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23,663+ open-access research outputs.
This paper investigates the existence and uniqueness of solutions for a nonlinear evolution equation governed by an m-accretive operator A in a Banach space, presenting a perturbation term that does n…
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…
This paper studies data-driven approaches to the continuous-time linear quadratic regulator (LQR) problem based on two existing parameterizations, namely a closed-loop (CL) parameterization from behav…
This paper investigates the heat equation on a bounded domain with a Robin boundary condition, where the reactivity parameter (or killing rate) is modeled as a continuous-time Markov chain. We analyze…
In modern parametric model training, full-batch gradient descent (and its variants) suffers due to progressively stronger biasing towards the exact realization of training data; this drives the system…
This work studies numerical integration by the M\"obius-transformed trapezoidal rule, which combines the classical trapezoidal rule with a change of variables induced by a M\"obius transformation that…
Let $\mathcal A$ be an $\mathbb F$-algebra and $\omega \in \mathcal A\langle x_1, \ldots, x_m \rangle$ which defines a map $\mathcal A^m \rightarrow \mathcal A$ by evaluation, called a polynomial map …
The accurate simulation of interface-dominated solid mechanics problems on complex microstructures remains challenging, particularly when interface-fitted quadrilateral or hexahedral meshes are diffic…
This paper is a continuation work of Ren et al. (2026) aiming to further devise q-learning algorithms for mean-field control (MFC) with controlled common noise. Based on the relaxed control formulatio…
We study the set of solutions to a parameterized, strongly convex optimization problem whose cost depends on uncertain, bounded parameters. We compute a certified outer approximation of the correspond…
In this paper, we prove that smooth Calabi--Yau hypersurfaces of degree $d$ over complete unramified discrete valuation rings with residue characteristic $p$ are perfectoid split if $p$ is larger than…
The Immersed Boundary Method has long served as a robust computational framework for fluid-structure interactions, yet the rigorous analysis of 1D Peskin filaments anchored to rigid boundaries remains…
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…
We prove that the directed five-dimensional torus $D_5(m) = \operatorname{Cay}((\mathbb{Z}_m)^5, \{e_0, e_1, e_2, e_3, e_4\})$ has a Hamilton decomposition for every odd integer $m \geq 3$. This is th…
Let $K$ be a finite $p$-adic field with uniformiser $\pi$. In this paper we study the image of the logarithm attached to a Lubin-Tate series $[\pi](X)$ on the maximal ideal of so-called $\pi$-regular …
The Alternating Direction Method of Multipliers (ADMM) is a widely used method for structured convex optimization, and its practical performance depends strongly on the choice of penalty and relaxatio…
We prove pathwise convergence of the layerwise evolution of tokens in a finite-depth, finite-width transformer model with MultiLayer Perceptron (MLP) blocks to a continuous-time stochastic interacting…
Lutwak's affine quermassintegral theory is a foundational component of modern affine Brunn--Minkowski theory. Developed in the 1980s, it provides affine analogues of the classical quermassintegrals an…
This paper develops a deep policy iteration method for high-dimensional finite-horizon mean-field games. We reformulate the game as a regenerative problem with deterministic cycles, which allows polic…
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