Research
Research
Research
Research
2,063+ open-access research outputs.
A convex polyhedron is Rupert if a hole can be cut into it (making its genus $1$) such that an identical copy of the polyhedron can pass through the hole. Resolving a conjecture of Jerrard-Wetzel-Yuan…
We give a general description of the spectral space of conjugacy classes of subgroups of Sp(2): it is a disjoint union of finitely many blocks, each dominated by a subgroup: of these blocks, 26 are of…
In this paper, we present an explicit and purely combinatorial characterization of the $m$-coloured quivers that appear within the $m$-coloured mutation class of a quiver of type $\mathbb{D}_n$. The $…
We generalize complex manifolds to manifolds with corners $X$, and to manifolds with generalized corners (g-corners) in the sense of the second author arXiv:1501.00401, using complex structures on the…
This is a sequel to the previous work of the author Yanagihara (2025). Let $\ell$ be an odd prime, let $N \geq 1$ be an integer, and let $\delta \geq 1$ be an $\ell^N$-th-power-free integer. Let $r,s,…
We introduce an extended exterior $(K,K^{\prime},\alpha_0)$--quasiconformal mapping method to study the asymptotic behavior at infinity of solutions to the supercritical phase Lagrangian mean curvatur…
Let $K$ be a complete discrete valuation field of characteristic $0$ with perfect residue field of characteristic $p>0$. Let $\mathbb{A}_K$ denote the imperfect coefficient ring of $(\varphi,\Gamma)$-…
This paper is about hypersurfaces with boundary lying in the Euclidean unit ball, which meet the unit sphere at a fixed angle $\theta\in(0,\frac{\pi}{2}]$. Such hypersurfaces are called $\theta$-capil…
In this paper, inspired by the work of Guan and Li (2015), we introduce a fourth-order centro-equiaffine invariant curve flow via the affine Minkowski formula. Without any smallness assumptions on the…
This paper presents a framework for local solutions to time-varying linear differential-algebraic equations (DAEs) with real meromorphic coefficients. The local solutions on compact intervals form a s…
I prove that the Borel directed graphs whose vertex set admits a partition into two Borel acyclic sets form a $\mathbf\Sigma^1_2$-complete set; equivalently, that deciding whether a Borel directed gra…
Alladi's duality identities (1977) provide a fundamental relation between the smallest and the $k$-th largest prime factors of integers. In this paper, we establish these dualities in the setting of g…
The chromatic redshift philosophy, introduced by Ausoni and Rognes, suggests that algebraic $K$-theory raises chromatic height by $1$. We show that the analogue of this philosophy fails in the case of…
This article provides a naturel sequel of previous works [6, 4] regarding the stability of travelling waves for a general one-dimensional Schr\"odinger equation (N LS) with non-zero condition at infin…
Discrete quantum groups were introduced as duals of compact quantum groups by Podle\'s and Woronowicz in 1990. They have been studied intrinsically by Effros and Ruan (1994) and by the author (1996). …
In \cite{[NE]} we introduce $\alpha$-expansions a real numbers in $(0,1]$, given by \[ \sum_{i=1}^{\infty}(\alpha-1)^{i-1}\alpha^{-(d_{1}+\dots+d_{i})}\] with $\alpha>1$ and $d_{i}\in\mathbb{N}$ and d…
We develop a geometric framework for the numerical integration of mechanical systems evolving on manifolds. After briefly reviewing classical numerical methods and highlighting their limitations and s…
Reconstruction in limited-angle digital breast tomosynthesis (DBT) suffers from slow convergence of low spatial-frequency components when using weighted data-fidelity terms within primal-dual optimiza…
Quantum graphs have been introduced by Duan, Severini, and Winter to describe the zero-error behaviour of quantum channels. Since then, quantum graph theory has become a field of study in its own righ…
For a function $F$ represented as $F(x)=\sum_{n=0}^\infty{f_n (x) e^{2 \pi i \lambda_n x}},$ where each $f_n$ satisfies $\operatorname{spec}(f_n) \subset [0, 1]$ and $(\lambda_n)_{n\geq 0}\subset \mat…
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