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arXiv:2310.08283v2 Announce Type: replace Abstract: We establish an analog of a theorem of Stallings which asserts the homomorphisms between the universal nilpotent quotients induced by...
arXiv:2311.00158v2 Announce Type: replace Abstract: We provide a complete classification of groups that can be realized as isometry groups of a translation surface $M$ with...
arXiv:2311.15289v2 Announce Type: replace Abstract: The \textit{generalized Tur\'an number} $\mathrm{ex}(n, T, F)$ is the maximum possible number of copies of $T$ in an $F$-free graph...
arXiv:2311.16389v2 Announce Type: replace Abstract: We study PL bordism theories from a quantitative perspective. Such theories include those of PL manifolds, ordinary homology theory, as...
arXiv:2311.16597v3 Announce Type: replace Abstract: We give a treatment of relative Calabi--Yau structures on functors between $R$-linear stable $\infty$-categories, with $R$ any $\mathbb{E}_\infty$-ring spectrum, generalizing...
arXiv:2312.15333v3 Announce Type: replace Abstract: We prove the Erd\H{o}s-Hajnal conjecture for the five-vertex path $P_5$; that is, there exists $c>0$ such that every $n$-vertex graph...
arXiv:2401.07806v3 Announce Type: replace Abstract: Optimal experimental design (OED) aims to choose the observations in an experiment to be as informative as possible, according to...
arXiv:2401.11930v3 Announce Type: replace Abstract: We discuss the common existential theory of all or almost all completions of a global function field.
arXiv:2401.14863v3 Announce Type: replace Abstract: F. Paulin proved that if the Gromov boundaries of two hyperbolic groups are quasi-Mobius equivalent, then the groups themselves are...
arXiv:2401.17912v2 Announce Type: replace Abstract: We study positive solutions of semilinear elliptic equations in a planar triangular domain under mixed boundary conditions, consisting of homogeneous...
arXiv:2402.02667v2 Announce Type: replace Abstract: Physics-Informed Neural Networks (PINNs) encounter accuracy limitations when solving the Allen--Cahn (AC) and Cahn--Hilliard (CH) partial differential equations (PDEs). To...
arXiv:2402.06899v4 Announce Type: replace Abstract: The X-ray transform on the plane or on the three-dimensional Euclidean space can be considered as the measurements of CT...
arXiv:2403.11302v3 Announce Type: replace Abstract: \emph{Koopman Regularization} is a constrained optimization-based method to learn the governing equations from sparse and corrupted samples of the vector...
arXiv:2404.09040v2 Announce Type: replace Abstract: This doctoral thesis covers several topics related to the construction and study of maximal determinant matrices with complex entries. The...
arXiv:2405.20406v2 Announce Type: replace Abstract: A complete classification of all finite bijective set-theoretic solutions $(S,s)$ to the Pentagon Equation is obtained. First, it is shown...
arXiv:2406.06513v3 Announce Type: replace Abstract: The critical exponent of an infinite word $\bf x$ is the supremum, over all finite nonempty factors $f$, of the...
arXiv:2407.00154v2 Announce Type: replace Abstract: We introduce a class of dg-algebras which generalize the classical Brauer graph algebras. They are constructed from mixed-angulations of surfaces...
arXiv:2407.14484v4 Announce Type: replace Abstract: A bottleneck in the theory of large-amplitude and multi-d viscous and relaxation shock stability is the development of nonlinear damping...
arXiv:2407.15262v2 Announce Type: replace Abstract: In this note we prove that the discrete Riesz potential $I_{\alpha}$ defined on $\mathbb{Z}^n$ is a bounded operator $H^p (\mathbb{Z}^n)...
arXiv:2408.05323v2 Announce Type: replace Abstract: We study groups whose co-word problems are ET0L languages, which we call coET0L groups, using an automaton based model due...
arXiv:2408.10118v4 Announce Type: replace Abstract: Fr\'echet regression extends the principles of linear regression to accommodate responses valued in generic metric spaces. While this approach has...
arXiv:2409.08029v2 Announce Type: replace Abstract: In this paper, we establish three Landau-type theorems for certain bounded poly-analytic functions, which generalize the corresponding result for bi-analytic...
arXiv:2409.11633v2 Announce Type: replace Abstract: This paper investigates the asymptotic behavior of the solution to a linear-quadratic stochastic optimal control problems. The so-called probability cell...
arXiv:2410.02882v2 Announce Type: replace Abstract: This paper presents an online learning-based adaptive control framework for density-matrix tracking in a two-level Lindblad-Gorini-Kossakowski-Sudarshan (LGKS) quantum system, in...