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arXiv:2405.09917v3 Announce Type: replace Abstract: We consider continuous maps of the interval which preserve the Lebesgue measure. Except for the identity map or $1 -...
arXiv:2405.17340v3 Announce Type: replace Abstract: We obtain $\Omega$-results for linear exponential sums with rational additive twists of small prime denominators weighted by Hecke eigenvalues of...
arXiv:2407.14674v4 Announce Type: replace Abstract: We introduce actions of a compact Lie group in two regularization processes: in De Rham's approximation process of currents on...
arXiv:2407.15367v3 Announce Type: replace Abstract: In the previous paper, we constructed two kinds of edge contractions for the affine super Yangian and a homomorphism from...
arXiv:2407.19254v3 Announce Type: replace Abstract: Let $\Omega$ be a convex domain in $\mathbb{C}^n$ and $\varphi$ a convex function on $\Omega$. We prove that $\log{K_{\Omega,\varphi}(z)}$ is...
arXiv:2408.07316v2 Announce Type: replace Abstract: For a Hausdorff space $Y$, a topological space $X$ and a map $g:X\to Y$, we present a connection between the...
arXiv:2408.07400v3 Announce Type: replace Abstract: Given a finite set $S$ of distinct primes, we propose a method to construct polylogarithmic motivic Chabauty-Kim functions for $\mathbb{P}^1...
arXiv:2409.00881v3 Announce Type: replace Abstract: Let $E/\mathbb{Q}$ be an elliptic curve. We say that $E$ has a near coincidence of level $(n,m)$ if $m \mid...
arXiv:2409.05450v4 Announce Type: replace Abstract: We show that given a lattice $\Gamma \subset \mathbb{R}^m \times \mathbb{R}^n$, and projections $p_1$ and $p_2$ onto $\mathbb{R}^m$ and $\mathbb{R}^n$...
arXiv:2409.05502v2 Announce Type: replace Abstract: We show that continuous epimorphisms between a class of subgroups of mapping class groups of orientable infinite-genus 2-manifolds with no...
arXiv:2410.18331v3 Announce Type: replace Abstract: Equipartition theory, beginning with the classical ham sandwich theorem, seeks the fair division of finite point sets in $\mathbb{R}^d$ by...
arXiv:2411.19694v4 Announce Type: replace Abstract: We investigate a perturbed Gelfand problem involving a mixed local-nonlocal $p$-Laplacian operator with singular nonlinearity: \begin{equation*} \begin{aligned} -\Delta_p u +...
arXiv:2412.11206v2 Announce Type: replace Abstract: We give an 'arithmetic regularity lemma' for groups definable in finite fields, analogous to Tao's 'algebraic regularity lemma' for graphs...
arXiv:2501.02862v4 Announce Type: replace Abstract: We show that a substantial portion of stochastic calculus can be developed along similar lines to ordinary calculus, with derivative-based...
arXiv:2501.04044v2 Announce Type: replace Abstract: In the paper, given two vector fields and the Witten deformation, we compute the spectral Einstein functional for the Witten...
arXiv:2501.04159v2 Announce Type: replace Abstract: Dual numbers are a well-established tool for computing derivatives and constitute the basis of forward-mode automatic differentiation. While the theoretical...
arXiv:2501.06539v4 Announce Type: replace Abstract: We construct a Neural Network that approximates the matrix multiplication operator for any activation function such that there exists a...
arXiv:2501.15668v2 Announce Type: replace Abstract: Smooth axially symmetric Helfrich topological spheres are either round or else they must satisfy a second order equation known as...
arXiv:2502.05180v3 Announce Type: replace Abstract: I prove Richard Soland's conjecture that for an efficient solution to a multicriteria optimization problem, there need not exist a...
arXiv:2502.09119v2 Announce Type: replace Abstract: We present a comprehensive computational model to simulate the coupled dynamics of aqueous humor flow and heat transfer in the...
arXiv:2502.18820v2 Announce Type: replace Abstract: As an analogue to the explicit formula in the stable case, the asymptotic behavior at the origin of the renormalized...
arXiv:2503.06657v2 Announce Type: replace Abstract: We extend the work of Galatos (2004) on nested sums, originally called generalised ordinal sums, of residuated lattices. We show...
arXiv:2503.11912v2 Announce Type: replace Abstract: We give a classification for the small-$\tau$ asymptotic behaviours of solutions to the degenerate third Painlev\'e equation, $u^{''}(\tau) = \frac{(u^{\prime}(\tau))^{2}}{u(\tau)}...
arXiv:2503.22816v2 Announce Type: replace Abstract: We introduce a novel numerical scheme for solving the Fokker-Planck equation of discretized Dean-Kawasaki models with a functional tensor network...