Research
Research
Research
Research
12,714+ open-access research outputs.
Abstract models of computation often treat the successor function $S$ on $\mathbb{N}$ as a primitive operation, even though its low-level implementations correspond to non-trivial programs operating o…
A fundamental open problem in the theory of the multidimensional compressible Navier-Stokes equations is whether smooth solutions can develop singularities in finite time. For constant viscosity coeff…
We propose the Adaptive Levenberg-Marquardt Third-Order Newton Method (ALMTON) for unconstrained nonconvex optimization, providing the first globally convergent realization of the unregularized third-…
Stochastic gradient methods are among the most widely used algorithms for large-scale optimization and machine learning. A key technique for improving the statistical efficiency and stability of these…
The NIST Handbook of Mathematical Functions (2010) and the NIST Digital Library of Mathematical Functions (2025) classify classical orthogonal polynomials through Bochner's 1929 algebraic-differential…
The triplication method for constructing strong starters in $Z_{3m}$ from starters in $Z_{m}$ (say, a starter of order 21 from a starter of order 7) was proposed by the authors in 2025. The method red…
Classical stability theory for stochastic programming relies on the Wasserstein-Fortet-Mourier duality, which requires the ground cost to be a distance. When using problem-dependent costs instead of m…
Along with the rapid development of new urban mobility options like ride-sharing over the past decade, on-demand micro-transit services stand out as a middle ground, bridging the gap between fixed-lin…
Weil-Petersson and Masur-Veech volumes measure the sizes of moduli spaces of Riemann surfaces equipped with hyperbolic and flat metrics, respectively. Over the past several decades, the computation of…
In this note, we introduce shifted quantum affine symmetric pairs of split simply-laced type, and construct their GKLO representations, following similar recent developments in the case of shifted twi…
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)…
We expand the basic geometric elements of the simplex method to linear programs in locally convex topological vector spaces and provide conditions under which the method converges in value to optimali…
We present a unified theoretical and computational framework for constructing reproducing kernels tailored to transport equations and adapted to Koopman eigenfunctions of nonlinear dynamical systems. …
The Casten-Holland and Matano theorem for interior reactions states that no nonconstant stable solutions exist in convex domains $\Omega$ of $\mathbb{R}^n$ under zero Neumann boundary conditions. In t…
A key challenge in 3D finite element models of coupled railway vehicle-bridge dynamics is the rigorous definition of kinematic constraints and the development of an efficient, robust solution. This pa…
Serrin's symmetry theorem shows that the classical overdetermined torsion problem forces the domain to be a ball. Extending this rigidity statement to merely Lipschitz (and more generally rough) domai…
Stochastic rounding (SR) is a probabilistic method used to round numbers to floating-point and fixed-point representations. In length $n$ summation, the worst-case error of SR grows as $\sqrt{n}$ with…
This paper focuses on optimization problems constrained by Parametric Variational Inequalities (PVI) defined on a moving set. Unlike most existing works on mathematical programs with equilibrium const…
Chemotaxis systems of Keller--Segel type constitute one of the central mathematical frameworks for understanding aggregation phenomena in biological and ecological systems. Over the past decades, the …
Rosenbloom and Tsfasman, in their foundational work on the $m$-metric, introduced algebraic-geometric codes defined by multiple points on a smooth projective curve $X$. This construction involves a di…
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