Research
Research
Research
Research
2,602+ open-access research outputs.
The Nash-Williams conjecture establishes degree sequence conditions ensuring Hamilton cycles in digraphs. An asymptotic version of this conjecture for large digraphs was independently derived by sever…
The medial axis $M_X$ of a closed set $X\subset \mathbb{R}^n$ is the set of points from the ambient space that admit more than one closest point in $X$. We study the problem of reaching the singularit…
We address Calder\'on's problem of stably determining the anisotropic complex admittivity $\sigma$ in a domain $\Omega\subset\mathbb{R}^n$, with $n\geq3$, representing a conducting medium, in terms of…
Let $K$ be an algebraically closed and complete non-archimedean and non-trivially valued field, and let $G$ be a reductive group scheme acting on a flat projective scheme $X$ defined over the base rin…
The longstanding Nash-Williams conjecture asserts that every $K_3$-divisible graph $G$ with $\delta(G)\ge 3n/4$ admits a triangle decomposition. In the random setting, Frankl and R\"odl showed that, w…
In the early 1990s, J.Bourgain proved a general result $K$-closedness result in the context of classical harmonic analysis. In this paper, we extend Bourgain's method to the semicommutative setting, m…
We establish local Calder\'on-Zygmund type estimates for weak solutions to nonlinear parabolic systems with $p$-growth and VMO coefficients. In particular, we prove that if the right-hand side belongs…
We show that two non-isometric, smooth, globally hyperbolic Lorentzian metrics can have the same hyperbolic Dirichlet-to-Neumann map on an infinite cylinder with timelike boundary.…
In this article, we study certain transcendental function spaces arising in potential theory within the framework of Orlicz spaces. Specifically, we generalize Bessel and Lizorkin-Triebel spaces to th…
We prove existence of weak solutions and weak-strong uniqueness for a mathematical model which couples the evolution of a phase-parameter $\varphi$ satisfying a Cahn-Hilliard type relation with the on…
We study the quantitative transfer of uniqueness from the classical to the fractional Calder\'on problem with exterior data. This allows us to deduce the first stability estimates for the principal pa…
We construct here global mild solutions in a critical setting for a class of transport-diffusion equations with a drift term that involves rough Calder{\'o}n-Zygmund operators.…
The Dynamic Mode Decomposition (DMD) and the more general Extended DMD (EDMD) are powerful tools for computational analysis of dynamical systems in data-driven scenarios. They are built on the theoret…
This paper presents a compilation of various formulas for calculating the Dunkl-Williams constant $DW(X)$ of a real normed linear space. The constant $DW_B(X)$ related to Birkhoff orthogonality is als…
Let $(X,\mathbf{q},\mu)$ be an ultra-RD-space with upper dimension $n\in(0,\infty)$; i.e., it is a quasi-ultrametric space of homogeneous type whose measure $\mu$ satisfies an additional reverse doubl…
We give a linear algebraic classification of Auslander regular acyclic monomial algebras via the Bruhat factorisation of the Coxeter matrix. Namely, we show under mild assumptions that a monomial acyc…
We demonstrate that the failure of $L^1$ regularity in Calder\'on-Zygmund theory is a universal phenomenon: every non-constant holomorphic function in $\C^n$ generates a counterexample to the Poisson …
The $n$-dimensional affine Weyl-Heisenberg group is a Lie group typically parameterized as $G_{aWH} = \mathbb{T} \times \mathbb{R}^n \times \widehat{\mathbb{R}^n} \times \mathrm{GL}(n, \mathbb{R})$, g…
We consider a Kobayashi-Warren-Carter (KWC) type total variation energy with a fidelity term. Since the energy is non-convex, the profiles of minimizers are quite different from those of the original …
We study a numerical reconstruction strategy for the potential in the fractional Calder\'on problem from a single partial exterior measurement. The forward model is the fractional Schr\"odinger equati…
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