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arXiv:2509.15877v2 Announce Type: replace Abstract: The star discrepancy is a quantitative measure of the uniformity of a point set in the unit cube. A central...
arXiv:2509.26298v2 Announce Type: replace Abstract: We present a novel multi-fluid model for compressible two-phase flows. The model is derived through a newly developed Stationary Action...
arXiv:2510.00470v4 Announce Type: replace Abstract: We introduce the notion of a Calabi--Yau quadruple as a generalization of Iyama--Yang's Calabi--Yau triple. For each $(d+1)$-Calabi--Yau quadruple, we...
arXiv:2510.03828v3 Announce Type: replace Abstract: We study additive patterns among the $x$-coordinates of rational points on elliptic curves. More generally, we investigate how rational points...
arXiv:2510.05765v2 Announce Type: replace Abstract: We construct relatively bounded toroidal and toric models of relatively bounded fibrations over curves.
arXiv:2510.11318v4 Announce Type: replace Abstract: In 2017, Clark Kimberling defined an interesting sequence ${\bf B} = 0100101100 \cdots$ of $0$'s and $1$'s by certain inflation...
arXiv:2510.12404v3 Announce Type: replace Abstract: In the context of metric measure spaces, we introduce an axiomatic formulation of mixed local and nonlocal $p$-energy forms. Within...
arXiv:2510.23999v4 Announce Type: replace Abstract: We propose an adaptive sampling method for the training of Physics Informed Neural Networks (PINNs) which allows for sampling based...
arXiv:2510.27098v2 Announce Type: replace Abstract: We establish nonuniqueness of solutions for Cauchy problems of semilinear heat equations with a wide class of nonlinearities. Specifically, we...
arXiv:2511.00292v2 Announce Type: replace Abstract: Trigonometric formulas for eigenvalues of $3 \times 3$ matrices that build on Cardano's and Vi\`ete's work on algebraic solutions of...
arXiv:2511.04482v2 Announce Type: replace Abstract: We develop pivotal and spherical versions of graded extension theory. We define the corresponding analogues of Brauer-Picard $2$-categorical groups and...
arXiv:2511.05283v2 Announce Type: replace Abstract: This paper focuses on decentralized composite optimization over networks without a central coordinator. We propose a novel decentralized symmetric ADMM...
arXiv:2511.21153v2 Announce Type: replace Abstract: In this short article, we prove that the Halton sequence, one of the most well-known low-discrepancy sequences, is not quasi-uniform...
arXiv:2511.21616v3 Announce Type: replace Abstract: The purpose of this work is twofold. First, we construct probabilistically strong solutions to the three-dimensional Euler equations perturbed by...
arXiv:2511.22605v2 Announce Type: replace Abstract: Littlewood--Paley theory began with the classic paper of Littlewood and Paley (J.\ E.\ Littlewood, R.\ E.\ A.\ C.\ Paley, {\em...
arXiv:2512.01565v2 Announce Type: replace Abstract: We propose FlexQP, an always-feasible convex quadratic programming (QP) solver based on an $\ell_1$ elastic relaxation of the QP constraints....
arXiv:2512.07085v2 Announce Type: replace Abstract: We propose a distributed accelerated primal-dual method with backtracking (D-APDB) for cooperative multi-agent constrained consensus optimization problems over an undirected...
arXiv:2512.12556v2 Announce Type: replace Abstract: We study simple extensions of pointed finite tensor categories, that is, tensor categories $\mathcal{C}$ admitting an abelian decomposition $\mathcal{C} \cong...
arXiv:2512.13469v2 Announce Type: replace Abstract: We establish homological stability for automorphisms of symmetric bilinear forms over a class of principal ideal domains that includes all...
arXiv:2512.16299v2 Announce Type: replace Abstract: This paper investigates Nekhoroshev-type stability for solutions of ultra-differentiable regularity in Schr\"odinger equations with non-local nonlinear terms, employing the method...
arXiv:2512.17805v2 Announce Type: replace Abstract: We develop a minimax theory for operator learning, where the goal is to estimate an unknown operator between separable Hilbert...
arXiv:2512.22025v2 Announce Type: replace Abstract: We give an elementary proof of some identities that express the squares of Riemann zeta function at integer points in...
arXiv:2512.24045v2 Announce Type: replace Abstract: In this short review paper the detailed analysis of six two-dimensional quantum {\it superintegrable} systems in flat space is presented....
arXiv:2512.24541v2 Announce Type: replace Abstract: We construct a diagrammatic categorification of the spherical module over the Hecke algebra. We establish a basis for the morphism...