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arXiv:2601.01761v2 Announce Type: replace Abstract: Let ${\mathbb F}_0$ be an algebraically closed field, with $char({\mathbb F}_0)=0$. In this article, for prime numbers $p\geq 2$, we...
arXiv:2601.03006v2 Announce Type: replace Abstract: In this paper, we study backward stochastic differential equations driven by G-Brownian motion where the generator has time-varying monotonicity with...
arXiv:2601.03086v3 Announce Type: replace Abstract: We propose a Pretrained Finite Element Method (PFEM),a physics driven framework that bridges the efficiency of neural operator learning with...
arXiv:2601.06128v3 Announce Type: replace Abstract: We study the finite sampling map $H \mapsto \bigl(v_{H,\Lambda}(x_k + i\eta)\bigr)_{k=1}^M$ for trace-normed canonical systems on $[0,\Lambda]$ with free tail...
arXiv:2601.07502v2 Announce Type: replace Abstract: In this paper, we study the number of moves in a multidimensional elephant random walk with stops. We establish several...
arXiv:2601.08362v2 Announce Type: replace Abstract: This paper introduces a stratification framework for nonlinear semidefinite programming (NLSDP) that reveals and utilizes the geometry behind the nonsmooth...
arXiv:2601.10217v2 Announce Type: replace Abstract: We characterize the nuclearity of Toeplitz operators $T_\mu: F_\alpha^p \to F_\alpha^q$ with Borel measure symbols for $1\leq p,q\leq \infty$. For...
arXiv:2601.10678v2 Announce Type: replace Abstract: It is well-known in the field of lossless data compression that probabilistic next-symbol prediction can be used to compress sequences...
arXiv:2601.11008v3 Announce Type: replace Abstract: We isolate the limit-stage filter construction needed for countable-support symmetric iterations built from standard successor-step symmetric systems. At successor stages...
arXiv:2601.11892v2 Announce Type: replace Abstract: We give a self-contained analytic proof of the continued fraction identity \[ -\frac{\pi}{4} = \cfrac{1}{-1+\cfrac{1^2}{-3+\cfrac{2^2}{-5+\cfrac{3^2}{-7+\cdots}}}} \] whose partial quotients are...
arXiv:2601.13158v2 Announce Type: replace Abstract: We obtain a new closed-form formula for the characteristic function of the asymmetric Student's $t$-distribution. As part of our analysis,...
arXiv:2601.15140v2 Announce Type: replace Abstract: We prove that homological filling functions over a ring $R$ equipped with the discrete norm are quasi-isometry invariants for all...
arXiv:2601.17079v2 Announce Type: replace Abstract: For an even integer $k\geq 2$, let $f$ be a primitive holomorphic cusp form of weight $k$ for the full...
arXiv:2601.19307v2 Announce Type: replace Abstract: We consider a multiscale stochastic compartmental model with three types of cells (stem cells, immature cells and mature cells) which...
arXiv:2601.19592v2 Announce Type: replace Abstract: Equipped with the operation of setwise multiplication induced by a (multiplicatively written) monoid $H$ on its parts, the collection of...
arXiv:2601.20128v2 Announce Type: replace Abstract: We present a novel exactly solvable ordinary differential equation model for rate-induced tipping: a dynamic phenomenon of dynamical systems where...
arXiv:2601.20500v2 Announce Type: replace Abstract: We prove an equivalence between a conjecture of Neumann and Praeger on Kronecker classes in algebraic number fields, and a...
arXiv:2601.22903v2 Announce Type: replace Abstract: Hyperbolic inversive distance circle packings on the $2$-sphere correspond to Koebe polyhedra in the Beltrami-Klein model $\mathbb{B}^{3}$ of hyperbolic $3$-space....
arXiv:2602.01441v2 Announce Type: replace Abstract: A key signature of MBL (many-body localization) is the slow rate at which information spreads. It is shown that the...
arXiv:2602.03162v3 Announce Type: replace Abstract: We present a structural resolution to the exact evaluation of the partition function $p_k(n)$, definitively overcoming the limitations of traditional...
arXiv:2602.03167v2 Announce Type: replace Abstract: Building on the classical work of C\'{o}rdoba--Fefferman and the recent work of Schippa, we establish $L^4$ reverse square function estimates...
arXiv:2602.04610v2 Announce Type: replace Abstract: A first-order structure $M$ is said to have the infinite sunflower property if, for each $k \in \mathbb{N}_+$ and each...
arXiv:2602.05254v2 Announce Type: replace Abstract: Capsets are subsets of $\mathbb{F}_3^n$ with no three points on a line and a capset is complete if it is...
arXiv:2602.07879v2 Announce Type: replace Abstract: We establish a structure theorem for the connected automorphism groups of smooth complete toroidal horospherical varieties, that is, toric fibrations...