Research
Research
Research
Research
15,102+ open-access research outputs.
Building on the genus-3 reduction $C_A : w^2 = \lambda^8 + A \lambda^4 + 1$ established in our companion paper (arXiv:2604.09328), we give an unconditional proof of the perfect-cuboid conjecture ("Con…
We address the problem of numerically approximating the velocity and pressure governed by the Stokes system when the boundary conditions are only partially known and thus do not uniquely determine the…
We consider smooth convex minimization over compact convex sets, i.e., $\min_{x \in C} f(x)$ with the (vanilla) Frank-Wolfe algorithm. Well-known lower bounds establish a worst-case $\Omega(1/t)$ prim…
As an alternative to PINNs, a Deep Ritz framework is proposed to solve fully nonlinear PDEs. A least-squares algorithm is advocated to decouple the nonlinearities from the variational features of seve…
Order picking travel dominates much of warehouse effort, and exact routing is especially valuable when storage is scattered so pick locations are not fixed in advance. We address the single picker rou…
We address the question of the large-time behavior of solutions to reaction-diffusion equations in periodic media. We start with the description of the asymptotic shape of the invasion set, which is c…
Body-fitted arbitrary Lagrangian-Eulerian (ALE) methods provide a sharp representation of the fluid-structure interface but rely on mesh-update strategies that incrementally deform a reference configu…
We propose a regularized Hessian-free Newton-type method for minimizing smooth convex functions with Lipschitz continuous Hessians. The algorithm constructs an approximate Hessian by finite difference…
We study stochastic differential equations on the $d$-dimensional flat torus $\mathbb{T}^d$ with drift and perturbation coefficients in $L^{\infty}(\mathbb{T}^d;\mathbb{R}^d)$ and additive non-degener…
Across science and engineering, mean-field methods have been a powerful and versatile approach for the analysis of systems of many interacting elements. However, common arguments used to characterize …
We study the set of image tuples arising from fixed cameras observing varying planar 3-dimensional point configurations. We derive a formula for the number of complex critical points of the triangulat…
Reliability-based topology optimization (RBTO) requires repeated estimation of small failure probabilities and their gradients, making conventional nested Monte Carlo approaches computationally prohib…
This paper presents an optimal network topology control framework using cutting-plane methods for efficient network partitioning with controllable edges. The objective is to enable real-time reconfigu…
A recent construction of linear complementary pairs (LCPs) of algebraic geometry codes is intimately linked to the identification of non-special divisors of small degree within a function field over a…
We develop efficient algorithms for a fundamental network design problem arising in potential-based flow models, which are central to many energy transport networks (e.g., hydrogen and electricity). I…
We study groups endowed with Alexandroff topologies and show that no non-discrete Alexandroff topology can turn a group into a topological group. This settles negatively the basic existence problem fo…
This paper studies the Nash equilibrium seeking problem for stochastic games under heavy-tailed noise. The gradient noise is considered to have a finite $\delta$-th moment ($1<\delta\le 2$), which gen…
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…
In this paper we first study the fixed-time stabilizability of discrete-time switched linear control systems. Using a geometric approach, we derive conditions under which such systems can be stabilize…
In this paper, we investigate non-abelian extensions of Lie algebras with derivations using several different approaches. We show that the theory of non-abelian extensions of a Lie algebra with a deri…
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