Research
Research
Research
Research
30,313+ open-access research outputs.
We derive a sharp upper bound on the residuals produced by the flexible GMRES (FGMRES) method. The bound shows that FGMRES exhibits two phases of convergence depending on the residual tolerance of the…
We investigate the unique stationary measure of a positive recurrent reflecting Brownian motion in the upper half-plane, where the direction of reflection is constant on each half-axis. The Laplace tr…
This paper studies data-driven approaches to the continuous-time linear quadratic regulator (LQR) problem based on two existing parameterizations, namely a closed-loop (CL) parameterization from behav…
We study scale-invariant geometric quantities associated with embedded closed curves in Euclidean three-space, with an emphasis on their behavior under optimization within a fixed knot type. Given a E…
In this paper, we study the three-dimensional inviscid incompressible resistive Hall-MHD system in the axisymmetric setting with nontrivial swirl velocity and purely azimuthal magnetic. Assuming only …
We address the question of the large-time behavior of solutions to reaction-diffusion equations in periodic media. We start with the description of the asymptotic shape of the invasion set, which is c…
We define the topological complexity sequence of a group as the sequence of topological complexities of its Milnor constructions. This sequence may be regarded as an intrinsic refinement of the topolo…
Revealing the interaction topology underlying strategic behavior is fundamental to prediction, intervention, and policy design in networked systems. Yet the interaction matrix is often unobservable, a…
We introduce root-to-leaf path random walks on double covers of graded signed graphs and analyze their behavior in a general setting. Viewing simplicial complexes within this framework, we show that t…
We study the asymptotic behavior of Stiefel--Whitney classes of irreducible orthogonal representations of the finite general linear groups $\mathrm{GL}_n(\mathbb{F}_q)$. Building on recent formulas ex…
We give a damped inexact Newton method for entropy-regularized least-squares on the nonnegative orthant that converges globally at a linear rate with $O(\log\epsilon^{-1})$ iteration complexity, local…
Optimization of quadratic functions and the quotient of those are relevant in subspace and iterative optimization methods. In this paper, the calculation of the generalized operator norm and extremal …
This paper considers the homogeneous Neumann initial-boundary value problem for Alopecia Areata chemotaxis model with weakly singular sensitivity. For any appropriately regular initial conditions,it i…
We study the entropy solution for a class of systems of nonlocal conservation laws in which the convective flux is convoluted with a kernel in both spatial and temporal variables. This formulation mod…
We study the optimization of (strongly) quasar-convex functions, a class that arises naturally in many machine learning and data science applications due to its favorable properties. The fundamental p…
This paper studies the Nash equilibrium seeking problem for stochastic games under heavy-tailed noise. The gradient noise is considered to have a finite $\delta$-th moment ($1<\delta\le 2$), which gen…
We employ a nonlocal method to study the asymptotic behavior at infinity ofsolutions to the two-dimensional supercritical Lagrangian mean curvature equation \[ \arctan \lambda_1(D^2u)+\arctan \lam…
We shall introduce a stability condition for a coherent sheaf associated to an elliptic surface. Then we study the behavior under relative Fourier-Mukai transforms.…
This paper explores the restriction behavior of silting-induced $t$-structures and co-$t$-structures on triangulated categories endowed with metrics. For compactly generated triangulated categories ad…
We propose a new second-order asymptotic-preserving (AP) dual formulation finite-volume (DF-FV) method for the thermal rotating shallow water (TRSW) equations. The TRSW system models geophysical flows…
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