Research
Research
Research
Research
2,436+ open-access research outputs.
Let $F$ be a finite field of odd characteristic. We prove that any set $A\subset F$ with $|A|\geq C|F|^{5/6}$ contains a nontrivial quadratic progression $(x, x+y, x+y^2), y\neq 0.$ For prime fields, …
We investigate the relation between neutral atomic hydrogen (HI) and dark matter halo mass (HIHM) using observations from the Deep Investigation of Neutral Gas Origins (DINGO) pilot survey 100h data, …
This paper introduces a rectified and renormalized Fisher-Bingham model for compositional data with zeros, motivated in part by the presence of zeros in microbiota studies. The approach represents com…
We present a framework for non-Abelian p-loop, fracton, and planon condensation in 3+1 dimensions by constructing extended cage-net fracton models using decoupled layers of the Hu-Geer-Wu (HGW) string…
For a graph $G$, let $f_o(G)$ denote the maximum order of an induced subgraph of $G$ all of whose vertices have odd degree, and let $\chi(G)$ denote the chromatic number of $G$. Scott (CPC, 1992) prov…
We study charge transport through a trivial-topological-trivial junction described by the continuous Qi-Wu-Zhang model, which realizes a two-dimensional Chern-insulating phase. The central region is t…
Generative engines (GEs) are reshaping information access by replacing ranked links with citation-grounded answers, yet current Generative Engine Optimization (GEO) methods optimize each instance in i…
We prove a rigidity result for certain critical Z/2 eigensections of the Laplacian on S^2 associated to a flat real line bundle determined by a branch-point configuration. More precisely, we show that…
The Qinghai-Tibetan Plateau (QTP), Earth's "Third Pole", profoundly shapes the Asian monsoon and regional climate and exerts far-reaching influence on the global climate system. Yet its role in organi…
In this paper, we study the Chevalley property of Cayley-Hamilton Hopf algebras in the sense of De Concini-Procesi-Reshetikhin-Rosso using discriminant ideals. For any affine Cayley-Hamilton Hopf alge…
Quantum algorithms on near-term quantum processors are typically executed using shallow quantum circuits composed of one- and two-qubit gates. However, as circuit depth and gate number increase, gate …
We formalize the Wu-Ritt characteristic set method for the triangular decomposition of polynomial systems in the Lean 4 theorem prover. Our development includes the core algebraic notions of the metho…
A proper orientation $D$ of an undirected graph $G$ is an orientation of $G$ such that $d_D^+(u)\not=d_D^+(v)$ for any edge $uv\in E(G)$. Denote the proper orientation number $\vec{\chi}(G)$ of an und…
Let $k \in \mathbb{N}$ and let $G$ be a simple graph with maximum degree $\Delta$. A $k$-colouring $\varphi$ of $G$ is an assignment of colours from $\{1,2,\ldots,k\}$ to the vertices of $G$. We call …
We prove a structural upper bound on the $p$-adic valuation of denominators of rationals belonging to a missing-digit set $K_{m,D}$, generalizing a key step in recent work of Lin, Wu, and Yang [arXiv:…
We study online covariance matrix estimation for Polyak--Ruppert averaged stochastic gradient descent (SGD). The online batch-means estimator of Zhu, Chen and Wu (2023) achieves an operator-norm conve…
Local topological markers are used to characterize Chern insulators in the presence of spatial inhomogeneities, such as boundaries and disorder. In this paper, we study the local Chern marker in syste…
Churn flow-the chaotic, oscillatory regime in vertical two-phase flow-has lacked a quantitative mathematical definition for over $40$ years. We introduce the first topology-based characterization usin…
This study numerically investigates heat transfer enhancement in laminar, incompressible viscoplastic nanofluid flow through the entrance region of a circular cylinder with a uniformly heated wall, in…
Let $E_1,\dots,E_n \subset \mathbb{R}^d$ be compact sets of positive diameter with Feng--Wu thickness at least $c>0$. Feng and Wu proved that $E_1+\cdots+E_n$ has non-empty interior when $n>2^{11}c^{-…
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