Tootfinder

France has been developing its own digital tools and platforms for governmental use. I hope other countries follow suit, rather than relying on Google or Microsoft for government and education systems: https://www.numerique.gouv.fr/uploads/DINUM-roadmap_EN.pdf

A fast and memoryless numerical method for solving fractional differential equations
Nicola Guglielmi, Ernst Hairer
https://arxiv.org/abs/2506.04188 https:…

A fast and memoryless numerical method for solving fractional differential equations
The numerical solution of implicit and stiff differential equations by implicit numerical integrators has been largely investigated and there exist many excellent efficient codes available in the scientific community, as Radau5 (based on a Runge-Kutta collocation method at Radau points) and Dassl, based on backward differentiation formulas, among the others. When solving fractional ordinary differential equations (ODEs), the derivative operator is replaced by a non-local one and the fractional …

This https://arxiv.org/abs/2004.09217 has been replaced.
link: https://scholar.google.com/scholar?q=a

Vanishing Chern classes for numerically flat Higgs bundles
I consider Higgs bundles satisfying a notion of ampleness that was introduce Bruzzo, Graña Otero and Hernández Ruipérez, and prove that the Chern classes of rank $r$ H-ample Higgs bundles over dimension $n$, polarized, smooth, complex, projective varieties are positive under opportune hypothesis. I extend this to non-negativeness of Chern classes of all numerically effective Higgs bundles; and use this condition to prove the vanishing of Chern classes of numerically flat Higgs bundles.

The number of primes not in a numerical semigroup
Yong-Gao Chen, Hui Zhu
https://arxiv.org/abs/2506.03625 https://arxiv.org/pdf/2506.…

The number of primes not in a numerical semigroup
For two coprime positive integers $a,b$, let $π^* (a, b)$ be the number of primes that cannot be represented as $au+bv$, where $u,v$ are nonnegative integers. In this paper, we prove that $π^* (a, b)\ge 0.014 π(ab-a-b)$ and pose following conjecture: $π^* (a, b)\ge \frac 12 π(ab-a-b)$, where $π(x)$ denotes the number of primes not exceeding $x$. This conjecture is confirmed for $1\le a\le 8$.

GP-Recipe: Gaussian Process approximation to linear operations in numerical methods
Christopher DeGrendele, Dongwook Lee
https://arxiv.org/abs/2506.03471 h…

GP-Recipe: Gaussian Process approximation to linear operations in numerical methods
We introduce new Gaussian Process (GP) high-order approximations to linear operations that are frequently used in various numerical methods. Our method employs the kernel-based GP regression modeling, a non-parametric Bayesian approach to regression that operates on the probability distribution over all admissible functions that fit observed data. We begin in the first part with discrete data approximations to various linear operators applied to smooth data using the most popular squared expone…

Good Morning ESWC2025! The last conference day is about to start. Looking forward to an interesting keynote, more presentations and interesting discussions! Most interesting to see for me this year was the presence of neurosymbolic topics almost everywhere in our community.
#eswc2025 #portoroz…

This https://arxiv.org/abs/2411.00296 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Applying numerosity to surreal integration
We introduce the concept of numerosity, a measure of a set's size, more precise than cardinality and satisfying the Euclid's principle "the whole is greater than a part" as a surreal number and provide an explicit formula for expressing numerosities of some sequences as surreal expressions, with examples. Then (mapping surreal numbers to divergent integrals and interpreting them as Laplace transforms) we introduce a surreal-valued function that shares many properties with the Dirac Delta distri…

Numerical solution of the wave equation outside a sphere
Michael J. Carley
https://arxiv.org/abs/2506.04809 https://arxiv.org/pdf/250…

Numerical solution of the wave equation outside a sphere
A method is presented for the fast evaluation of the transient acoustic field generated outside a spherical surface by sources inside the surface. The method employs Lebedev quadratures, which are the optimal method for spatial integration, and Lagrange interpolation and differentiation in an advanced time algorithm for the evaluation of the transient field. Numerical testing demonstrates that the approach gives near machine-precision accuracy and a speed-up in evaluation time which depends on …

Numerical invariants of hyper-K\"ahler manifolds
Olivier Debarre, Chen Jiang
https://arxiv.org/abs/2506.04177 https://arxiv.org/…

Numerical invariants of hyper-Kähler manifolds
We study various constraints on the Beauville quadratic form and the Huybrechts-Riemann-Roch polynomial for hyper-Kähler manifolds, mostly in dimension 6 and in the presence of an isotropic class. In an appendix, Chen Jiang proves that in general, the Huybrechts-Riemann-Roch polynomial can always be written as a linear combination with nonnegative coefficients of certain explicit polynomials with positive coefficients. This implies that the Huybrechts-Riemann-Roch polynomial satisfies a curi…

Numerical analysis for constrained and unconstrained Q-tensor energies for liquid crystals
Heiko Gimperlein, Ruma R. Maity
https://arxiv.org/abs/2506.04880

Numerical analysis for constrained and unconstrained Q-tensor energies for liquid crystals
This paper introduces a comprehensive finite element approximation framework for three-dimensional Landau-de Gennes $Q$-tensor energies for nematic liquid crystals, with a particular focus on the anisotropy of the elastic energy and the Ball-Majumdar singular potential. This potential imposes essential physical constraints on the eigenvalues of the $Q$-tensor, ensuring realistic modeling. We address the approximation of regular solutions to nonlinear elliptic partial differential equations with…