Research
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Research
Research
2,201+ open-access research outputs.
We establish the approximate controllability in $L^2$ for the nonlinear Benjamin-Ono equation on torus via two-dimensional control input. Our proof is based on adaptations of geometric control approac…
Let $-\Delta_{\mathbb{H}}+V$ be the Schr\"odinger operator on $\mathbb{H}$ where $V \in L^p(\mathbb{H}) \cap L^\infty(\mathbb{H})$ for some $p > 0$. If $(X_n)$ is a uniformly discrete sequence of comp…
In this paper, we first extend the explicit formula \cite{gerard2023explicit} for the classical Benjamin-Ono equation to each flow of the Benjamin-Ono hierarchy on line. We then use this representatio…
By using parallel corona decomposition, the Kerman-Sawyer trace inequality is extended from Lebesgue spaces to product Morrey spaces.…
By using a Hedberg-type inequality, the Adams trace inequality is extended from Lebesgue spaces to product Morrey spaces.…
We investigate the Benjamin-Feir instability of small-amplitude gravity-capillary Stokes waves in deep water for the full water wave equations. While modulational instability has been classically pred…
We study dimensions of sets projected to an $(n-2)$-dimensional family of hyperplanes in $\mathbb{R}^n$ under curvature conditions. Let $n\ge 3$ and $\Sigma \subset S^{n-1}$ be an $(n-2)$-dimensional …
Let $A$ be a commutative ring with unity, and $M$ a finitely generated $A$-module. In 1971, Morris Orzech showed that any surjective $A$-module homomorphism from a submodule of $M$ to $M$ must be an i…
We develop a framework for the fifth-order Kadomtsev--Petviashvili equation on $\mathbb{T}_x \times \mathbb{R}_y$ within a mean-zero KP-adapted Sobolev scale. A localized high-order feedback acting on…
Let $H$ be a graph and let $\delta_{\chi}(H,r)$ denote the infimum of $c$ such that every $H$-free graph with minimum degree at least $cn$ is $r$-colorable. The \textit{chromatic profile} of $H$ is de…
In this paper, we study the weighted boundedness of the Dunkl fractional integral operator (i.e., Dunkl Stein-Weiss inequality) associated with the Dunkl operator on $\mathbb{R}$. Indeed, we obtain th…
Given two hypergraphs $G$ and $H$, the weak saturation number $\operatorname{\mathrm{wsat}}(G,H)$ is the minimum number of edges in a spanning subhypergraph $F$ of $G$ such that the missing edges of $…
In this paper, we focus on the study of immanantal polynomials for linear combination matrices composed of the degree matrix and adjacency matrix of a graph. First, applying the concept of vertex orie…
We consider a class of large-scale interacting systems with one conservation law satisfying the ``degree-preserving property'', and study the classification of their invariant measures and their hydro…
We show that the geometric classification of smooth projective curves admitting infinitely many points of degree $d\leq 5$ extends from number fields to function fields of characteristic 0. Over numbe…
This article is concerned with Kronecker flows on the infinite torus. The work is partly motivated by the fact that many Hamiltonian PDEs and systems on infinite lattices admit invariant tori, of poss…
For first passage percolation (FPP) on Euclidean lattices $\mathbb{Z}^d$ with $d\ge 2$, it is expected that the variance of the first passage time between two points grows sublinearly in the distance …
We prove that for almost all symmetric spaces $X$ and for any sequence of compact locally symmetric spaces $Y_n$ which is uniformly discrete, has a uniform spectral gap, and converges in the sense of …
We develop a continuous-time model for the long-term dynamics of adaptive stochastic optimization, focusing on bias-corrected Adam-type methods. Starting from a finite-sum setting, we identify a canon…
We prove that activation saturation imposes a structural dynamical limitation on autonomous Neural ODEs $\dot{h}=f_\theta(h)$ with saturating activations ($\tanh$, sigmoid, etc.): if $q$ hidden layers…
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