We also present\nan explicit example for the deterministic system where three different point\nvortices collapse.\n", "doi": "10.1007/s10114-020-9256-x", "arxiv_id": "1906.10191", "pdf_urls": ["https://arxiv.org/pdf/1906.10191"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Sin. (Engl. Ser.) 37 (2021), no. 3, 408-422", "categories": "math.PR"}
{"title": "Uniqueness to some inverse source problems for the wave equation in\n  unbounded domains", "year": 2019, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Guanghui Hu", "Yavar Kian", "Yue Zhao"], "abstract": "  This paper is concerned with inverse acoustic source problems in an unbounded\ndomain with dynamical boundary surface data of Dirichlet kind. The measurement\ndata are taken at a surface far away from the source support. We prove\nuniqueness in recovering source terms of the form $f(x)g(t)$ and $f(x_1,x_2,t)\nh(x_3)$, where $g(t)$ and $h(x_3)$ are given and $x=(x_1, x_2, x_3)$ is the\nspatial variable in three dimensions. Without these a priori information, we\nprove that the boundary data of a family of solutions can be used to recover\ngeneral source terms depending on both time and spatial variables. For moving\npoint sources radiating periodic signals, the data recorded at four receivers\nare proven sufficient to uniquely recover the orbit function. Simultaneous\ndetermination of embedded obstacles and source terms was verified in an\ninhomogeneous background medium using the observation data of infinite time\nperiod. Our approach depends heavily on the Laplace transform.\n", "doi": "10.1007/s10255-020-0917-4", "arxiv_id": "1907.02619", "pdf_urls": ["https://arxiv.org/pdf/1907.02619"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES Volume: 36\n  Issue: 1 Pages: 134-150 Published:JAN 2020", "categories": "math.AP"}
{"title": "On the best constants associated with $n$-distances", "year": 2019, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Gergely Kiss", "Jean-Luc Marichal"], "abstract": "  We pursue the investigation of the concept of $n$-distance, an $n$-variable\nversion of the classical concept of distance recently introduced and\ninvestigated by Kiss, Marichal, and Teheux. We especially focus on the\nchallenging problem of computing the best constant associated with a given\n$n$-distance. In particular, we define and investigate the best constants\nrelated to partial simplex inequalities. We also introduce and discuss some\nsubclasses of $n$-distances defined by considering some properties. Finally, we\ndiscuss an interesting link between the concepts of $n$-distance and\nmultidistance.\n", "doi": "10.1007/s10474-020-01023-8", "arxiv_id": "1907.06586", "pdf_urls": ["https://arxiv.org/pdf/1907.06586"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Hungarica, 161(1):341-365, 2020", "categories": "math.MG"}
{"title": "The best extending cover-preserving geometric lattices of semimodular\n  lattices", "year": 2019, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Peng He", "Xue-ping Wang"], "abstract": "  In 2010, G\\'{a}bor Cz\\'{e}dli and E. Tam\\'{a}s Schmidt mentioned that the\nbest cover-preserving embedding of a given semimodular lattice is not known yet\n[A cover-preserving embedding of semimodular lattices into geometric lattices,\nAdvances in Mathematics 225 (2010) 2455-2463]. That is to say: What are the\ngeometric lattices $G$ such that a given finite semimodular lattice $L$ has a\ncover-preserving embedding into $G$ with the smallest $|G|$? In this paper, we\npropose an algorithm to calculate all the best extending cover-preserving\ngeometric lattices $G$ of a given semimodular lattice $L$ and prove that the\nlength and the number of atoms of every best extending cover-preserving\ngeometric lattice $G$ equal the length of $L$ and the number of non-zero\njoin-irreducible elements of $L$, respectively. Therefore, we comprehend the\nbest cover-preserving embedding of a given semimodular lattice.\n", "doi": "10.1007/s10114-023-1531-1", "arxiv_id": "1908.00749", "pdf_urls": ["https://arxiv.org/pdf/1908.00749"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Sinica 39 (2023) 1369-1388", "categories": "math.CO"}
{"title": "The existence of a nontrivial weak solution to a double critical problem\n  involving fractional Laplacian in ${\\R}^n$ with a Hardy term", "year": 2019, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Gongbao Li", "Tao Yang"], "abstract": "  In this paper, we consider the existence of nontrivial weak solutions to a\ndouble critical problem involving fractional Laplacian with a Hardy term:\n\\begin{equation} \\label{eq0.1} (-\\Delta)^{s}u-{\\gamma} {\\frac{u}{|x|^{2s}}}=\n{\\frac{{|u|}^{ {2^{*}_{s}}(\\beta)-2}u}{|x|^{\\beta}}}+ \\big [ I_{\\mu}*\nF_{\\alpha}(\\cdot,u) \\big](x)f_{\\alpha}(x,u),\n  \\ \\ u \\in {\\dot{H}}^s(\\R^{n}) \\end{equation} where $s \\in(0,1)$, $0\\leq\n\\alpha,\\beta<2s<n$, $\\mu \\in (0,n)$, $\\gamma<\\gamma_{H}$,\n$I_{\\mu}(x)=|x|^{-\\mu}$, $F_{\\alpha}(x,u)=\\frac{ {|u(x)|}^{ {2^{\\#}_{\\mu}\n}(\\alpha)} }{ {|x|}^{ {\\delta_{\\mu} (\\alpha)} } }$, $f_{\\alpha}(x,u)=\\frac{\n{|u(x)|}^{{ 2^{\\#}_{\\mu} }(\\alpha)-2}u(x) }{ {|x|}^{ {\\delta_{\\mu} (\\alpha)} }\n}$, $2^{\\#}_{\\mu} (\\alpha)=(1-\\frac{\\mu}{2n})\\cdot 2^{*}_{s} (\\alpha)$,\n$\\delta_{\\mu} (\\alpha)=(1-\\frac{\\mu}{2n})\\alpha$,\n${2^{*}_{s}}(\\alpha)=\\frac{2(n-\\alpha)}{n-2s}$ and\n$\\gamma_{H}=4^s\\frac{\\Gamma^2(\\frac{n+2s}{4})} {\\Gamma^2(\\frac{n-2s}{4})}$. We\nshow that problem (\\ref{eq0.1}) admits at least a weak solution under some\nconditions.\n  To prove the main result, we develop some useful tools based on a weighted\nMorrey space. To be precise, we discover the embeddings \\begin{equation}\n\\label{eq0.2} {\\dot{H}}^s(\\R^{n}) \\hookrightarrow\n{L}^{2^*_{s}(\\alpha)}(\\R^{n},|y|^{-\\alpha}) \\hookrightarrow\nL^{p,\\frac{n-2s}{2}p+pr}(\\R^{n},|y|^{-pr}) \\end{equation} where $s \\in (0,1)$,\n$0<\\alpha<2s<n$, $p\\in[1,2^*_{s}(\\alpha))$, $r=\\frac{\\alpha}{ 2^*_{s}(\\alpha)\n}$; We also establish an improved Sobolev inequality.\n  By using mountain pass lemma along with an improved Sobolev inequality, we\nobtain a nontrivial weak solution to problem (\\ref{eq0.1}) in a direct way. It\nis worth while to point out that the improved Sobolev inequality could be\napplied to simplify the proof of the main results in \\cite{NGSS} and\n\\cite{RFPP}.\n", "doi": "10.1007/s10473-020-0613-8", "arxiv_id": "1908.02536", "pdf_urls": ["https://arxiv.org/pdf/1908.02536"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math Sci ,2020", "categories": "math.AP"}
{"title": "On the integrability of the Abel and of the extended Li\\'{e}nard\n  equations", "year": 2019, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Man Kwong Mak and Tiberiu Harko"], "abstract": "  We present some exact integrability cases of the extended Li\\'{e}nard\nequation $y^{\\prime \\prime }+f\\left( y\\right) \\left(y^{\\prime\n}\\right)^{n}+k\\left( y\\right) \\left(y^{\\prime }\\right)^{m}+g\\left(y\\right)\ny^{\\prime }+h\\left( y\\right) =0$, with $n>0$ and $m>0$ arbitrary constants,\nwhile $f(y)$, $k(y)$, $g(y)$, and $h(y)$ are arbitrary functions. The solutions\nare obtained by transforming the equation Li\\'{e}nard equation to an equivalent\nfirst kind first order Abel type equation given by $\\frac{dv}{dy} =f\\left(\ny\\right) v^{3-n}+k\\left( y\\right) v^{3-m}+g\\left( y\\right) v^{2}+h\\left(\ny\\right) v^{3}$, with $v=1/y^{\\prime }$. As a first step in our study we obtain\nthree integrability cases of the extended quadratic-cubic Li\\'{e}nard equation,\ncorresponding to $n=2$ and $m=3$, by assuming that particular solutions of the\nassociated Abel equation are known. Under this assumption the general solutions\nof the Abel and Li\\'{e}nard equations with coefficients satisfying some\ndifferential conditions can be obtained in an exact closed form. With the use\nof the Chiellini integrability condition, we show that if a particular solution\nof the Abel equation is known, the general solution of the extended quadratic\ncubic Li\\'{e}nard equation can be obtained by quadratures. The Chiellini\nintegrability condition is extended to generalized Abel equations with\n$g(y)\\equiv 0$ and $h(y)\\equiv 0$, and arbitrary $n$ and $m$, thus allowing to\nobtain the general solution of the corresponding Li\\'{e}nard equation. The\napplication of the generalized Chiellini condition to the case of the reduced\nRiccati equation is also considered.\n", "doi": "10.1007/s10255-019-0847-1", "arxiv_id": "1908.03730", "pdf_urls": ["https://arxiv.org/pdf/1908.03730"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematicae Applicatae Sinica, English Series, 35, 4,\n  (2019), 722-736", "categories": "math.CA math-ph math.MP nlin.SI"}
{"title": "Countably compact group topologies on the free Abelian group of size\n  continuum (and a Wallace semigroup) from a selective ultrafilter", "year": 2019, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["A. C. Boero", "I. Castro-Pereira and A. H. Tomita"], "abstract": "  We prove that the existence of a selective ultrafilter implies the existence\nof a countably compact Hausdorff group topology on the free Abelian group of\nsize continuum. As a consequence, we show that the existence of a selective\nultrafilter implies the existence of a Wallace semigroup (i.e., a countably\ncompact both-sided cancellative topological semigroup which is not a\ntopological group).\n", "doi": "10.1007/s10474-019-00991-w", "arxiv_id": "1909.03607", "pdf_urls": ["https://arxiv.org/pdf/1909.03607"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Hungarica 159 414--428 (2019)", "categories": "math.GN"}
{"title": "A note on product sets of random sets", "year": 2019, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Carlo Sanna"], "abstract": "  Given two sets of positive integers $A$ and $B$, let $AB := \\{ab : a \\in A,\\,\nb \\in B\\}$ be their product set and put $A^k := A \\cdots A$ ($k$ times $A$) for\nany positive integer $k$. Moreover, for every positive integer $n$ and every\n$\\alpha \\in [0,1]$, let $\\mathcal{B}(n, \\alpha)$ denote the probabilistic model\nin which a random set $A \\subseteq \\{1, \\dots, n\\}$ is constructed by choosing\nindependently every element of $\\{1, \\dots, n\\}$ with probability $\\alpha$. We\nprove that if $A_1, \\dots, A_s$ are random sets in $\\mathcal{B}(n_1, \\alpha_1),\n\\dots, \\mathcal{B}(n_s, \\alpha_s)$, respectively, $k_1, \\dots, k_s$ are fixed\npositive integers, $\\alpha_i n_i \\to +\\infty$, and $1/\\alpha_i$ does not grow\ntoo fast in terms of a product of $\\log n_j$; then $|A_1^{k_1} \\cdots\nA_s^{k_s}| \\sim \\frac{|A_1|^{k_1}}{k_1!}\\cdots\\frac{|A_s|^{k_s}}{k_s!}$ with\nprobability $1 - o(1)$. This is a generalization of a result of Cilleruelo,\nRamana, and Ramar\\'e, who considered the case $s = 1$ and $k_1 = 2$.\n", "doi": "10.1007/s10474-019-01014-4", "arxiv_id": "1909.05188", "pdf_urls": ["https://arxiv.org/pdf/1909.05188"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Hungarica 162 (2020), 76-83", "categories": "math.NT"}
{"title": "Proof of two supercongruences of truncated hypergeometric series\n  ${}_4F_3$", "year": 2019, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Guo-Shuai Mao"], "abstract": "  In this paper, we prove two supercongruences conjectured by Z.-W. Sun via the\nWilf-Zeilberger method. One of them is, for any prime $p>3$, \\begin{align*}\n\\sum_{n=0}^{(p-1)/2}\\frac{6n+1}{(-512)^n}\\binom{2n}n^3&\\equiv\np\\left(\\frac{-2}p\\right)+\\frac{p^3}4\\left(\\frac2p\\right)E_{p-3}\\pmod{p^4},\n\\end{align*} where $\\left(\\frac{\\cdot}p\\right)$ stands for the Legendre symbol,\nand $E_{n}$ is the $n$-th Euler number.\n", "doi": "10.1007/s10114-023-1152-8", "arxiv_id": "1910.09983", "pdf_urls": ["https://arxiv.org/pdf/1910.09983"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Sinica, English Series (2024) 40(4), 1015--1028", "categories": "math.NT math.CO"}
{"title": "Transportation cost inequalities for stochastic reaction-diffusion\n  equations with L\\'evy noises and non-Lipschitz reaction terms", "year": 2019, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Yutao Ma", "Ran Wang"], "abstract": "  For stochastic reaction-diffusion equations with L\\'evy noises and\nnon-Lipschitz reaction terms, we prove that $W_1H$ transportation cost\ninequalities hold for their invariant probability measures and for their\nprocess-level laws on the path space with respect to the $L^1$-metric. The\nproofs are based on the Galerkin approximations.\n", "doi": null, "arxiv_id": "1911.02180", "pdf_urls": ["https://arxiv.org/pdf/1911.02180"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Sinica, English Series, 2019", "categories": "math.PR"}
{"title": "Time analyticity for heat equation on gradient shrinking Ricci solitons", "year": 2019, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Jia-Yong Wu"], "abstract": "  On a complete non-compact gradient shrinking Ricci soliton, we prove the\nanalyticity in time for smooth solutions of the heat equation with quadratic\nexponential growth in the space variable. This growth condition is sharp. As an\napplication, we give a necessary and sufficient condition on the solvability of\nthe backward heat equation in a class of functions with quadratic exponential\ngrowth on shrinkers.\n", "doi": "10.1007/s10473-022-0424-1", "arxiv_id": "1911.02735", "pdf_urls": ["https://arxiv.org/pdf/1911.02735"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Sci., 42, 1690-1700, 2022", "categories": "math.DG"}
{"title": "On Algebraic Conditions for the Non-Vanishing of Linear Forms in Jacobi\n  Theta-Constants", "year": 2019, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Carsten Elsner and Veekesh Kumar"], "abstract": "  Elsner, Luca and Tachiya proved in 2019 that the values of the Jacobi-theta\nconstants $\\theta_3(m\\tau)$ and $\\theta_3(n\\tau)$ are algebraically independent\nover $\\mathbb{Q}$ for distinct integers $m,n$ under some conditions on $\\tau$.\nOn the other hand, in 2018 Elsner and Tachiya also proved that three values\n$\\theta_3(m\\tau),\\theta_3(n\\tau)$ and $\\theta_3(\\ell \\tau)$ are algebraically\ndependent over $\\mathbb{Q}$. In this article we prove the non-vanishing of\nlinear forms in $\\theta_3(m\\tau)$, $\\theta_3(n\\tau)$ and $\\theta_3(\\ell \\tau)$\nunder various conditions on $m,n,\\ell$, and $\\tau$. Among other things we prove\nthat for odd and distinct positive integers $m,n>3$ the three numbers\n$\\theta_3(\\tau)$, $\\theta_3(m\\tau)$ and $\\theta_3(n \\tau)$ are linearly\nindependent over $\\overline{\\mathbb{Q}}$ when $\\tau$ is an algebraic number of\nsome degree greater or equal to 3. In some sense this fills the gap between the\nabove-mentioned former results on theta constants. A theorem on the linear\nindependence over $\\mathbb{C(\\tau)}$ of the functions $\\theta_3(a_1\n\\tau),\\ldots,\\theta_3(a_m \\tau)$ for distinct positive rational numbers $a_1,\n\\ldots a_m$ is also established.\n", "doi": "10.1007/s10474-024-01449-4", "arxiv_id": "1911.06513", "pdf_urls": ["https://arxiv.org/pdf/1911.06513"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Hungarica (2024)", "categories": "math.NT"}
{"title": "Oscillations of the error term in the prime number theorem", "year": 2019, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Jan-Christoph Schlage-Puchta"], "abstract": "  Let $\\sigma+i\\gamma$ be a zero of the Riemann zeta function to the right of\nthe line $\\frac{1}{2}+it$. We show that this zero causes large oscillations of\nthe error term of the prime number theorem. Our result is close to optimal both\nin terms of the magnitude and in the localization of large values for the error\nterm.\n", "doi": null, "arxiv_id": "1912.00853", "pdf_urls": ["https://arxiv.org/pdf/1912.00853"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Hungar. 156 (2018), 303-308", "categories": "math.NT"}
{"title": "On the algebraic functional equation of the eigenspaces of mixed signed\n  Selmer groups of elliptic curves with good reduction at primes above $p$", "year": 2019, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Suman Ahmed", "Meng Fai Lim"], "abstract": "  Let $p$ be an odd prime number, and let $E$ be an elliptic curve defined over\na number field which has good reduction at every prime above $p$. Under\nsuitable assumptions, we prove that the $\\eta$-eigenspace and the\n$\\bar{\\eta}$-eigenspace of mixed signed Selmer group of the elliptic curve are\npseudo-isomorphic. As a corollary, we show that the $\\eta$-eigenspace is\ntrivial if and only if the $\\bar{\\eta}$-eigenspace is trivial. Our results can\nbe thought as a reflection principle which relate an Iwasawa module in a given\neigenspace with another Iwasawa module in a \"reflected\" eigenspace.\n", "doi": "10.1007/s10114-020-9556-1", "arxiv_id": "1912.09023", "pdf_urls": ["https://arxiv.org/pdf/1912.09023"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Sinica (English Series) 37 (2021), no. 2, 289-305", "categories": "math.NT"}
{"title": "The Thue-Morse and Rudin-Shapiro sequences at primes in principal number\n  fields", "year": 2020, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Sary Drappeau", "Gautier Hanna"], "abstract": "  We consider a numeration system in the ring of integers ${\\mathcal O}_K$ of a\nnumber field, which we assume to be principal. We prove that the property of\nbeing a prime in ${\\mathcal O}_K$ is decorrelated from two fundamental examples\nof automatic sequences relative to the chosen numeration system: the Thue-Morse\nand the Rudin-Shapiro sequences. This is an analogue, in ${\\mathcal O}_K$, of\nresults of Mauduit-Rivat which were concerned with the case $K={\\mathbb Q}$.\n", "doi": "10.1007/s10474-020-01030-9", "arxiv_id": "2001.07017", "pdf_urls": ["https://arxiv.org/pdf/2001.07017"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Hung. 162, No. 1, 130-186 (2020)", "categories": "math.NT"}
{"title": "On quasiconformal close-to-convex harmonic mappings involving starlike\n  functions", "year": 2020, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Zhi-Gang Wang", "Xin-Zhong Huang", "Zhi-Hong Liu and Rahim Kargar"], "abstract": "  In the present paper, we discuss several basic properties of a class of\nquasiconformal close-to-convex harmonic mappings with starlike analytic part,\nsuch results as coefficient inequalities, an integral representation, a growth\ntheorem, an area theorem, and radii of close-to-convexity of partial sums of\nthe class, are derived.\n", "doi": null, "arxiv_id": "2002.03099", "pdf_urls": ["https://arxiv.org/pdf/2002.03099"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Sinica (Chinese Series), 63 (2020), 565-576", "categories": "math.CV"}
{"title": "Double weakness", "year": 2020, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Shimon Garti and Saharon Shelah"], "abstract": "  We prove that, consistently, there exists a weakly but not strongly\ninaccessible cardinal $\\lambda$ for which the sequence $\\langle\n2^\\theta:\\theta<\\lambda\\rangle$ is not eventually constant and the weak diamond\nfails at $\\lambda$. We also prove that consistently diamond fails but a\nparametrized version of weak diamond holds at some strongly inaccessible\n$\\lambda$.\n", "doi": "10.1007/s10474-021-01132-y", "arxiv_id": "2002.03573", "pdf_urls": ["https://arxiv.org/pdf/2002.03573"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Hungarica, vol. 163 (2), 2021, pages 379-391", "categories": "math.LO"}
{"title": "The linear unicyclic hypergraph with the second or third largest\n  spectral radius", "year": 2020, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Chao Ding", "Yi-Zheng Fan", "Jiang-Chao Wan"], "abstract": "  The spectral radius of a uniform hypergraph is defined to be that of the\nadjacency tensor the hypergraph. It is known that the unique unicyclic\nhypergraph with the largest spectral radius is a nonlinear hypergraph, and the\nunique linear unicyclic hypergraph with the largest spectral radius is a power\nhypergraph. In this paper we determine the the unique linear unicyclic\nhypergraph with the second or third largest spectral radius, where the former\nhypergraph is a power hypergraph and the latter hypergraph is a non-power\nhypergraph.\n", "doi": "10.1007/s10114-020-0089-4", "arxiv_id": "2002.04415", "pdf_urls": ["https://arxiv.org/pdf/2002.04415"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Sinica English Series, 36(2020), 1140-1150", "categories": "math.CO"}
{"title": "Congruence classes and maximal nonbases", "year": 2020, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Melvyn B. Nathanson"], "abstract": "  The set $A$ is an asymptotic nonbasis of order $h$ for an additive abelian\ngroup $X$ if there are infinitely many elements of $X$ not in the $h$-fold\nsumset $hA$. For all $h \\geq 2$, this paper constructs new classes of\nasymptotic nonbases of order $h$ for $\\mathbf{Z}$ and for $\\mathbf{N}_0$ that\nare not subsets of maximal asymptotic nonbases.\n", "doi": null, "arxiv_id": "2004.02367", "pdf_urls": ["https://arxiv.org/pdf/2004.02367"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Hungarica 161 (2020), 768--779", "categories": "math.NT"}
{"title": "A uniform set with fewer than expected arithmetic progressions of length\n  4", "year": 2020, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["W. T. Gowers"], "abstract": "  An example is presented of a subset $A$ of $\\mathbb Z_N$ of density $\\alpha$\nsuch that the largest non-trivial Fourier coefficient of the characteristic\nfunction of $A$ is very small, but the probability that a random arithmetic\nprogression (mod $N$) of length 4 lies in $A$ is significantly smaller than\n$\\alpha^4$.\n", "doi": "10.1007/s10474-020-01072-z", "arxiv_id": "2004.07598", "pdf_urls": ["https://arxiv.org/pdf/2004.07598"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Hungarica (2020)", "categories": "math.CO"}
{"title": "Minimum pair degree condition for tight Hamiltonian cycles in\n  $4$-uniform hypergraphs", "year": 2020, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Joanna Polcyn", "Christian Reiher", "Vojt\\v{e}ch R\\\"odl", "Andrzej\n  Ruci\\'nski", "Mathias Schacht", "Bjarne Sch\\\"ulke"], "abstract": "  We show that every 4-uniform hypergraph with $n$ vertices and minimum pair\ndegree at least $(5/9+o(1))n^2/2$ contains a tight Hamiltonian cycle. This\ndegree condition is asymptotically optimal.\n", "doi": "10.1007/s10474-020-01078-7", "arxiv_id": "2005.03391", "pdf_urls": ["https://arxiv.org/pdf/2005.03391"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Hungarica 161 (2020), no. 2, 647--699", "categories": "math.CO"}
{"title": "Ergodic theorems for laminations and foliations: recent results and\n  perspectives", "year": 2020, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Viet-Anh Nguyen"], "abstract": "  This report discusses recent results as well as new perspectives in the\nergodic theory for Riemann surface laminations, with an emphasis on singular\nholomorphic foliations by curves. The central notions of these developments are\nleafwise Poincar\\'e metric, directed positive harmonic currents, multiplicative\ncocycles and Lyapunov exponents. We deal with various ergodic theorems for such\nlaminations: Random and Operator Ergodic Theorems, (Geometric) Birkhoff Ergodic\nTheorems, Oseledec Multiplicative Ergodic Theorem and Unique Ergodicity\nTheorems. Applications of these theorems are also given. In particular, we\ndefine and study the canonical Lyapunov exponents for a large family of\nsingular holomorphic foliations on compact projective surfaces. Topological and\nalgebro-geometric interpretations of these characteristic numbers are also\ntreated.\n  These results highlight the strong similarity as well as the fundamental\ndifferences between the ergodic theory of maps and that of Riemann surface\nlaminations. Most of the results reported here are known. However, sufficient\nconditions for abstract heat diffusions to coincide with the leafwise heat\ndiffusions (Subsection 5.2) are new ones.\n", "doi": null, "arxiv_id": "2005.07176", "pdf_urls": ["https://arxiv.org/pdf/2005.07176"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Vietnam.(2020)", "categories": "math.DS math.AG math.CV math.DG"}
{"title": "On the number of $k$-compositions of $n$ satisfying certain coprimality\n  conditions", "year": 2020, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["L\\'aszl\\'o T\\'oth"], "abstract": "  We generalize the asymptotic estimates by Bubboloni, Luca and Spiga (2012) on\nthe number of $k$-compositions of $n$ satisfying some coprimality conditions.\nWe substantially refine the error term concerning the number of\n$k$-compositions of $n$ with pairwise relatively prime summands. We use a\ndifferent approach, based on properties of multiplicative arithmetic functions\nof $k$ variables and on an asymptotic formula for the restricted partition\nfunction.\n", "doi": "10.1007/s10474-021-01147-5", "arxiv_id": "2006.04500", "pdf_urls": ["https://arxiv.org/pdf/2006.04500"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Hungar. 164 (1) (2021), 135-156", "categories": "math.NT math.CO"}
{"title": "Generalized Ces\\`aro operators on Dirichlet-type spaces", "year": 2020, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Jianjun Jin and Shuan Tang"], "abstract": "  In this note, we introduce and study a new kind of generalized Ces\\`aro\noperators $\\mathcal{C}_{\\mu}$, induced by a positive Borel measure $\\mu$ on\n$[0, 1)$, between the Dirichlet-type spaces. We characterize the measures $\\mu$\nfor which $\\mathcal{C}_{\\mu}$ is bounded (compact) from one Dirichlet-type\nspace $\\mathcal{D}_{\\alpha}$ into another one $\\mathcal{D}_{\\beta}$.\n", "doi": null, "arxiv_id": "2007.07548", "pdf_urls": ["https://arxiv.org/pdf/2007.07548"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Sci. Ser. B (Engl. Ed.) 42 (2022), no. 1, 212-220", "categories": "math.CA math.CV"}
{"title": "Multiplicity of solutions for a class of critical Schr\\\"odinger-Poisson\n  system with two parameters", "year": 2020, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Yongpeng Chen and Zhipeng Yang"], "abstract": "  We study a class of critical Schr\\\"odinger-Poisson system of the form\n\\begin{equation*} \\begin{cases} -\\Delta u+\\lambda V(x)u+\\phi u=\\mu\n|u|^{p-2}u+|u|^{4}u& \\quad x\\in \\mathbb{R}^3,\\\\ -\\Delta \\phi=u^2&\\quad x\\in\n\\mathbb{R}^3,\\\\ \\end{cases} \\end{equation*} where $\\lambda, \\mu>0$ are two\nparameters, $p\\in(4,6)$ and $V$ satisfies some potential well conditions. By\nusing the variational arguments, we prove the existence of positive ground\nstate solutions for $\\lambda$ large enough and $\\mu>0$, and their asymptotical\nbehavior as $\\lambda\\to\\infty$. Moreover, by using Ljusternik-Schnirelmann\ntheory, we obtain the existence of multiple positive solutions if $\\lambda$ is\nlarge and $\\mu$ is small.\n", "doi": null, "arxiv_id": "2007.13830", "pdf_urls": ["https://arxiv.org/pdf/2007.13830"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Sci. Ser. A (Chin. Ed.) 41, no.6, 1750-1767,2021", "categories": "math.AP"}
{"title": "Quasi-quadratic modules in valuation ring and valued field", "year": 2020, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Masato Fujita", "Masaru Kageyama"], "abstract": "  This is a revised version of the previous version with a new appendix\nconsisting of characteristic two case. We define quasi-quadratic modules in a\ncommutative ring generalizing the notion of quadratic modules. The main theorem\nis a structure theorem of quasi-quadratic modules in a subring $A$ of a\n$2$-henselian valued field $(K,{\\bf val})$ whose residue class field $F$ of\ncharacteristic $\\neq 2$. We further assume that the valuation ring $B$ is\ncontained in $A$. Set $H={\\bf val}(A^\\times)$ and $G_{\\geq e}=\\{g \\in G\\;|\\; g\n\\geq e\\}$. The notation $\\mathfrak X_R$ denotes the set of all the\nquasi-quadratic modules in a commutative ring $R$. Our structure theorem\nasserts that there exists a one-to-one correspondence between $\\mathfrak X_A$\nand a subset $\\mathcal T_F^{ H \\cup G_{\\geq e}}$ of $\\prod_{g \\in H \\cup\nG_{\\geq e}}\\mathfrak X_F$. We explicitly construct the map $\\Theta: \\mathfrak\nX_A \\rightarrow \\mathcal T_F^{ H \\cup G_{\\geq e}}$ and its inverse. We also\ngive explicit expressions of $\\Theta(\\mathcal M \\cap \\mathcal N)$ and\n$\\Theta(\\mathcal M+\\mathcal N)$ for $\\mathcal M, \\mathcal N \\in \\mathfrak X_A$.\n  In addition, we briefly investigate the case in which the field $F$ is of\ncharacteristic two in the appendix as well.\n", "doi": "10.1007/s10474-023-01333-7", "arxiv_id": "2008.03494", "pdf_urls": ["https://arxiv.org/pdf/2008.03494"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Hungr., 2023", "categories": "math.AC math.LO math.RA"}
{"title": "Stronger versions of sensitivity for minimal group actions", "year": 2020, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Jian Li", "Yini Yang"], "abstract": "  We study several stronger versions of sensitivity for minimal group actions,\nincluding $n$-sensitivity, thick $n$-sensitivity and blockily thick\n$n$-sensitivity, and characterize them by the regionally proximal relation.\n", "doi": "10.1007/s10114-021-0511-6", "arxiv_id": "2008.06898", "pdf_urls": ["https://arxiv.org/pdf/2008.06898"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Sin. (Engl. Ser.) 37 (2021), no. 12, 1933--1946", "categories": "math.DS"}
{"title": "On monochromatic solutions to $x-y=z^2$", "year": 2020, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Tom Sanders"], "abstract": "  For $k \\in \\mathbb{N}$, write $S(k)$ for the largest natural number such that\nthere is a $k$-colouring of $\\{1,\\dots,S(k)\\}$ with no monochromatic solution\nto $x-y=z^2$. That $S(k)$ exists is a result of Bergelson, and a simple example\nshows that $S(k) \\geq 2^{2^{k-1}}$. The purpose of this note is to show that\n$S(k)\\leq 2^{2^{2^{O(k)}}}$.\n", "doi": "10.1007/s10474-020-01079-6", "arxiv_id": "2008.07297", "pdf_urls": ["https://arxiv.org/pdf/2008.07297"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Hungar. 161 (2020), no. 2, 550-556", "categories": "math.CO"}
{"title": "Kunneth Theorems for Vietoris-Rips Homology", "year": 2020, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Antonio Rieser and Alejandra Trujillo"], "abstract": "  We prove a Kunneth theorem for the Vietoris-Rips homology and cohomology of a\nsemi-uniform space. We then interpret this result for graphs, where we show\nthat the Kunneth theorem holds for graphs with respect to the strong graph\nproduct. We finish by computing the Vietoris-Rips cohomology of the torus\nendowed with diferent semi-uniform structures.\n", "doi": "10.1007/s10474-022-01220-7", "arxiv_id": "2009.05833", "pdf_urls": ["https://arxiv.org/pdf/2009.05833"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Hungarica, volume 166, pages 239-253 (2022)", "categories": "math.AT cs.CG math.CO"}
{"title": "Ancient solutions of the homogeneous Ricci flow on flag manifolds", "year": 2020, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Stavros Anastassiou", "Ioannis Chrysikos"], "abstract": "  For any flag manifold $M=G/K$ of a compact simple Lie group $G$ we describe\nnon-collapsing ancient invariant solutions of the homogeneous unnormalized\nRicci flow. Such solutions emerge from an invariant Einstein metric on $M$, and\nby [B\\\"oLS17] they must develop a Type I singularity in their extinction finite\ntime, and also to the past. To illustrate the situation we engage ourselves\nwith the global study of the dynamical system induced by the unnormalized Ricci\nflow on any flag manifold $M=G/K$ with second Betti number $b_{2}(M)=1$, for a\ngeneric initial invariant metric. We describe the corresponding dynamical\nsystems and present non-collapsed ancient solutions, whose $\\alpha$-limit set\nconsists of fixed points at infinity of ${\\mathscr{M}}^G$. Based on the\nPoincar\\'{e} compactification method, we show that these fixed points\ncorrespond to invariant Einstein metrics and we study their stability\nproperties, illuminating thus the structure of the system's phase space.\n", "doi": "10.17398/2605-5686.36.1.99", "arxiv_id": "2009.05985", "pdf_urls": ["https://arxiv.org/pdf/2009.05985"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Extracta Mathematicae Vol. 36, Num. 1 (2021), 99-145", "categories": "math.DG math.DS"}
{"title": "Seemingly injective von Neumann algebras", "year": 2020, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Gilles Pisier"], "abstract": "  We show that a QWEP von Neumann algebra has the weak* positive approximation\nproperty if and only if it is seemingly injective in the following sense: there\nis a factorization of the identity of $M$ $$Id_M=vu: M{\\buildrel\nu\\over\\longrightarrow} B(H) {\\buildrel v\\over\\longrightarrow} M$$ with $u$\nnormal, unital, positive and $v$ completely contractive. As a corollary, if $M$\nhas a separable predual, $M$ is isomorphic (as a Banach space) to $B(\\ell_2)$.\nFor instance this applies (rather surprisingly) to the von Neumann algebra of\nany free group. Nevertheless, since $B(H)$ fails the approximation property\n(due to Szankowski) there are $M$'s (namely $B(H)^{**}$ and certain finite\nexamples defined using ultraproducts) that are not seemingly injective.\nMoreover, for $M$ to be seemingly injective it suffices to have the above\nfactorization of $Id_M$ through $B(H)$ with $u,v$ positive (and $u$ still\nnormal).\n", "doi": null, "arxiv_id": "2010.13743", "pdf_urls": ["https://arxiv.org/pdf/2010.13743"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Scientia 41 (2021) 2055--2085", "categories": "math.OA math.FA"}
{"title": "A new proof of the Gaffney's inequality for differential forms on manifolds-with-boundary: the variational approach \\`{a} la Kozono--Yanagisawa", "year": 2020, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Siran Li"], "abstract": "Let $(\\mathcal{M},g_0)$ be a compact Riemannian manifold-with-boundary. We present a new proof of the classical Gaffney's inequality for differential forms in boundary value spaces over $\\mathcal{M}$, via the variational approach \\`{a} la Kozono--Yanagisawa [$L^r$-variational inequality for vector fields and the Helmholtz--Weyl decomposition in bounded domains, Indiana Univ. Math. J. 58 (2009), 1853--1920] combined with global computations based on the Bochner's technique.", "doi": null, "arxiv_id": "2011.00933", "pdf_urls": ["https://arxiv.org/pdf/2011.00933"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Sci. Ser. B (Engl. Ed.) 42 (2022), no. 4, 1427-1452", "categories": "math.AP math.DG math.HO"}
{"title": "On the termination of flips for log canonical generalized pairs", "year": 2020, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Guodu Chen and Nikolaos Tsakanikas"], "abstract": "  We prove the termination of flips for 4-dimensional pseudo-effective NQC log\ncanonical generalized pairs. As main ingredients, we verify the termination of\nflips for 3-dimensional NQC log canonical generalized pairs, and show that the\ntermination of flips for pseudo-effective NQC log canonical generalized pairs\nwhich admit NQC weak Zariski decompositions follows from the termination of\nflips in lower dimensions.\n", "doi": "10.1007/s10114-023-0116-3", "arxiv_id": "2011.02236", "pdf_urls": ["https://arxiv.org/pdf/2011.02236"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Sin. (Engl. Ser.) 39 (2023), 967-994", "categories": "math.AG"}
{"title": "Maximizing the Minimum and Maximum Forcing Numbers of Perfect Matchings\n  of Graphs", "year": 2020, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Qian qian Liu and He ping Zhang"], "abstract": "  Let $G$ be a simple graph with $2n$ vertices and a perfect matching. The\nforcing number $f(G,M)$ of a perfect matching $M$ of $G$ is the smallest\ncardinality of a subset of $M$ that is contained in no other perfect matching\nof $G$. Among all perfect matchings $M$ of $G$, the minimum and maximum values\nof $f(G,M)$ are called the minimum and maximum forcing numbers of $G$, denoted\nby $f(G)$ and $F(G)$, respectively. Then $f(G)\\leq F(G)\\leq n-1$. Che and Chen\n(2011) proposed an open problem: how to characterize the graphs $G$ with\n$f(G)=n-1$. Later they showed that for a bipartite graph $G$, $f(G)=n-1$ if and\nonly if $G$ is a complete bipartite graph $K_{n,n}$. In this paper, we\ncompletely solve the problem of Che and Chen, and show that $f(G)=n-1$ if and\nonly if $G$ is a complete multipartite graph or a graph obtained from complete\nbipartite graph $K_{n,n}$ by adding arbitrary edges in the same partite set.\nFor all graphs $G$ with $F(G)=n-1$, we prove that the forcing spectrum of each\nsuch graph $G$ forms an integer interval by matching 2-switches and the minimum\nforcing numbers of all such graphs $G$ form an integer interval from\n$\\lfloor\\frac{n}{2}\\rfloor$ to $n-1$.\n", "doi": null, "arxiv_id": "2011.10172", "pdf_urls": ["https://arxiv.org/pdf/2011.10172"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Sin., Engl. Ser.2023", "categories": "math.CO"}
{"title": "Phase transitions for products of characteristic polynomials under Dyson\n  Brownian motion", "year": 2020, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Peter J. Forrester and Dang-Zheng Liu"], "abstract": "  We study the averaged products of characteristic polynomials for the Gaussian\nand Laguerre $\\beta$-ensembles with external source, and prove Pearcey-type\nphase transitions for particular full rank perturbations of source. The phases\nare characterised by determining the explicit functional forms of the scaled\nlimits of the averaged products of characteristic polynomials, which are given\nas certain multidimensional integrals, with dimension equal to the number of\nproducts.\n", "doi": "10.1007/s10114-020-9445-7", "arxiv_id": "2012.13786", "pdf_urls": ["https://arxiv.org/pdf/2012.13786"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Sinica, English Series 2020", "categories": "math.PR math-ph math.MP"}
{"title": "Monge-Amp\\`{e}re type equations on almost Hermitian manifolds", "year": 2021, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Jiaogen Zhang"], "abstract": "  In this paper, we consider the Monge-Amp\\`{e}re type equations on compact\nalmost Hermitian manifolds. We derive $C^{\\infty}$ a priori estimates under the\nexistence of an admissible $\\mathcal{C}$-subsolution. Finally, we obtain an\nexistence result if there exists an admissible supersolution.\n", "doi": "10.1007/s10114-022-0394-1", "arxiv_id": "2101.00380", "pdf_urls": ["https://arxiv.org/pdf/2101.00380"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta. Math. Sin.-English Ser. (2022)", "categories": "math.DG math.AP"}
{"title": "Cancellable elements of the lattice of monoid varieties", "year": 2021, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Sergey V. Gusev", "Edmond W. H. Lee"], "abstract": "  The set of all cancellable elements of the lattice of semigroup varieties has\nrecently been shown to be countably infinite. But the description of all\ncancellable elements of the lattice $\\mathbb{MON}$ of monoid varieties remains\nunknown. This problem is addressed in the present article. The first example of\na monoid variety with modular but non-distributive subvariety lattice is first\nexhibited. Then a necessary condition of the modularity of an element in\n$\\mathbb{MON}$ is established. These results play a crucial role in the\ncomplete description of all cancellable elements of the lattice $\\mathbb{MON}$.\nIt turns out that there are precisely five such elements.\n", "doi": "10.1007/s10474-021-01177-z", "arxiv_id": "2101.02418", "pdf_urls": ["https://arxiv.org/pdf/2101.02418"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Hungar. 165 (2021), 156-168", "categories": "math.GR"}
{"title": "Rational numbers represented by sign-variable Cantor series", "year": 2021, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Symon Serbenyuk"], "abstract": "  The present article is devoted to representations of rational numbers in\nterms sign-variable Cantor expansions. The main attention is given to one of\nthe discussions given by J. Galambos in [4].\n", "doi": "10.1007/s10474-021-01163-5", "arxiv_id": "2101.08161", "pdf_urls": ["https://arxiv.org/pdf/2101.08161"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Hungarica 164, 580--592 (2021)", "categories": "math.NT"}
{"title": "Homotopy theory of Moore flows (II)", "year": 2021, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Philippe Gaucher"], "abstract": "  This paper proves that the q-model structures of Moore flows and of\nmultipointed $d$-spaces are Quillen equivalent. The main step is the proof that\nthe counit and unit maps of the Quillen adjunction are isomorphisms on the\nq-cofibrant objects (all objects are q-fibrant). As an application, we provide\na new proof of the fact that the categorization functor from multipointed\n$d$-spaces to flows has a total left derived functor which induces a category\nequivalence between the homotopy categories. The new proof sheds light on the\ninternal structure of the categorization functor which is neither a left\nadjoint nor a right adjoint. It is even possible to write an inverse up to\nhomotopy of this functor using Moore flows.\n", "doi": "10.17398/2605-5686.36.2.157", "arxiv_id": "2102.07513", "pdf_urls": ["https://arxiv.org/pdf/2102.07513"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Extracta Mathematicae, vol. 36 (2), 157-239, 2021", "categories": "math.CT math.AT"}
{"title": "Pluriclosed manifolds with constant holomorphic sectional curvature", "year": 2021, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Peipei Rao and Fangyang Zheng"], "abstract": "  A long-standing conjecture in complex geometry says that a compact Hermitian\nmanifold with constant holomorphic sectional curvature must be K\\\"ahler when\nthe constant is non-zero and must be Chern flat when the constant is zero. The\nconjecture is known in complex dimension $2$ by the work of Balas-Gauduchon in\n1985 (when the constant is zero or negative) and by Apostolov-Davidov-Muskarov\nin 1996 (when the constant is positive). For higher dimensions, the conjecture\nis still largely unknown. In this article, we restrict ourselves to pluriclosed\nmanifolds, and confirm the conjecture for the special case of Strominger\nK\\\"ahler-like manifolds, namely, for Hermitian manifolds whose Strominger\nconnection (also known as Bismut connection) obeys all the K\\\"ahler symmetries.\n", "doi": null, "arxiv_id": "2104.01319", "pdf_urls": ["https://arxiv.org/pdf/2104.01319"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Sinica (English Series) 2022, Vol. 38, No.6,\n  pp.1094-1104", "categories": "math.DG"}
{"title": "Almost paracontact almost paracomplex Riemannian manifolds as extensions\n  of 2-dimensional space-forms", "year": 2021, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Mancho Manev", "Veselina Tavkova"], "abstract": "  Almost paracontact Riemannian manifolds of the lowest dimension are studied,\nwhose paracontact distributions are equipped with an almost paracomplex\nstructure. These manifolds are constructed as a product of a real line and a\n2-dimensional Riemannian space-form. Their metric is obtained in two ways: as a\ncone metric and as a hyperbolic extension of the metric of the underlying\nparacomplex 2-manifold. The resulting manifolds are studied and characterized\nin terms of the classification used and their curvature properties.\n", "doi": null, "arxiv_id": "2104.11053", "pdf_urls": ["https://arxiv.org/pdf/2104.11053"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Universitatis Comenianae, 2022, vol. 91, no. 1,\n  69-79", "categories": "math.DG"}
{"title": "$\\mathsf{PFA}$ and $\\omega_1$-free compact spaces", "year": 2021, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Alan Dow and Klaas Pieter Hart"], "abstract": "  The Proper Forcing Axiom implies that compact Hausdorff spaces are either\nfirst-countable or contain a converging $\\omega_1$-sequence.\n", "doi": "10.1007/s10474-021-01197-9", "arxiv_id": "2104.13698", "pdf_urls": ["https://arxiv.org/pdf/2104.13698"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Hungarica (2022)", "categories": "math.GN math.LO"}
{"title": "A subsolution theorem for the Monge-Amp\\`{e}re equation over an almost\n  Hermitian manifold", "year": 2021, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Jiaogen Zhang"], "abstract": "  Let $\\Omega\\subseteq M$ be a bounded domain with a smooth boundary\n$\\partial\\Omega$, where $(M,J,g)$ is a compact, almost Hermitian manifold. The\nmain result of this paper is to consider the Dirichlet problem for a complex\nMonge-Amp\\`{e}re equation on $\\Omega$. Under the existence of a $C^{2}$-smooth\nstrictly $J$-plurisubharmonic ($J$-psh for short) subsolution, we can solve\nthis Dirichlet problem. Our method is based on the properties of subsolutions\nwhich have been widely used for fully nonlinear elliptic equations over\nHermitian manifolds.\n", "doi": null, "arxiv_id": "2107.00167", "pdf_urls": ["https://arxiv.org/pdf/2107.00167"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Sci. Ser. B (Engl. Ed.) 42 (2022), no. 5, 2040--2062", "categories": "math.AP math.DG"}
{"title": "Explicit RIP matrices: an update", "year": 2021, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Kevin Ford", "Denka Kutzarova", "George Shakan"], "abstract": "  Leveraging recent advances in additive combinatorics, we exhibit explicit\nmatrices satisfying the Restricted Isometry Property with better parameters.\nNamely, for $\\varepsilon=3.26\\cdot 10^{-7}$, large $k$ and $k^{2-\\varepsilon}\n\\le N\\le k^{2+\\varepsilon}$, we construct $n \\times N$ RIP matrices of order\n$k$ with $k = \\Omega( n^{1/2+\\varepsilon/4} )$.\n", "doi": null, "arxiv_id": "2108.01794", "pdf_urls": ["https://arxiv.org/pdf/2108.01794"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Hungarica 168 (2022), 509-515", "categories": "math.CO cs.IT math.IT"}
{"title": "Non-generators in complete lattices and semilattices", "year": 2021, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Paolo Lipparini"], "abstract": "  As well-known, in a finitary algebraic structure the set $\\Gamma$ of all the\nnon-generators is the intersection of all the maximal proper substructures. In\nparticular, $\\Gamma$ is a substructure.\n  We show that the corresponding statements hold for complete semilattices but\nfail for complete lattices, when as the notion of substructure we take complete\nsubsemilattices and complete sublattices, respectively.\n", "doi": "10.1007/s10474-022-01232-3", "arxiv_id": "2108.03303", "pdf_urls": ["https://arxiv.org/pdf/2108.03303"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Hungarica 166, 423--431 (2022)", "categories": "math.RA"}
{"title": "$n$-exact categories arising from $n$-exangulated categories", "year": 2021, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Jian He and Panyue Zhou"], "abstract": "  Let $\\mathscr{C}$ be a Krull-Schmidt $n$-exangulated category and\n$\\mathscr{A}$ be an $n$-extension closed subcategory of $\\mathscr{C}$. Then\n$\\mathscr{A}$ inherits the $n$-exangulated structure from the given\n$n$-exangulated category in a natural way. This construction gives\n$n$-exangulated categories which are not $n$-exact categories in the sense of\nJasso nor $(n+2)$-angulated categories in the sense of Geiss-Keller-Oppermann\nin general. Furthermore, we also give a sufficient condition on when an\n$n$-exangulated category $\\mathscr{A}$ is an $n$-exact category. These results\ngeneralize work by Klapproth and Zhou.\n", "doi": null, "arxiv_id": "2109.12954", "pdf_urls": ["https://arxiv.org/pdf/2109.12954"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Sinica, English Series volume 39, pages1781-1794\n  (2023)", "categories": "math.RT math.CT"}
{"title": "A generalization of simplest number fields and their integral basis", "year": 2021, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Laszlo Remete"], "abstract": "  An integral basis of the simplest number fields of degree 3,4 and 6 over\n$\\mathbb{Q}$ are well-known, and widely investigated. We generalize the\nsimplest number fields to any degree, and show that an integral basis of these\nfields is repeating periodically.\n", "doi": "10.1007/s10474-020-01093-8", "arxiv_id": "2111.08341", "pdf_urls": ["https://arxiv.org/pdf/2111.08341"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Math. Hungar. 163 (2) (2021), 437-461", "categories": "math.NT"}
{"title": "Hilbert genus fields of some number fields with high degrees", "year": 2021, "venue_abbr": "Acta Math.", "venue_name": "Acta Mathematica", "authors": ["Mohamed Mahmoud Chems-Eddin", "Moulay Ahmed Hajjami and Mohammed Taous"], "abstract": "  The aim of this paper is to give some properties of Hilbert genus fields and\n  construct the Hilbert genus fields of the fields\n$L_{m,d}:=\\mathbb{Q}(\\zeta_{2^m},\\sqrt{d})$, where $m\\geq 3$ is a positive\ninteger and $d$ is a square-free integer whose prime divisors are congruent to\n$\\pm 3\\pmod 8$ or $9\\pmod{16}$.\n", "doi": "10.1007/s40306-022-00489-8", "arxiv_id": "2111.10143", "pdf_urls": ["https://arxiv.org/pdf/2111.10143"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Acta Mathematica Vietnamica (2022)", "categories": "math.NT"}