Research
Research
Research
Research
4,098+ open-access research outputs.
In modern parametric model training, full-batch gradient descent (and its variants) suffers due to progressively stronger biasing towards the exact realization of training data; this drives the system…
Partially ordered patterns (POPs) generalize classical permutation patterns and have been extensively studied in the contexts of permutations, words, compositions, and partitions. Burstein, Han, Kitae…
This paper is a continuation work of Ren et al. (2026) aiming to further devise q-learning algorithms for mean-field control (MFC) with controlled common noise. Based on the relaxed control formulatio…
The Immersed Boundary Method has long served as a robust computational framework for fluid-structure interactions, yet the rigorous analysis of 1D Peskin filaments anchored to rigid boundaries remains…
We study properties of the following four classes of operators on the Fock space in $\mathbb C^n:$ 1) weakly localized operators; 2) sufficiently localized operators in the sense of Xia and Zheng; 3) …
Genome-Scale Metabolic Models (GEMs) describe the interactions between genes, proteins, and the biochemical reactions that underpin an organism's metabolism aiming to computationally simulate function…
We propose, analyze, and numerically validate a correction adaptive two-grid finite element method (CAT-GFEM) for nonselfadjoint or indefinite elliptic problems. In contrast to the adaptive two-grid f…
A longest path in a graph is called a detour. Denote by $a(k,n)$ the minimum number of detours in a connected graph with minimum degree $k$ and order $n,$ and denote by $b(k,n)$ the minimum odd number…
Let $A:=\mathbb{C}[z_+,z_-]\otimes \Lambda(\theta_1,\theta_2,\theta_3)$, with $z_\pm$ even and $\theta_1,\theta_2,\theta_3$ odd. For a reductive Lie algebra $\mathfrak g$, let $\mathfrak g[A]:=\mathfr…
We establish regularity results for viscosity solutions to a class of quasilinear parabolic equations exhibiting nonhomogeneous degeneracy or singularity (a double phase regime) of the form \[ u_t - \…
The main aim of this paper is to study chains of model structures arising from cotorsion pairs in extriangulated categories. Starting with a hereditary Hovey triple, we construct further hereditary Ho…
We extend the entropy-stable oscillation-eliminating discontinuous Galerkin spectral element method (ES-OEDG) on curvilinear meshes to adaptive mesh refinement (AMR) grids with nonconforming interface…
Let $\kappa'(G)$ and $\tau(G)$ denote the edge connectivity and the spanning tree packing number of a graph $G$, respectively. Recently, Zhang and Fan [J. Graph Theory 112 (2) (2026) 128--144] posed t…
Let $X$ be a normal projective variety of dimension $d\ge 4$ and let $f$ be a zero-entropy automorphism of $X$. Denote by $k$ the degree growth rate of $f$, so that $\mathrm{deg}_1(f^n) \asymp n^{k}$.…
In this paper, we consider the global spherically symmetric strong solution to the compressible Navier-Stokes equations with far-field vacuum and density-denpendent degenerate viscosity which is refer…
Let $S$ be an $\mathbb N$-graded Koszul Artin-Schelter regular algebra and let $\sigma$ be a graded algebra automorphism of $S$. We study the stable category of graded maximal Cohen-Macaulay modules o…
We study the surjectivity of certain maps involving local cohomology modules, which we can realize as a dual version of part of the investigation developed by Bhatt, Blickle, Lyubeznik, Singh and Zhan…
Let $k$ be a field of characteristic $p,$ and $f : X \to S$ a smooth proper morphism of smooth $k$-schemes. Katz's formula gives a relationship between the Kodaira--Spencer map of $f,$ and an invarian…
For the fixed-size Brualdi--Hoffman--Turan problem forbidding the fish graph $H(4,3)$, Zheng and Zhang proved that every $H(4,3)$-free graph of even size $m \ge 38$ without isolated vertices satisfies…
We prove a relative volume comparison theorem of Petersen-Wei for both $L^P$-bound of Bakry-\'{E}mery Ricci curvature and gradient of potential function. As an application, we give a modified proof fo…
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