Research
Research
Research
Research
16,198+ open-access research outputs.
We construct bounded, commuting projections for the three-dimensional de Rham complex with the additional property that the projections preserve the trace of functions/fields if the latter is a piecew…
Partially ordered patterns (POPs) generalize classical permutation patterns and have been extensively studied in the contexts of permutations, words, compositions, and partitions. Burstein, Han, Kitae…
The Nash-Williams conjecture establishes degree sequence conditions ensuring Hamilton cycles in digraphs. An asymptotic version of this conjecture for large digraphs was independently derived by sever…
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 properties of the following four classes of operators on the Fock space in $\mathbb C^n:$ 1) weakly localized operators; 2) sufficiently localized operators in the sense of Xia and Zheng; 3) …
In the context of studying $C^*$-algebras generated by Toeplitz operators acting on the poly-Bergman space $\mathcal{A}^2_{n}(\Pi)$ of the upper half-plane $\Pi$, we introduce a system of all-but-one …
We conjecture that any scalar-flat K\"ahler surface in which the Weyl tensor acting on 2-forms annihilates the Ricci form must be either Ricci-flat or locally isometric to a Riemannian product of two …
We show that the $\ell^p$-pseudofunctions, which were recently shown to lead to exotic completions of group $C^*$-algebras by Wiersma and the second named author, can be used to construct well-behaved…
It is known that the small eigenvalues of the Laplacian of a Riemann surface close to the boundary of the modular space can be well approximated by the eigenvalues of the discrete Laplacian on a certa…
Let $K$ be a field with $2 \in K^\times$, and let $H_W$ denote the standard hyperbolic form on $W \oplus W^*$. We study the exterior spinor model $S = \bigwedge V(W)$ together with the spin-to-orthogo…
Many large-scale optimization problems decompose into a master problem and scenario subproblems, a structure that can be exploited by Benders decomposition. In Benders decomposition, each iteration ma…
Let $K$ be an algebraically closed and complete non-archimedean and non-trivially valued field, and let $G$ be a reductive group scheme acting on a flat projective scheme $X$ defined over the base rin…
A fundamental conjecture formulated by Thakur in 2009, which has guided significant developments in function field arithmetic, asserts that multiple zeta values (MZV's) in positive characteristic of f…
Genome-Scale Metabolic Models (GEMs) describe the interactions between genes, proteins, and the biochemical reactions that underpin an organism's metabolism aiming to computationally simulate function…
Tilings of a surface of negative Euler characteristic by n-gons with n\ge 7 is a finite problem. We develop the algorithm for finding all the tilings for fixed number of tiles and present the calculat…
We analyze a nonlocal coupled system arising as the Euler--Lagrange equations of an energy functional involving regional fractional Laplacians of orders $s_1$ and $s_2$ ($ 0 < s_1,s_2 < 1$), each acti…
We analyze the inverse problem of recovering geometric information from the return map induced by a round-trip between a convex core C and an admissible domain. This process defines a discrete dynamic…
We derive an identity for the determinant of the sum of two $n\times n$ matrices, $A$ and $B$, whose entries are defined via contour integrals. Specifically, we consider $A(i,j)=\frac{1}{2\pi\mathrm{i…
We propose, analyze, and numerically validate a correction adaptive two-grid finite element method (CAT-GFEM) for nonselfadjoint or indefinite elliptic problems. In contrast to the adaptive two-grid f…
A longest path in a graph is called a detour. Denote by $a(k,n)$ the minimum number of detours in a connected graph with minimum degree $k$ and order $n,$ and denote by $b(k,n)$ the minimum odd number…
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