Research
Research
Research
Research
498+ open-access research outputs.
This thesis develops numerical and theoretical approaches for understanding and analyzing singularity formation in Partial Differential Equations (PDEs). The singularity formation in the Navier-Stokes…
Electroencephalography (EEG) source imaging aims to reconstruct the spatial distribution of neural activity within the brain from non-invasive scalp measurements. This inverse problem is severely ill-…
Inspired by the adaptive Golden Ratio Algorithm (aGRAAL), we propose two new methods for solving monotone variational inequalities. We show that by selecting the momentum parameter beyond the golden r…
Inspired by the Taubes-Wu construction of $\mathcal{C}^{1,\alpha}$ two-valued harmonic functions by the use of symmetry, we construct minimal surfaces with stratified branching sets as graphs of $\mat…
In this work, we propose new variants of Anderson acceleration and nonlinear GMRES for general fixed-point iterations, based on modified least-squares problems associated with the methods. To solve th…
In this paper, we concentrate on investigating the self-similar singular solutions of Keller-Segel model with signal consumption ($-uv^{\alpha}$) and singular sensitivity. We perform a detailed explor…
Since the pioneering work of James E. Broadwell, discrete velocity models (DVMs) have played a fundamental role in approximating the Boltzmann equation and in the analysis of non-equilibrium gas dynam…
We determine the phase diagram of the Anderson tight-binding model on random regular graphs with Gaussian disorder and sufficiently large degree. In particular, we prove that if the degree is fixed an…
For a generic discrete-time algorithm (DTA): $z^+=g(z,s)$, where $s$ is the step size, Lu (Math. Program., 194(1):1061--1112, 2022) proposed an $O(s^r)$-resolution ordinary differential equation (ODE)…
Model predictive control offers a powerful framework for managing constrained systems, but its repeated online optimization can become computationally prohibitive. Multiparametric programming addresse…
Dantzig-Wolfe reformulation is a widely used technique for obtaining stronger relaxations in the context of branch-and-bound methods for solving integer optimization problems. Arc-Flow reformulations …
Global self-similar solutions to the parabolic Hardy-H\'enon equation $$ u_t=\Delta u^m+|x|^{\sigma}u^p, \quad (x,t)\in\mathbb{R}^N\times(0,\infty), $$ are classified in the range of exponents $m\geq1…
We establish new integral inequalities for the numerical radius and the operator norm of bounded linear operators on Hilbert spaces. Our results refine classical triangle-type and operator matrix ineq…
Linear viscoelastic materials are commonly described by continuous relaxation spectra, yet practical measurements and simulations employ discrete Prony series. In the Laplace frequency domain, the dis…
Contraction algebras are noncommutative algebras introduced by Donovan and Wemyss to classify of 3-dimensional flops. Wemyss conjectures that contraction algebras can be deformed to a single semisimpl…
Colored interlacing triangles, introduced by Aggarwal-Borodin-Wheeler (2024), provide the combinatorial framework for the Central Limit Theorem for probability measures arising from the Lascoux-Lecler…
The teaching of matrix multiplication in secondary education is often limited to the mechanical application of the row-by-column algorithm, leaving aside its interpretation as a geometric transformati…
We develop a systematic analysis of the metaplectic semigroup $\mathrm{Mp}_+(d,\mathbb{C})$ associated with positive complex symplectic matrices, a notion introduced almost simultaneously and independ…
The Muon optimizer has recently attracted attention due to its orthogonalized first-order updates, and a deeper theoretical understanding of its convergence behavior is essential for guiding practical…
Tail Value-at-Risk (TVaR) is a widely adopted risk measure playing a critically important role in both academic research and industry practice in insurance. In data applications, TVaR is often estimat…
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