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arXiv:2602.15308v2 Announce Type: replace Abstract: The coefficients $A_n(\alpha,\beta,\omega)$ in the Maclaurin expansion $(1+\omega z)^{\alpha}(1-z)^{-\beta}= \sum_{n=0}^{\infty} A_n(\alpha,\beta,\omega)z^n$ are studied, where $\omega,z \in \mathbb{C}$ with $|z| <...
arXiv:2602.15905v2 Announce Type: replace Abstract: We study the Lagarias inequality, an elementary criterion equivalent to the Riemann Hypothesis. Using a continuous extension of the harmonic...
arXiv:2602.16027v2 Announce Type: replace Abstract: The primary objective of this paper is to employ methods from analytic number theory to investigate the mean value properties...
arXiv:2602.16048v2 Announce Type: replace Abstract: In this paper, we study the Calabi-Yau conjectures for complete minimal hypersurfaces $\Sigma^{n}\subset \mathbb{R}^{n+1}$ in dimensions $n\ge 3$. These conjectures...
arXiv:2602.16126v2 Announce Type: replace Abstract: We study the nonlinear multiplicative stochastic heat equation on Dirichlet spaces with white in time noise under weak disorder. We...
arXiv:2602.16566v2 Announce Type: replace Abstract: We study interacting bosons on a three-dimensional Bravais lattice with positive hopping amplitudes and on-site repulsive interactions. We prove that,...
arXiv:2602.16635v2 Announce Type: replace Abstract: We establish the existence of a non-trivial, branched immersion of a closed Riemann surface $\Sigma$ with constant mean curvature (CMC)...
arXiv:2405.11454v2 Announce Type: replace-cross Abstract: We study gradient testing and gradient estimation of smooth functions using only a comparison oracle that, given two points, indicates...
arXiv:2409.17971v3 Announce Type: replace-cross Abstract: In this work we investigate how quantum expanders (i.e. quantum channels with few Kraus operators but a large spectral gap)...
arXiv:2410.12306v2 Announce Type: replace-cross Abstract: Auction is applied for trade with various mechanisms. A simple but practical question is which mechanism, typically first-price or second-price...
arXiv:2501.09313v2 Announce Type: replace-cross Abstract: For a system of partial differential equations (PDEs) $F = 0$ admitting a local (point, contact, or higher) symmetry $X$...
arXiv:2504.20167v3 Announce Type: replace-cross Abstract: The non-Hermiticity of the system gives rise to a distinct knot topology in the complex eigenvalue spectrum, which has no...
arXiv:2506.12819v2 Announce Type: replace-cross Abstract: Computationally cheap yet accurate dynamical models are a key requirement for real-time capable nonlinear optimization and model-based control. When given...
arXiv:2506.16480v5 Announce Type: replace-cross Abstract: For the simple system of a point-like particle confined to a straight line, I compile, initially in a concise table,...
arXiv:2509.04583v2 Announce Type: replace-cross Abstract: We propose an instance-wise adaptive sampling framework for constructing compact and informative training datasets for supervised learning of inverse problem...
arXiv:2509.16333v2 Announce Type: replace-cross Abstract: Communication over a quantum multiple access channel (MAC) is considered with classical feedback. Since the no-cloning prohibits universal copying of...
arXiv:2509.22138v2 Announce Type: replace-cross Abstract: Wasserstein distances define a metric between probability measures on arbitrary metric spaces, including meta-measures (measures over measures). The resulting Wasserstein...
arXiv:2510.20220v2 Announce Type: replace-cross Abstract: Recent research has focused on mitigating algorithmic bias in clustering by incorporating fairness constraints into algorithmic design. Notions such as...
arXiv:2511.10601v2 Announce Type: replace-cross Abstract: We carry out a complete analysis of the toric elliptic and genus-one fibrations of all 474 million reflexive polytopes in...
arXiv:2512.05637v2 Announce Type: replace-cross Abstract: Boundary-catalytic branching processes describe a broad class of natural phenomena where the population of diffusing particles grows due to their...
arXiv:2512.08225v2 Announce Type: replace-cross Abstract: We suggest that the chiral $(\mathfrak{e}_8)_1$ theory -- in many senses the simplest VOA -- may have Haagerup symmetry $\mathcal{H}_i$...
arXiv:2601.14517v2 Announce Type: replace-cross Abstract: Partial differential equations (PDEs) are central to scientific modeling. Modern workflows increasingly rely on learning-based components to support model reuse,...
arXiv:2602.04550v2 Announce Type: replace-cross Abstract: Standard approaches to quantum statistical inference rely on measurements that induce a collapse of the wave function, effectively consuming the...
arXiv:2602.10798v2 Announce Type: replace-cross Abstract: We develop a mixed control framework that combines absolutely continuous controls with impulse interventions subject to stochastic execution delays. The...