Research
Research
Research
Research
1,071+ open-access research outputs.
The bull is a graph consisting of a triangle and two pendant edges. The P_5 is the chordless path on five vertices. The house is the complement of a P_5. A graph is k-critical if it is k-chromatic but…
We give a unified proof of property $R_\infty$ for the Higman groups $H_n$ ($n\ge 4$) and for their generalizations studied by Martin and Horbez--Huang. As a key step, we prove that the automorphism g…
This paper investigates the distribution of integral points on projective varieties via two distinct methods: the Ru-Vojta theorem and our higher-dimensional generalization of the Huang-Levin-Xiao ine…
We deduce from a theorem of Dvorak--Norin that the separation and treewidth profiles of graphs are asymptotically equivalent, resolving a question of Huang--Hume--Kelly--Lam. As an application, we cal…
Since the pioneering work of Korteweg (1901) and the subsequent refinement of capillary fluid models by Dunn and Serrin (1985), the global existence of strong solutions to the multi-dimensional compre…
Higham's conjecture on the growth factor of complex symmetric positive definite matrices is a longstanding problem in the stability theory of Gaussian elimination without pivoting. It asserts that eve…
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…
Let $V$ be a grading-restricted vertex algebra and let $A^\infty(V)=U^\infty(V)/Q^\infty(V)$ be the associative algebra constructed by Huang, where $U^\infty(V)$ is the space of column-finite infinite…
The study of partial-twuality polynomials originates from the classical operations of geometric duality and Petrie duality on cellularly embedded graphs. These involutions generate the symmetric group…
By a 2-ring we mean a groupoid with a structure analogous to that of a ring, up to coherent isomorphisms. Two different notions of 2-ring appear in the literature: the notion of {\em Ann-category}, du…
We study the long-time asymptotic behavior of small-data solutions to the three-dimensional Vlasov--Riesz system with the inverse power-law potential $\lambda |x|^{-\alpha}$ in the strictly long-range…
We prove that for any smooth polarized complex $n$-dimensional manifold $(X, L_X)$ which admits an extremal K\"ahler metric in $c_1(L_X)$, and for any integer $k$ large enough (in terms of a bound dep…
This paper studies the number of limit cycles, known as the Smale-Pugh problem, for the generalized Abel equation \begin{align*} \frac{dx}{d\theta}=A(\theta)x^p+B(\theta)x^q, \end{align*} where $A$ …
In this paper, a three-dimensional competitive Lotka-Volterra system with four limit cycles is constructed for class 28 in Zeeman's classification. Combined with existing results -- from Gyllenberg an…
We present a novel classification of unitarizable supermodules over special linear Lie superalgebras using an algebraic quadratic Dirac operator introduced by Huang and Pand\v{z}i\'c and a correspondi…
The present note is to make minor correction on the assumption of Theorem 1.2 and its proof in our paper [arXiv:2111.02059, Jinrui Huang, Yinghui Wang, Huanyao Wen and Rizhao Zi, {\it J. Differential …
In this paper we introduce the following Yamabe problem for the quotient between the $Q$ curvature and the scalar curvature $R$: Find a conformal metric $g$ in a given conformal class $[g_0]$ with \…
We consider the global optimization of a non-convex potential $U : \mathbb{R}^d \to \mathbb{R}$ and extend the controlled simulated annealing framework introduced by Molin et al. (2026) to the class o…
We show that the full-flag Johnson graph has spectral gap equal to that of its Schreier quotient arising from the point-stabiliser equitable partition. Our results confirm two conjectures posed by Hua…
We expand the basic geometric elements of the simplex method to linear programs in locally convex topological vector spaces and provide conditions under which the method converges in value to optimali…
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