Research
Research
Research
Research
23,682+ open-access research outputs.
We study policy iteration (PI) for deterministic infinite-horizon discounted optimal control problems, whose value function is characterized by a stationary Hamilton--Jacobi--Bellman (HJB) equation. A…
We present a 5D-lifted analytic-profile program for finite-time singularity formation in the 3D incompressible Navier--Stokes equations on the periodic torus $\T^3$. The core of the construction is a …
We study the direct and inverse spectral theory for a class of finite Hermitian banded matrices. Using the theory of matrix orthogonal polynomials, we provide an explicit procedure for reconstructing …
In this paper, we study two local--nonlocal settings for parabolic--elliptic evolution systems. In our problems we have a disjoint partition of the spacial domain $\Omega$ as $\Omega=A\cup B$ and we f…
The Optimal Polynomial Intersection (OPI) problem is the following: Given sets $S_1, \ldots, S_m \subseteq \mathbb{F}$ and evaluation points $a_1, \ldots, a_m \in \mathbb{F}$, find a polynomial $Q \in…
We consider a nonlocal curve evolution belonging to a hierarchy of models for the dynamics of an inextensible elastic filament in a 3D Stokes fluid. This model captures the principal part of a full fr…
We develop novel asymptotic-preserving (AP) deterministic particle methods for collisional plasma models, including both Landau--Fokker--Planck and Dougherty collision operators, under hydrodynamic sc…
We present an integrated version of the global program proving that every prescribed prime \(q_0\ge 5\) occurs in some \(3\times 3\) magic square whose nine entries are distinct positive primes. The m…
In this work, we aim at efficiently solving a parametrized family of optimal transport problems by using model order reduction methods. We propose a reduced-order model by adding to the primal (respec…
Explicit Runge-Kutta (RK) integration of hyperbolic initial-boundary value problems with time-dependent Dirichlet data often displays order reduction: the observed convergence order falls below the no…
Benchmark problems play a central role in assessing the performance of numerical optimization algorithms. However, many existing constrained multiobjective optimization benchmark problems rely on over…
The data-driven linear quadratic regulator (ddLQR) is a widely studied control method for unknown dynamical systems with disturbance. Existing approaches, both indirect, i.e., those that identify a mo…
We survey recent progress on the birational geometry of foliations on complex varieties. We focus on the MMP viewpoint: singularities, adjunction and applications to the MMP for foliations on surfaces…
In this paper, we propose an unfitted finite element method to solve PDE-constrained shape optimization problems via shape gradient flow. The shape gradient flow system consists of the state equation,…
We study the Wasserstein projection of a compactly supported probability measure onto the class of measures whose density ratio is bounded, and we place this projection in a broader program connecting…
The concept of input-independent computational time for chemistry-based analog computers was introduced in Anderson-Joshi (2025), where it was shown that arithmetic operations can be computed in a fix…
A $\left(\gamma_{1}, \gamma_{2}\right)$ space of order $n$ is a space of univariate functions spanned by $\left\{\gamma_{1}^{n-k}(x), \gamma_{2}^{k}(x)\right\}_{k=0}^{n}$. A $\left(\gamma_{1}, \gamma_…
We firstly show that due to their resplendency ordered henselian valued fields admit relative field quantifier elimination in the Denef--Pas language expanded by linear orders in the field and residue…
The Koopman-von Neumann equation describes the evolution of wavefunctions associated with autonomous ordinary differential equations and can be regarded as a quantum physics-inspired formulation of cl…
We consider two-dimensional periodic gravity water waves with constant nonzero vorticity $\gamma$, in infinite depth and with periodic boundary conditions. We prove that, if the characteristic wave nu…
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