Tootfinder

A note on new type degenerate Srirling numbers of the first kind
Taekyun Kim, Dae san Kim, Kyo-Shin Hwang, Dmitry V. Dolgy
https://arxiv.org/abs/2509.03415 https://

A note on new type degenerate Srirling numbers of the first kind
We introduce a new sequence of unsigned degenerate Stirling numbers of the first kind. Following the work of Adell-Lekuona, who represented unsigned Stirling numbers of the first kind as multiples of the expectations of specific random variables, we express our new numbers as finite sums of multiples of the expectations of certain random variables. We also provide a representation of these new numbers as finite sums involving the classical unsigned Stirling numbers of the first kind. As an inve…

Local H\"older Regularity for Quasilinear Elliptic Equations with Mixed Local-Nonlocal Operators, Variable Exponents, and Weights
Juan Pablo Alcon Apaza
https://arxiv.org/abs/2507.01899

Local Hölder Regularity for Quasilinear Elliptic Equations with Mixed Local-Nonlocal Operators, Variable Exponents, and Weights
We establish local boundedness and local Hölder continuity of weak solutions to the following prototype problem: $$ -\operatorname{div}\left(|x|^{-2 β}|\nabla u|^{\mathbf{q}-2} \nabla u\right)+(-Δ)_{p(\cdot, \cdot), β}^{s(\cdot, \cdot)} u=0 \quad \text { in } \quad Ω, $$ where $Ω\subset \mathbb{R}^n, n \geq 2$, is a bounded domain. The nonlocal operator is defined by $$ (-Δ)_{p(\cdot, \cdot), β}^{s(\cdot, \cdot)} u(x):=\mathrm{P} . \mathrm{V} . \int_Ω \frac{&#…

Cooperative Sensing Enhanced UAV Path-Following and Obstacle Avoidance with Variable Formation
Changheng Wang, Zhiqing Wei, Wangjun Jiang, Haoyue Jiang, Zhiyong Feng
https://arxiv.org/abs/2508.21316

Cooperative Sensing Enhanced UAV Path-Following and Obstacle Avoidance with Variable Formation
The high mobility of unmanned aerial vehicles (UAVs) enables them to be used in various civilian fields, such as rescue and cargo transport. Path-following is a crucial way to perform these tasks while sensing and collision avoidance are essential for safe flight. In this paper, we investigate how to efficiently and accurately achieve path-following, obstacle sensing and avoidance subtasks, as well as their conflict-free fusion scheduling. Firstly, a high precision deep reinforcement learning (…

A robust Likelihood Ratio Test for high-dimensional MANOVA -- with excellent performance
Carlos A. Coelho
https://arxiv.org/abs/2507.01261 https://

A robust Likelihood Ratio Test for high-dimensional MANOVA -- with excellent performance
The present paper answers the following questions related with high-dimensional manova: (i) is it possible to develop a likelihood ratio test for high-dimensional manova? (ii) would such test perform well? (iii) would it be able to outperform existing tests? (iv) would it be applicable to extremely small samples? (v) would it be applicable to non-normal random variables, as uniform, extremely skewed distributions, or even heavy tailed distributions with success? (vi) would it have a nice, rathe…

Binomial edge ideals of Cameron-Walker graphs
Takayuki Hibi, Sara Saeedi Madani
https://arxiv.org/abs/2509.01150 https://arxiv.org/pdf/2509.01150

Binomial edge ideals of Cameron-Walker graphs
Let $G$ be a Cameron--Walker graph on $n$ vertices and $J_G$ the binomial edge ideal of $G$. Let $S$ denote the polynomial ring in $2n$ variables over a field. It is shown that the following conditions are equivalent: (i) $S/J_G$ is Cohen--Macaulay; (ii) $J_G$ is unmixed; (iii) $\dim (S/J_G) = n+1$; (iv) (a) $n = 3$ and $G$ is a path of length $2$ or (b) $n = 5$ and $G$ is a path of length $4$ or (c) $n=5$ and $G$ is obtained by attaching a path of length $2$ to a triangle. Moreover, the depth …

Random burning of the Euclidean lattice
Guillaume Blanc, Alice Contat
https://arxiv.org/abs/2509.02562 https://arxiv.org/pdf/2509.02562

Random burning of the Euclidean lattice
The burning number of a graph is the minimal number of steps that are needed to burn all of its vertices, with the following burning procedure: at each step, one can choose a point to set on fire, and the fire propagates constantly at unit speed along the edges of the graph. In this paper, we consider two natural random burning procedures in the discrete Euclidean torus $\mathbb{T}_n^d$, in which the points that we set on fire at each step are random variables. Our main result deals with the ca…

Nondegenerate hyperplane covers of the hypercube
Lisa Sauermann, Zixuan Xu
https://arxiv.org/abs/2507.00773 https://arxiv.org/pdf/250…

Nondegenerate hyperplane covers of the hypercube
We consider collections of hyperplanes in $\mathbb{R}^n$ covering all vertices of the $n$-dimensional hypercube $\{0,1\}^n$, which satisfy the following nondegeneracy condition: For every $v\in \{0,1\}^n$ and every $i=1,\dots,n$, we demand that there is a hyperplane $H$ in the collection with $v\in H$ such that the variable $x_i$ appears with a non-zero coefficient in the hyperplane equation describing $H$. We prove that every collection $\mathcal{H}$ of hyperplanes in $\mathbb{R}^n$ covering $…

Raiders Could Face Patriots Without Star Player After Injury Update https://heavy.com/sports/nfl/las-vegas-raiders/las-vegas-patriots-christian-gonzalez-update/?adt_ei=[email]

Towards a compleat theory of ecosystem size spectra
Ralf Schwamborn
https://arxiv.org/abs/2509.00023 https://arxiv.org/pdf/2509.00023

Towards a compleat theory of ecosystem size spectra
The regularity of ecosystem size spectra is one of the most intriguing and relevant phenomena on our planet. Aquatic size spectra generally show a log-linearly downtrending shape, following a power-law distribution. A constant log-linear slope has been reported for many marine pelagic ecosystems, often being approximately b = -1. Conversely, there are variable trophic-level-biomass relationships (trophic pyramids). The contrasting observations of a constant biomass (M) spectrum slope and highly…

Robert Kraft promises Patriots turnaround following worst two-year run in owner's history with franchise

https://www.cbssports.com/nfl/news/ro…