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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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• #### An adaptive multiresolution ultra-weak discontinuous Galerkin method for nonlinear Schrödinger equations ﻿

(Springer, 2021-01-25)
This paper develops a high-order adaptive scheme for solving nonlinear Schrödinger equations. The solutions to such equations often exhibit solitary wave and local structures, which make adaptivity essential in improving ...
• #### Series representations and simulations of isotropic random fields in the Euclidean space ﻿

(American Mathematical Society, 2021-12-07)
This paper introduces the series expansion for homogeneous, isotropic and mean square continuous random fields in the Euclidean space, which involves the Bessel function and the ultraspherical polynomial, but differs from ...
• #### Ages of main-sequence turnoff stars from the GALAH survey ﻿

(American Astronomical Society, 2022-04-01)
Main-sequence turnoff (MSTO) stars are good tracers of Galactic populations since their ages can be reliably estimated from atmospheric parameters. Based on the GALAH survey, we use the Yale rotation evolution code to ...
• #### Scalar and vector tomography for the weighted transport equation with application to helioseismology ﻿

(De Gruyter Open Ltd, 2022-04-08)
Motivated by the application to helioseismology, we demonstrate uniqueness and stability for a class of inverse problems of the weighted transport equation. Using A-analytic functions, this inverse problem is expressed as ...
• #### A Class of Adaptive Multiresolution Ultra-Weak Discontinuous Galerkin Methods for Some Nonlinear Dispersive Wave Equations ﻿

(Society for Industrial and Applied Mathematics Publications, 2022-03-29)
In this paper, we propose a class of adaptive multiresolution (also called the adaptive sparse grid) ultra-weak discontinuous Galerkin (UWDG) methods for solving some nonlinear dispersive wave equations including the ...
• #### Instantaneous frequency-embedded synchrosqueezing transform for signal separation ﻿

(Frontiers Media S.A., 2022-03-17)
The synchrosqueezing transform (SST) and its variants have been developed recently as an alternative to the empirical mode decomposition scheme to model a non-stationary signal as a superposition of amplitude- and ...
• #### Design, construction and operation of the ProtoDUNE-SP liquid argon TPC ﻿

(IOP Publishing, 2022-01-04)
The ProtoDUNE-SP detector is a single-phase liquid argon time projection chamber (LArTPC) that was constructed and operated in the CERN North Area at the end of the H4 beamline. This detector is a prototype for the first ...
• #### Some constructions of formally self-adjoint conformally covariant polydifferential operators ﻿

(Elsevier, 2022-03-10)
We introduce the notion of formally self-adjoint conformally covariant polydifferential operators and give some constructions of families of such operators. In one direction, we show that any homogeneous conformally ...
• #### Deformations of Q-curvature II ﻿

(Springer, 2022-02-11)
This is the second article of a sequence of research on deformations of Q-curvature. In the previous one, we studied local stability and rigidity phenomena of Q-curvature. In this article, we mainly investigate the volume ...
• #### Bayesian variable selection and estimation in quantile regression using a quantile-specific prior ﻿

(Springer Science and Business Media Deutschland GmbH, 2022-01-19)
Asymmetric Laplace (AL) specification has become one of the ideal statistical models for Bayesian quantile regression. In addition to fast convergence of Markov Chain Monte Carlo, AL specification guarantees posterior ...
• #### Torus actions, maximality, and non-negative curvature ﻿

(De Gruyter, 2021-09-03)
Let $ℳ_0^n$ be the class of closed, simply connected, non-negatively curved Riemannian n-manifolds admitting an isometric, effective, isotropy-maximal torus action. We prove that if $M \in ℳ_0^n$ then M is equivariantly ...
• #### Seasonal variation of multiple-muon cosmic ray air showers observed in the NOvA detector on the surface ﻿

(American Physical Society, 2021-07-30)
We report the rate of cosmic ray air showers with multiplicities exceeding 15 muon tracks recorded in the NOvA Far Detector between May 2016 and May 2018. The detector is located on the surface under an overburden of 3.6 ...
• #### Hyperbolic cosine ratio and hyperbolic sine ratio random fields ﻿

(Elsevier, 2021-12)
This paper introduces several vector random fields whose finite-dimensional characteristic functions are of hyperbolic type, including generalized logistic, hyperbolic secant, hyperbolic tangent, hyperbolic cosine ratio, ...
• #### K-combined random fields: Basic properties and stochastic orderings ﻿

(Taylor and Francis, 2021-05-17)
This paper introduces the K-combined vector random field, whose finite-dimensional characteristic functions are made up of certain power functions and whose finite-dimensional density functions are comprised of the modified ...
• #### Multi-scale phase-field modeling of layer-by-layer powder compact densification during solid-state direct metal laser sintering ﻿

(Elsevier, 2021-05-01)
Solid-state direct metal laser sintering (S-DMLS) builds structures by using laser energy to sinter powder particles in a layer-by-layer manner. Powder size distribution (PSD) is an important parameter governing the ...
• #### Potential flow in a multiply connected circle domain using series methods ﻿

(Elsevier, 2021-08)
We study series solutions to potential flow over an assembly of disks in the complex plane. Boundary value problems are solved for both streaming flow uniform at infinity and flow with circulation using Laurent series. If ...
• #### Fairest edge usage and minimum expected overlap for random spanning trees ﻿

(Elsevier, 2021-05)
Random spanning trees of a graph $G$ are governed by a corresponding probability mass distribution (or "law"), $\mu$ defined on the set of all spanning trees of $G$ This paper addresses the problem of choosing $\mu$ in ...
• #### Increasing stability in acoustic and elastic inverse source problems ﻿

(SIAM Publ, 2020-10-22)
We study increasing stability in the inverse scattering source problem for the Helmholtz equation and the classical Lamé system in the three dimensional space from boundary data at multiple wave numbers. As additional data ...
• #### Stability and the inverse gravimetry problem with minimal data ﻿

(e Gruyter Open Ltd, 2020-10-11)
The inverse problem in gravimetry is to find a domain ð • inside the reference domain ω from boundary measurements of gravitational force outside ω. We found that about five parameters of the unknown ð • can be stably ...
• #### Almost non-negatively curved 4-manifolds with torus symmetry ﻿

(American Mathematical Society, 2020-08-14)
We prove that if a closed, smooth, simply-connected 4-manifold with a circle action admits an almost non-negatively curved sequence of invariant Riemannian metrics, then it also admits a non-negatively curved Riemannian ...