Tootfinder

New constructions and bounds for nonabelian Sidon sets with applications to Tur\'an-type problems
John Byrne, Michael Tait
https://arxiv.org/abs/2509.07750 https://

New constructions and bounds for nonabelian Sidon sets with applications to Turán-type problems
An $S_k$-set in a group $Γ$ is a set $A\subseteqΓ$ such that $α_1\cdotsα_k=β_1\cdotsβ_k$ with $α_i,β_i\in A$ implies $(α_1,\ldots,α_k)=(β_1,\ldots,β_k)$. An $S_k'$-set is a set such that $α_1β_1^{-1}\cdotsα_kβ_k^{-1}=1$ implies that there exists $i$ such that $α_i=β_i\text{ or }β_i=α_{i+1}$. We give explicit constructions of large $S_k$-sets in the group $S_n$ and $S_2$-sets in $S_n\times S_n$ and $A_n\times A_n$. We give probabilistic constructions for `nice' groups which o…

Products of Tribonacci Numbers that are the Products of Factorials
Pranabesh Das, J. C. Saunders
https://arxiv.org/abs/2510.06520 https://arxiv.org/pdf/251…

Products of Tribonacci Numbers that are the Products of Factorials
In 2014 Marques and Lengyel gave all of the solutions to the equation $T_n=m!$, where $T_n$ is the $n$th term of the Tribonacci sequence $0,1,1,2,4,7,13,24,\ldots$. In 2023 Alahmadi and Luca generalized their result to the equation $T_n=m_1!m_2!\cdots m_k!$ for every $k\in\mathbb{N}$, where $m_1\leq m_2\leq\ldots\leq m_k$ listing all the solutions to this equation. Here we generalize these results further and give all the solutions to $T_nT_{n+1}T_{n+2}\cdots T_{n+r}=m_1!m_2!\cdots m_k!$ and $ …

Non-homogeneous Schrodinger systems with sign-changing and general nonlinearities: Infinitely many solutions
Guanwei Chen
https://arxiv.org/abs/2509.07652 https://

Non-homogeneous Schrodinger systems with sign-changing and general nonlinearities: Infinitely many solutions
In this paper, we study the non-homogeneous nonlinear Schrödinger system $$\left\{ \begin{array}{ll} -\triangle u_j+V_j(x) u_j=g_j(x,u_1,\cdots,u_m)+h_j(x),& x\in Ω,\\ \\ u_j:=u_j(x)=0,& x\in \partialΩ,\\ \\ j=1,2,\cdots,m, \end{array}\right. $$ where $Ω\subset\mathbb{R}^{N}$ ($N\ge2$) is a bounded smooth domain, $(g_1,\cdots,g_m)$ is the gradient of $G(x,U)\in C^1(Ω\times\mathbb{R}^m,\mathbb{R})$, $G(x,U)$ may be sign-changing, and it is super-quadratic or asymptotically-quadratic as $
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#FotoVorschlag 'Nicht ganz scharf aber trotzdem gut'
Taubenschwänzchen (Macroglossum stellatarum)

Pixel-Perfect Depth with Semantics-Prompted Diffusion Transformers
Gangwei Xu, Haotong Lin, Hongcheng Luo, Xianqi Wang, Jingfeng Yao, Lianghui Zhu, Yuechuan Pu, Cheng Chi, Haiyang Sun, Bing Wang, Guang Chen, Hangjun Ye, Sida Peng, Xin Yang
https://arxiv.org/abs/2510.07316

Pixel-Perfect Depth with Semantics-Prompted Diffusion Transformers
This paper presents Pixel-Perfect Depth, a monocular depth estimation model based on pixel-space diffusion generation that produces high-quality, flying-pixel-free point clouds from estimated depth maps. Current generative depth estimation models fine-tune Stable Diffusion and achieve impressive performance. However, they require a VAE to compress depth maps into latent space, which inevitably introduces \textit{flying pixels} at edges and details. Our model addresses this challenge by directly…

Validation of collision-free spheres of Stewart-Gough platforms for constant orientations using the Application Programming Interface of a CAD software
Bibekananda Patra, Rajeevlochana G. Chittawadigi, Sandipan Bandyopadhyay
https://arxiv.org/abs/2510.08408

Validation of collision-free spheres of Stewart-Gough platforms for constant orientations using the Application Programming Interface of a CAD software
This paper presents a method of validation of the size of the largest collision-free sphere (CFS) of a 6-6 Stewart-Gough platform manipulator (SGPM) for a given orientation of its moving platform (MP) using the Application Programming Interface (API) of a CAD software. The position of the MP is updated via the API in an automated manner over a set of samples within a shell enclosing the surface of the CFS. For each pose of the manipulator, each pair of legs is investigated for mutual collisions…

🇺🇦 #NowPlaying on #KEXP's #VarietyMix
cutouts:
🎵 Narc
#cutouts
https://cutouts.bandcamp.com/track/narc-2
https://open.spotify.com/track/2BuGghIgkJ28S46UkIaX2j

Replaced article(s) found for physics.bio-ph. https://arxiv.org/list/physics.bio-ph/new
[1/1]:
- Design principles of the cytotoxic CD8 T-cell response
Obinna A. Ukogu, Zachary Montague, Gr\'egoire Altan-Bonnet, Armita Nourmohammad

General Recurrence Multidimensional Zeckendorf Representations
Jiarui Cheng, Steven J. Miller, Sebastian Rodriguez-Labastida, Tianyu Shen, Alan Sun, Garrett Tresch
https://arxiv.org/abs/2510.07237

General Recurrence Multidimensional Zeckendorf Representations
We present a multidimensional generalization of Zeckendorf's Theorem (any positive integer can be written uniquely as a sum of non-adjacent Fibonacci numbers) to a large family of linear recurrences. This extends work of Anderson and Bicknell-Johnson in the multi-dimensional case when the underlying recurrence is the same as the Fibonacci one. Our extension applies to linear recurrence relations defined by vectors $\vec{\mathbf{c}} = (c_1, c_2, \ldots, c_k)$ such that $c_1\geq c_2\geq\cdots \ge…

Global well-posedness and large time behavior of 3D incompressible inhomogeneous magnetohydrodynamic equations in the exterior of a cylinder
Jitao Liu, Min Liu
https://arxiv.org/abs/2509.06293

Global well-posedness and large time behavior of 3D incompressible inhomogeneous magnetohydrodynamic equations in the exterior of a cylinder
When the vaccum is allowed, if the global existence and uniqueness of strong solutions to three dimensional incompressible inhomogeneous magnetohydrodynamic equations holds true or not has always been a challenging open problem, even for the magnetofluids with special structures. In this paper, through deeply exploring the internal structure and characteristic of axisymmetric flows, we obtain some new discoveries and give a partial answer to above issue. More precisely, we prove that the axisym…