Tootfinder

Star decompositions via orientations
Viktor Harangi
https://arxiv.org/abs/2506.05194 https://arxiv.org/pdf/2506.05194

Star decompositions via orientations
A $k$-star decomposition of a graph is a partition of its edges into $k$-stars (i.e., $k$ edges with a common vertex). The paper studies the following problem: given $k \leq d/2$, does the random $d$-regular graph have a $k$-star decomposition (asymptotically almost surely, provided that the number of edges is divisible by $k$)? Delcourt, Greenhill, Isaev, Lidický, and Postle proved the a.a.s. existence for every odd $k$ using earlier results regarding orientations satisfying certain degree co…

This https://arxiv.org/abs/2505.16529 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Modular forms of CM type mod $\ell$
We say that a normalized modular form without complex multiplication is of CM type modulo $\ell$ by an imaginary quadratic field $K$ if its Fourier coefficients $a_p$ are $0$ modulo a prime ideal dividing $\ell$ for every prime $p$ inert in $K$. In this paper, we address the following problem: Given a weight 2 cuspidal Hecke eigenform $f$ without CM which is of CM type modulo $\ell$ by an imaginary quadratic field $K$, does there exist a congruence modulo $\ell$ between $f$ and a genuine CM m…

A Positivity-Preserving Finite Element Framework for Accurate Dose Computation in Proton Therapy
Ben S. Ashby, Abdalaziz Hamdan, Tristan Pryer
https://arxiv.org/abs/2506.01105

A Positivity-Preserving Finite Element Framework for Accurate Dose Computation in Proton Therapy
We present a stabilised finite element method for modelling proton transport in tissue, incorporating both inelastic energy loss and elastic angular scattering. A key innovation is a positivity-preserving formulation that guarantees non-negative fluence and dose, even on coarse meshes. This enables reliable computation of clinically relevant quantities for treatment planning. We derive a priori error estimates demonstrating optimal convergence rates and validate the method through numerical ben…

Population Synthesis Study on the Binary Origin of Type Ibn Supernovae
Takatoshi Ko, Tomoya Kinugawa, Daichi Tsuna, Ryosuke Hirai, Yuki Takei
https://arxiv.org/abs/2506.00931

Population Synthesis Study on the Binary Origin of Type Ibn Supernovae
Type Ibn supernovae (SNe) are a class of SN explosions whose progenitors are surrounded by dense helium-rich circumstellar matter (CSM). Some models have been proposed for how to form the dense CSM, with promising scenarios involving either binaries with a low-mass ($\lesssim 3~M_\odot$) helium (He) star, or mergers following common envelope phases between a He star and a compact object. Using rapid binary population synthesis calculations, we estimate the event rate of these channels and compa…

On the Farrell--Tate $K$-theory of $\text{Out}(F_n)$
Naomi Andrew, Irakli Patchkoria
https://arxiv.org/abs/2505.21803 https://arxiv.o…

On the Farrell--Tate $K$-theory of $\text{Out}(F_n)$
Using Lück's Chern character isomorphism we obtain a general formula in terms of centralisers for the $p$-adic Farrell--Tate $K$-theory of any discrete group $G$ with a finite classifying space for proper actions. We apply this formula to $\text{Out}(F_n)$. The case $n=p+1$ turns out to be especially interesting for the following reason: Up to conjugacy there is exactly one order $p$ element in $\text{Out}(F_{p+1})$ which does not lift to an order $p$ element in $\text{Aut}(F_{p+1})$. We compu…

Exocomets of $\beta$ Pictoris I: Exocomet destruction, sodium and disk line variability in 17 years of HARPS observations
H. J. Hoeijmakers, K. P. Jaworska, B. Prinoth
https://arxiv.org/abs/2505.21625

Exocomets of $β$ Pictoris I: Exocomet destruction, sodium and disk line variability in 17 years of HARPS observations
The young $β$ Pictoris system has been monitored with high-resolution optical spectrographs for decades. These observations have revealed strongly variable absorption in the Ca II H\&K lines attributed to in-falling cometary bodies. Since 2003, over 9000 HARPS observations of $β$ Pictoris have been taken and many of these have not yet been used for exocomet studies. We search these spectra for new exocomet phenomenology enabled by the long time coverage and large volume of this dataset. We sy…