Research
Research
Research
Research
1,632+ open-access research outputs.
High-order partial differential equations (PDEs) require derivative regularity that standard $C^0$ finite element infrastructures do not directly provide on unstructured meshes. We propose a mesh-intr…
In this paper, we study Hardy-type uncertainty principles and unique continuation properties for linear covariant Schrodinger equations with variable coefficients in the presence of bounded electric a…
I was interested in the work of Solomon Marcus in Mathematical Linguistics as a high-school student. Later, I had the opportunity to discuss with him about many topics. He was a polymath. We wrote a p…
We present a mathematical model of a market with $m$ shares traded across $n$ investor groups, each one with similar motivations and trading strategies. The market of each asset consists of a fixed am…
The moduli space of cubic surfaces and its compactifications are classical and date back to the mid-nineteenth century. Recently, Schock described compactifications of moduli spaces of fully marked cu…
We show that the wheel classes in the Kontsevich graph complex $GC_d$ admit representatives supported on graphs with only $3$- and $4$-valent vertices. This verifies that Merkulov's low-valence conjec…
Given a pair of finite posets $A \subseteq P$, the function counting integer-valued order preserving extensions of an order preserving map $\lambda : A\rightarrow \mathbb{Z}$ from $A$ to $P$ is given …
An exact magnetic system over a closed manifold $M$ consists of a pair $(g,\alpha)$, where $g$ is a Riemannian metric and $\alpha$ is a 1-form encoding a magnetic field. In this context, we consider a…
Many classical identities arise from nothing more mysterious than looking at the same object in two different ways. A number, a function, or a combinatorial object may admit several natural decomposit…
Integrating renewable generation, hydrogen production, and renewable ammonia (RA) synthesis into power-to-ammonia (P2A) systems creates interactions across electricity and hydrogen markets. Limited op…
In this paper, we study the closed timelike geodesics of de-Sitter tori with one singularity and prove their uniqueness in their free homotopy class. We introduce the notion of timelike marked length …
We study a family of periodically weighted Aztec diamond dimer models near their turning points. We establish that, asymptotically, as $N\rightarrow\infty$, their fluctuations there, scaled by $\sqrt{…
Despite hydrogen being central to Europe's decarbonisation strategy, only a small share of renewable hydrogen projects reached final investment decision. A key barrier is uncertainty about how future …
We verify Tutte's $3$-flow conjecture in the class of Cayley graphs on solvable groups of order $2n$, where $n$ is square-free. The proof relies on a new necessary and sufficient condition for a simpl…
Let $p$ be a prime number, and let $\mathbb{G}$ be a compact $p$-adic Lie group. This work provides multiplier theorems for invariant operators on $\mathbb{G}$ acting on $L^r_\alpha(\mathbb{G})$, $1<r…
The theory of sharp geometric inequality in $\mathbb{R}^n$ and inside convex cone has been well-developed, much less known for sharp capillary geometric inequality outside convex domain. Recently, Fus…
The theory of polyptych lattices is a framework to obtain a family of toric degenerations whose polytopes are related by piecewise-linear transformations. It can be regarded as a generalization of tor…
We present a priori error analysis for a fully discrete, parallelizable, explicit loosely coupled scheme for the time-dependent Stokes-Biot problem. The method decouples the fluid and poroelastic subp…
We study the fully mixed formulation of the Biot equations, which is characterized by a symmetric coupling between flow and deformation. This structure enables the use of stable mixed finite elements …
Topological simplification is the process of reducing complexity of a function while maintaining its essential features. Its goal is to find a new filter function, which reorders cells of the input co…
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