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arXiv:2510.12244v5 Announce Type: replace Abstract: Qualification conditions (also termed constraint qualifications) help avoid pathological behavior at domain boundaries in convex analysis. By generalizing facial reduction...
arXiv:2510.18755v2 Announce Type: replace Abstract: We prove that the jump quasi-seminorm of order $\varrho= 2$ for a general Ornstein--Uhlenbeck semigroup $\left(\mathcal H_t\right)_{t>0}$ in $\mathbb R^n$...
arXiv:2510.22402v5 Announce Type: replace Abstract: In this paper, we introduce a model-free, real-time, dynamic optimization and control method for a class of rigid body dynamics....
arXiv:2511.03818v2 Announce Type: replace Abstract: If a rational homology 3-sphere $M$ bounds a rational homology 4-ball $W$, then the kernel of the inclusion-induced homomorphism $H_1(M;\mathbb{Z})\to...
arXiv:2511.13304v2 Announce Type: replace Abstract: Automated proof assistants are a technology pre-empting mistakes in mathematics. In our practice we have seen that reasoning about planar...
arXiv:2511.18426v2 Announce Type: replace Abstract: In this paper, we develop a unified approach to study the intersection Betti numbers of moduli spaces of one-dimensional semistable...
arXiv:2511.22000v2 Announce Type: replace Abstract: We consider the Landau-Lifshitz-Gilbert equation (LLG) that models time-dependent micromagnetic phenomena. We propose a full discretization that employs first-order finite...
arXiv:2512.03452v3 Announce Type: replace Abstract: In this paper, we develop a novel numerical framework, namely the stochastic interacting particle-field method with particle-in-cell acceleration (SIPF-PIC), for...
arXiv:2512.08196v2 Announce Type: replace Abstract: In this paper, we investigate dead-core problems for fully nonlinear degenerate parabolic equations with strong absorption, \begin{equation*} |Du|^{p} F(D^{2}u) -...
arXiv:2512.08850v2 Announce Type: replace Abstract: In classical factorization theory, an integral domain is called \emph{atomic} if every nonzero nonunit element can be written as a...
arXiv:2512.13123v4 Announce Type: replace Abstract: Deciding when to stop stochastic gradient descent (SGD) has long remained unresolved in a statistically rigorous sense. While SGD is...
arXiv:2512.15391v2 Announce Type: replace Abstract: Uniform interpolation is a strengthening of interpolation that holds for certain propositional logics. The starting point of this chapter is...
arXiv:2512.17533v2 Announce Type: replace Abstract: We introduce a new, relatively simple, line-breaking construction of the $\alpha$-stable tree which realises its random finite-dimensional distributions. This is...
arXiv:2512.18463v2 Announce Type: replace Abstract: We introduce a quantitative version of polynomial cohomology for discrete groups and show that it coincides with usual group cohomology...
arXiv:2512.19282v5 Announce Type: replace Abstract: We establish a local topological obstruction to the simultaneous flattening of Berry curvature in spin--orbit-coupled Bose--Einstein condensates (SOC BECs), which...
arXiv:2512.19544v2 Announce Type: replace Abstract: We determine the Picard number and the Ulrich complexity of general bidouble covers of the projective plane, providing the first...
arXiv:2512.23957v2 Announce Type: replace Abstract: We study the sine-Gordon measure defined on each homotopy class. The energy space decomposes into infinitely many such classes indexed...
arXiv:2601.01145v2 Announce Type: replace Abstract: In this paper, we systematically investigate the nilpotentizer and nilpotent graph for a Lie superalgebra over the field of characteristic...
arXiv:2601.02655v2 Announce Type: replace Abstract: We construct compact hyperbolic 3-manifolds with totally geodesic boundary, such that the closed 3-pseudomanifolds obtained by coning off the boundary...
arXiv:2601.03041v2 Announce Type: replace Abstract: This paper develops a bridge between bi-Hamiltonian structures of Poisson-Lie type, contact Hamiltonian dynamics, and the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) formalism for...
arXiv:2601.04437v2 Announce Type: replace Abstract: Let $K$ be a number field of degree $d$ so that $K/\mathbb Q$ is a Galois extension. The {\it normal...
arXiv:2601.07809v3 Announce Type: replace Abstract: We construct an irreducible rational curve of degree 10 in $CP^2$ which has 12 triple points and a union of...
arXiv:2601.08651v2 Announce Type: replace Abstract: In this work, we construct examples of holomorphic functions in $D_2(\B_2)$, the Dirichlet space on $\B_2$, for which there exists...
arXiv:2601.09509v2 Announce Type: replace Abstract: By the work of Hernandez-Leclerc, Leclerc-Plamondon, and Keller-Scherotzke, affine graded Nakajima quiver varieties associated with a Dynkin quiver $Q$ admit...