Research
Research
Research
Research
24,560+ open-access research outputs.
In this paper, we study the $L^p$-boundedness of Stein's square function $\mathfrak{S}^{\alpha}(\mathcal{L})$ associated with the sub-Laplacian $\mathcal{L}$ on M\'etivier group $G$. A key aspect of o…
We consider the problem of finding the (unique) minimal Walrasian equilibrium price in multi-item, multi-unit auction models: there are multiple indivisible items for sale, with several units of each …
We introduce G\r{a}rding polynomials, a class of real multivariate polynomials defined via positivity regions invariant under translation by positive directions and closed under strictly positive affi…
Convex maximization encompasses a broad class of optimization problems and is generally NP-hard, even for low-rank objectives. This paper investigates structural conditions under which convex maximiza…
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…
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 initiate the study of Reidemeister hardness of Legendrian unknot front projections. Using normal rulings, we obstruct several infinite families of hard unknot diagrams from being drawn with max-tb …
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 a calculus for counting pseudoholomorphic disks with boundary in tropical Lagrangians contained in almost toric manifolds, using our previous work with Venugopalan. The results are mostly 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…
Using the characterizations in terms of various differential operators including partial, normal, and tangential derivatives, we extend the family of Bergman spaces of $\mathcal H$-harmonic functions …
We prove that if a small Hankel operator on the product Hardy space belongs to some Schatten class $S^p$, $p < \infty$, then it has a symbol in product BMO. In other words, the conclusion of Nehari's …
We study the central limit theorem (CLT) for linear eigenvalue statistics of several types of matrix models, whose entries are having exploding moments, i.e., moments of the entries are increasing wit…
Modeling time-harmonic Maxwell problems in heterogeneous media presents significant mathematical and computational challenges. Due to the inherent non-elliptic structure and non-coercive nature of Max…
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…
Behling, Bello-Cruz, Lara-Urdaneta, Oviedo, and Santos showed that the circumcentric direction $d$ of a finitely generated polyhedral cone $\KK\subset\RR^n$ admits an inscribed Euclidean ball of radiu…
Using model theory and differential algebra, we give necessary conditions for algebraic ordinary differential equations to have a complex Pfaffian solution on some complex domain. These tools also all…
Power grid infrastructure is an increasingly significant source of wildfire ignitions and poses severe risks to communities in fire-prone regions. Public Safety Power Shutoffs (PSPS) have emerged as a…
The paper focuses on the development of numerical methods for the compressible Euler equations. It is well-known that if the Mach number is small, the system becomes stiff and hence explicit schemes s…
We study stochastic ordering of system lifetimes with dependent and heterogeneous components whose marginal distributions are obtained through transformations of a common baseline. The dependence stru…
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