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The collection of peer-reviewed research articles (co)authored by faculty of the Department of Mathematics and Statistics.
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Item On a class of quasilinear operators on smooth metric measure spaces(International Press, Inc., 2024-12-30) Li, Xiaolong; Tu, Yucheng; Wang, KuiWe derive sharp estimates on the modulus of continuity for solutions of a large class of quasilinear isotropic parabolic equations on smooth metric measure spaces, with Dirichlet or Neumann boundary conditions if the boundary is non-empty. We also derive optimal lower bounds for the first Dirichlet eigenvalue of a class of homogeneous quasilinear operators, which include non-variational operators. The main feature is that this class of quasilinear operators has corresponding one-dimensional operators, which allow sharp comparisons with solutions of one-dimensional equations. © 2024 International Press, Inc.. All rights reserved.Item An upper bound for the first nonzero Steklov eigenvalue(EDP Sciences, 2025-01-06) Li, Xiaolong; Wang, Kui; Wu, HaotianLet (Mn, g) be a complete simply connected n-dimensional Riemannian manifold with curvature bounds Sectg g < κ for κ < 0 and Ricg g (n - 1)Kg for K < 0. We prove that for any bounded domain Ω ⊂ Mn with diameter d and Lipschitz boundary, if Ω∗ is a geodesic ball in the simply connected space form with constant sectional curvature κ enclosing the same volume as Ω, then σ1(Ω) < Cσ1(Ωz.ast;), where σ1(Ω) and σ1(Ω∗) denote the first nonzero Steklov eigenvalues of Ω and Ω∗ respectively, and C = C(n, κ,K, d) is an explicit constant. When κ = K, we have C = 1 and recover the Brock-Weinstock inequality, asserting that geodesic balls uniquely maximize the first nonzero Steklov eigenvalue among domains of the same volume, in Euclidean space and the hyperbolic space. © The authors. Published by EDP Sciences, SMAI 2025.Item Product manifolds and the curvature operator of the second kind(Mathematical Sciences Publishers, 2024-11-20) Li, XiaolongWe investigate the curvature operator of the second kind on product Riemannian manifolds and obtain some optimal rigidity results. For instance, we prove that the universal cover of an n-dimensional nonflat complete locally reducible Riemannian manifold with (Formula presented)-nonnegative (respectively, (Formula presented)-nonpositive) curvature operator of the second kind must be isometric to (Formula presented) (respectively, (Formula presented)) up to scaling. We also prove analogous optimal rigidity results for (Formula presented) and (Formula presented), n1, n2 ≥ 2, among product Riemannian manifolds, as well as for (Formula presented) and (Formula presented), m1, m2 ≥ 1, among product Kähler manifolds. The approach is pointwise and algebraic. © 2024 The Author, under license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). Open Access made possible by subscribing institutions via Subscribe to Open.Item First measurement of the total inelastic cross section of positively charged kaons on argon at energies between 5.0 and 7.5 GeV(American Physical Society, 2024-11-14) Burgardt, D.; Meyer, Holger; Muether, Mathew; Roy, P.; Shivakoti, Sushil; Solomey, NickolasProtoDUNE Single-Phase (ProtoDUNE-SP) is a 770-ton liquid argon time projection chamber that operated in a hadron test beam at the CERN Neutrino Platform in 2018. We present a measurement of the total inelastic cross section of charged kaons on argon as a function of kaon energy using 6 and 7 GeV/c beam momentum settings. The flux-weighted average of the extracted inelastic cross section at each beam momentum setting was measured to be 380±26 mbarns for the 6 GeV/c setting and 379±35 mbarns for the 7 GeV/c setting. © 2024 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP3.Item Method to reduce noise for measurement of 7Be and 8B solar neutrinos on gallium-71(Elsevier B.V., 2025-03) Folkerts, Jonathan; Solomey, Nickolas; Hartsock, Brooks; Nolan, Tyler; Pacheco, Octavio; Pawloski, GregoryGallium solar neutrino experiments have historically used radiochemical counting to determine the event rate. A detector which directly measures the ejected electron and a nuclear de-excitation gamma could reduce background counting rates by way of a double-pulse technique. We find this reduction could be as large as 6 orders of magnitude in a 1.5 ton detector when compared with experiments that allow ground-state transitions. In our process, the detector measures the excited nuclear final state of the germanium after an electron neutrino interacts with gallium nucleus through the charged-current interaction. This results in a loss of approximately 90% of the total neutrino signal, but higher energy processes are less suppressed. The neutrinos resulting from this higher energy selection are predominantly from the 8B and 7Be solar neutrino fluxes. © 2024