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arXiv:2601.19039v1 Announce Type: new Abstract: We show that a circle and square of the same area in $\mathbb{R}^2$ are equidecomposable by translations using $\mathbf{\Delta}^0_2$ pieces....
arXiv:2601.19043v1 Announce Type: new Abstract: We establish that the minimum number of arcs required to partition the Galois projective plane $\text{PG}(2,q)$ is $q+1$. Furthermore, we...
arXiv:2601.19045v1 Announce Type: new Abstract: We answer a recent question of Cs\'oka and Vidny\'anszky [arXiv:2407.10006] and give an alternate proof of one of their results....
arXiv:2601.19046v1 Announce Type: new Abstract: A locally checkable labeling problem (LCL) on a group $\Gamma$ asks one to find a labeling of the Cayley graph...
arXiv:2601.19050v1 Announce Type: new Abstract: We show that up to isomorphism there are exactly twenty pairs $(C,E)$, where $C$ is a genus-$2$ curve over ${\mathbf...
arXiv:2601.19056v1 Announce Type: new Abstract: Many structured systems admit locally consistent descriptions that nevertheless fail to globalize when constrained by an ambient reference or feasibility...
arXiv:2601.19058v1 Announce Type: new Abstract: It is well known that the Gibbs inequality, which says that the Gibbs ratio is bounded above and below by...
arXiv:2601.19068v1 Announce Type: new Abstract: We prove that for any linear 3-graph on $n$ vertices without a path of length 5, the number of edges...
arXiv:2601.19071v1 Announce Type: new Abstract: We consider the parametric estimation of the Ornstein-Uhlenbeck process driven by a non-Gaussian $\alpha$-stable L\'{e}vy process with the stable index...
arXiv:2601.19075v1 Announce Type: new Abstract: We consider the non-homogeneous abstract linear Schr\"odinger and wave equations with zero initial conditions, defined by operators of strip-type and...
arXiv:2601.19083v1 Announce Type: new Abstract: Tilings of a surface of negative Euler characteristic by n-gons with n\ge 7 is a finite problem. One extreme of...
arXiv:2601.19084v1 Announce Type: new Abstract: In this paper we study the classical solution to the master equation arising from mean-field games (MFGs) driven by jump-diffusion...
arXiv:2601.19097v1 Announce Type: new Abstract: Timelike Liouville field theory (also known as imaginary Liouville theory or imaginary Gaussian multiplicative chaos) is expected to describe two-dimensional...
arXiv:2601.19101v1 Announce Type: new Abstract: We introduce a minimal multiscale framework that links within-host virus dynamics to population-level SIRS epidemiology through explicit, bidirectional coupling. At...
arXiv:2601.19110v1 Announce Type: new Abstract: We investigate the hydrodynamic limit of the Vlasov--Fokker--Planck--Navier--Stokes system in the light particle regime, where the particle relaxation takes place...
arXiv:2601.19126v1 Announce Type: new Abstract: Quantum differential privacy provides a rigorous framework for quantifying privacy guarantees in quantum information processing. While classical correlations are typically...
arXiv:2601.19145v1 Announce Type: new Abstract: Motivated by infinite-dimensional ecological and biological models such as reaction-diffusion SPDEs and stochastic functional differential equations, we develop a general...
arXiv:2601.19163v1 Announce Type: new Abstract: We consider a distance-regular graph $\Gamma=(X, \mathcal R)$ called the bilinear forms graph $H_q(D,N-D)$; we assume $N>2D\geq 6$ and $q...
arXiv:2601.19164v1 Announce Type: new Abstract: We introduce the notion of the $\infty$-category of (complete) derived $G$-graded modules over a $G$-graded ring $R$ for a torsion-free...
arXiv:2601.19172v1 Announce Type: new Abstract: In this paper, we propose a novel sixth-order compact time-splitting scheme, denoted as $ S_{6\text{c}}$, for solving the Dirac equation...
arXiv:2601.19177v1 Announce Type: new Abstract: In this paper, let $f$ be a Hecke cusp form for $SL(2,\mathbb{Z})$. We establish an asymptotic formula for the mixed...
arXiv:2601.19183v1 Announce Type: new Abstract: Large-scale decentralized learning frameworks such as federated learning (FL), require both communication efficiency and strong data security, motivating the study...
arXiv:2601.19195v1 Announce Type: new Abstract: We study the sum-of-squares (SOS) rank of simple and diagonal biquadratic forms. For simple biquadratic forms in $3 \times 3$...
arXiv:2601.19196v1 Announce Type: new Abstract: We study the problem of maximizing the first Laplace-Beltrami eigenvalue normalized by area in a conformal class on a torus....