Tootfinder

The Snapshot Problem for the Euler-Poisson-Darboux Equation
Fulton Gonzalez, Jue Wang, Jens Christensen, Tomoyuki Kakehi
https://arxiv.org/abs/2507.13257 h…

The Snapshot Problem for the Euler-Poisson-Darboux Equation
The generalized Euler-Poisson-Darboux (EPD) equation with complex parameter $α$ is given by $$ Δ_x u=\frac{\partial^2 u}{\partial t^2}+\frac{n-1+2α}{t}\,\frac{\partial u}{\partial t}, $$ where $u(x,t)\in \mathscr E(\mathbb R^n\times \mathbb R)$, with $u$ even in $t$. For $α=0$ and $α=1$ the solution $u(x,t)$ represents a mean value over spheres and balls, respectively, of radius $|t|$ in $\mathbb R^n$. In this paper we consider existence and uniqueness results for the following t…

Special Cases of the Shafarevich Conjecture for Complete Intersections in Abelian Varieties
Frank Lu
https://arxiv.org/abs/2506.14935 https://

Special Cases of the Shafarevich Conjecture for Complete Intersections in Abelian Varieties
In this paper, we prove the Shafarevich conjecture for certain complete intersections of hypersurfaces in abelian varieties defined over a number field $K$ using the Lawrence-Venkatesh method. The main new inputs we need are computation of certain Euler characteristics of these complete intersections and a big monodromy statement for the variation of Hodge structure arising from the middle cohomology of a family of such complete intersections. Following \cite{ls25}, we prove the latter by relat…

Apropos HŸyre og Peter FrŸlich sine angrep på fag de ikke forstår eller kan kvantifisere nytteverdien av — jeg var inne på temaet på bloggen forleden: https://filmschoolteacher.info/fredsnotes/2025/07/25/why-we-ar-t/
(Jobber med en norsk versjon, men d…

This https://arxiv.org/abs/2111.14384 has been replaced.
link: https://scholar.google.com/scholar?q=a

Zero cycles, Mennicke symbols and $\mathrm{K}_1$-stability of certain real affine algebras
Let $R$ be a reduced real affine algebra of (Krull) dimension $d \ge 2$ such that either $R$ has no real maximal ideals, or the intersection of all real maximal ideals in $R$ has height at least one. In this article, we prove the following: (1) the $d$-th Euler class group $\text{E}^d(R)$, defined by Bhatwadekar-R.~Sridharan, is canonically isomorphic to the Levine-Weibel Chow group of zero cycles $\text{CH}_0(\text{Spec}(R))$; (2) the universal Mennicke symbol $\text{MS}_{d+1}(R)$ is canonical…