Research
Research
Research
Research
6,999+ 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…
Let $ n \in \mathbb{N} $ with $ n \geq 3 $, and let $\mathcal{G} = \{G_i:i\in [n]\} $ be a family of $ n $-vertex graphs on a common vertex set $V$, where the graphs in the family do not need to be di…
Hill functions, dominant in gene regulatory network modeling, carry fundamental limitations: at non-integer cooperativity exponents, routine when fitting dose-response data, derivatives diverge at the…
In this paper, we prove several rigidity results for complete noncompact manifolds with nonnegative intermediate curvatures. We show that when either $3\leq n\leq 5$, $1\leq m\leq n-1$, or $6\leq n\le…
For the boundary value problem $$\left\{ \begin{array}{rcll} -\Delta_p u+u^{p-1}&=&|x|^{\alpha}u^{q-1}&\mbox{in }\Omega,\\ \frac{\displaystyle\partial u}{\displaystyle\partial{\bf n}}&=&0&\mbox{on }\p…
We consider the two families of even polynomials $\Xi_n$ and $\Lambda_n$ studied in~\cite{TallaWaffo2026arxiv2602.16761}, together with the rescaled polynomials $\widetilde{\Xi}_n(x):=\Xi_n(\sqrt{x})$…
We develop a terminal-defect method for the double Dixie cup problem and use it to prove the finite-variance extremality conjecture of Doumas and Papanicolaou. For every \(m\ge1\) and \(N\ge2\), among…
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…
Proving representability of derived moduli stacks of solutions to non-linear elliptic partial differential equations generally requires significant analytic machinery. In this paper, we instead show t…
We prove explicit finite-$N$ lower bounds for $\mathbb P(\bigcup_{k=1}^N A_k)$ when the $\sigma$-algebras generated by an event sequence satisfy quantitative $\varphi$- or $\alpha$-mixing bounds. The …
We find out that the main result of the article The asymptotic uniform distribution of subset sums can be proven much more easily, using an explicit formula proposed by Li and Wan.…
For every nonzero integer $m$ and every integer $n \ge 1$, the $n$\textsuperscript{th} harmonic number $H_n = 1 + \tfrac12 + \dots + \tfrac1n$ satisfies the identity \[ H_n \;=\; \frac{1}{m}\,\sum_{…
We study the expected number of rolls required for the cumulative sum of a fair six-sided die to first enter a prescribed target set $H\subset\mathbb{Z}_{\ge0}$. A one-variable dynamic-programming for…
Schatten class properties of commutators $[b,T]$ of pointwise multipliers $b$ and singular integral operators $T$ have been characterised in a variety of settings. An abstract framework, covering many…
This paper is devoted to investigating the interior $C^{1, \alpha}$ regularity of viscosity solutions to the nonlocal double phase equations $$ \int_{\mathbb{R}^d} \left(\frac{|u(x)-u(y)|^{p-2}(u(x)-u…
We study edge-colorings of the complete $p$-graph on $n$ vertices that contain no three edges $A,B,C$ of distinct colors such that the symmetric difference of $A$ and $B$ is contained in $C$. For $p…
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 define real link Floer homology for strongly invertible and doubly periodic links in closed real $3$-manifolds with connected fixed sets, which generalizes real Heegaard Floer homolo…
In this paper, we study the stochastic homogenization for a class of symmetric random walks in random conductance model, whose one-step transition probability from $x$ to $y$ is proportional to $|x-y|…
We connect generalizations of the classical Hurwitz class numbers coming from two different frameworks: one introduced by Pei and Wang, arising from the generalized Cohen--Eisenstein series, and anoth…
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