Research
Research
Research
Research
180+ open-access research outputs.
Christoph, Dragani\'{c}, Gir\~{a}o, Hurley, Michel, and M\"{u}yesser conjectured that, when $d\mid n$, the expected number of cycles in a uniformly random cycle-factor of a directed $d$-regular graph …
In this survey, we review recent developments in extending Hodge theory to differential forms with values in bundles equipped with singular metrics, based on joint work with Ya Deng, Christopher D. Ha…
Motivated by the classical Hilbert's Sixteenth Problem, we extend some main developments obtained for Hilbert's number in the polynomial setting to the piecewise polynomial context. Specifically, we s…
We use contemporary mathematical notation to describe the method for determining the age of the ecclesiastical moon as mandated by pope Gregory XIII and elaborated in the book of Christopher Clavius \…
Recently, Maggiorano et al. (2025) claimed that they have developed a strongly polynomial-time combinatorial algorithm for the nucleolus in convex games that is based on the reduced game approach and …
In this work, we prove the existence of a 2-cycle in an integrodifference equation with a Laplace kernel and logistic growth function, connecting two non-trivial fixed points of the second iterate of …
The Effros-Shen algebra corresponding to an irrational number $\theta$ can be described by an inductive sequence of direct sums of matrix algebras, where the continued fraction expansion of $\theta$ e…
The existence theory for solutions to the Boltzmann equation in bounded domains has primarily been developed within uniformly bounded function classes, such as $L^{\infty}_{x,v}$, as in [Duan-Huang-Wa…
We investigate the maximal number $N_h(m)$ of normally hyperbolic limit tori in three-dimensional polynomial vector fields of degree $m$, which extends the classical notion of Hilbert numbers to highe…
The cycle space of a graph $G$, denoted $C(G)$, is a vector space over ${\mathbb F}_2$, spanned by all incidence vectors of edge-sets of cycles of $G$. If $G$ has $n$ vertices, then $C_n(G)$ denotes t…
We study a weakly non-linear Fokker-Planck equation with BGK heat thermostats in a spatially bounded domain with conservative Maxwell boundary conditions, presenting a space-dependent accommodation co…
The cycle space $\mathcal{C}(G)$ of a graph $G$ is defined as the linear space spanned by all cycles in $G$. For an integer $k\ge 3$, let $\mathcal{C}_k (G)$ denote the subspace of $\mathcal{C}(G)$ ge…
In their famous 1974 paper introducing the local lemma, Erd\H{o}s and Lov\'asz posed a question-later referred by Erd\H{o}s as one of his three favorite open problems: What is the minimum number of ed…
This paper is devoted to the hydrodynamic limit for the linear Boltzmann equation, in the case of a heavy tail equilibrium and a cross section which depends on the space variable and which degenerates…
Star formation feedback can drive large-scale, multi-phase galactic outflows. The dynamical and thermodynamical interaction between the hot and cooler phases is a prime focus of both observational and…
Christoph Scheiner was one of the most outstanding astronomers in the history of the sunspot observations. His book, Rosa Ursina, is the reference work regarding the study of the earliest sunspot reco…
We consider an interacting system of particles with value in $\mathbb{R}^d \times \mathbb{R}^d$, governed by transport and diffusion on the first component, on that may serve as a representative model…
Motivated by the recent results of Andreis-Iyer-Magnanini (2023), we provide a short proof, revisiting the one of Escobedo-Mischler-Perthame (2002), that for a large class of coagulation kernels, any …
We consider complex rational vector fields that admit a first integral whose logarithmic derivative lies in a finite extension of the rational function field $K$. In view of the Prelle-Singer theorem,…
Beautimeter is a new tool powered by generative pre-trained transformer (GPT) technology, designed to evaluate architectural and urban beauty. Rooted in Christopher Alexander's theory of centers, this…
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