Research
Research
Research
Research
23,682+ open-access research outputs.
This work is concerned with the probabilistic representation of solutions to the $p$-Laplace evolution equation $\frac{\partial u}{\partial t}={\rm div}(|\nabla u|^{p-2}\nabla u)$ in $(0,\infty)\times…
We study a thermodynamically consistent diffuse-interface model that describes the motion of two macroscopically immiscible, incompressible, and viscous Newtonian fluids with unmatched densities. This…
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 study sequential interventions under prerequisite constraints. In this setting, admissible intervention sequences are paths in the ideal lattice of a finite prerequisite poset rather than unconstra…
In this paper, we propose a quadratic reformulation theory for rational-like functions. Based on this theory, we develop the Quadratic Conservation Elevation (QCE) method, which combines the Scalar Au…
Conservation laws are conventionally discretized through floating-point flux evaluation, with invariants obtained by cancellation of approximate interface contributions and admissible weak solutions s…
We define the notion of couple density $(D, \mathbf b)$ where $D$ is a non-empty subset of $\mathbb Z^{m}$ and $ \mathbf b$ a fixed element in $\{0, \cdots, q-2\}^{m};$ We determine a minimum in terms…
Building on work of Kuhlmann and Lisinski, we study the theory of the Hahn series field $\mathbb{F}_{q}(\!(\mathbb{Q})\!)$, over a finite field $\mathbb{F}_{q}$, equipped with the $t$-adic valuation, …
We explore the nonlinear dynamics of classical field theories containing ghost degrees of freedom, focusing on two coupled scalar fields with opposite kinetic terms in (1+1) and (2+1) dimensional Mink…
We propose a sharp-interface model for solid-state dewetting of thin films with wetting potential, where the wetting effect is incorporated through a thickness-dependent surface energy. The model is g…
We study a discrete-time random feature method for nonlinear, time-dependent partial differential equations. In contrast to continuous-time formulations that treat time as an additional input variable…
The evaluation homomorphisms from the super Yangian $\Ymn$ to the universal enveloping algebra $\U(\gl_{m|n})$ allows one to regard the covariant tensor module of $\gl_{m|n}$ as $\Ymn$ modules. We stu…
The continuous linear $P(k; N, w)$ and circular scan statistics $P_c(k; N, w)$ are fundamental tools in probability and spatial statistics, frequently used to detect clustering in uniform data. Let $X…
In renewable power-to-ammonia (ReP2A) systems, the intermittency of wind and solar generation propagates through electrolytic hydrogen production and induces thermal instability in the ammonia synthes…
This article presents a partial differential equation (PDE) of Keller-Segel (KS) type that reproduces patterns commonly observed during the growth of brain microvasculature. We provide mathematical in…
This paper provides second-order optimality conditions for optimization problems with generalized equation constraints (GEPs), a framework that encompasses several important and challenging models in …
In this paper, for the first time, we extend the Over/Under/Off Set/Logic/Probability used in uncertain theories (such as: fuzzy, neutrosophic and extensions) to the Over/Under/Off Mass that could be …
The combination of data and models, enhanced by AI methodologies, leads to the paradigm called Digital Twins. This concept is expected to bring unprecedented support to personalized medicine. The comb…
We prove that the (suitably rescaled) moments of certain discrete measures on the unit interval, which are related to the numerical evaluation of zeta series with missing digits in radix $b$, are asym…
We study finite-horizon quadratic control of linear systems with bilinear observations, in which the control input affects not only the state dynamics but also the partial observations of the state. I…
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