arXiv:2608. 28274v1 Announce Type: new Abstract: Let $n\ge2$ be even, let $\lambda=(\lambda_1,\ldots,\lambda_n)\in\mathbb{R}^n$ have pairwise distinct coordinates, and define the difference-power matrix \[ A_d(\lambda) := \bigl[(\lambda_r-\lambda_s)^d\bigr]_{r,s=1}^n, \qquad d\in\mathbb{N}.
By Kun Li, Li Tie, Peng Wang, Zihan Liu
arXiv:2609.27836v1 Announce Type: cross
Abstract: Let $P$ be an irreducible reversible Markov kernel on a $m$-state space $\Omega$, and denote its right spectral gap $\gamma=1-\lambda_2(P)$. From a s...
By Yanjin Xiang, Zhihua Zhang
arXiv:2607. 23004v1 Announce Type: cross Abstract: Let $t(N)$ be the largest $t$ for which there exist distinct sets $A_1,\dots,A_t \subseteq \{1,\dots,N\}$ such that $A_i \cap A_j$ is a nonempty arithmetic progression for all $i \neq j$ (Erdos Problem #272).
By Zhanfu Yang
arXiv:2608. 17802v1 Announce Type: new Abstract: Let $\varepsilon_1,\ldots,\varepsilon_n$ be independent Rademacher signs and let $a=(a_1,\ldots,a_n)\in\R^n$ satisfy the normalization below.
By Peigan Gao, Jian Qian
arXiv:2609.13476v1 Announce Type: cross
Abstract: At a 2021 AIM workshop, Guo conjectured that the positive square energy s+ = E+_2 should inherit the familiar edge-addition monotonicity of the spect...
By Koyar Afrasyab
arXiv:2608. 03368v1 Announce Type: new Abstract: For $n$ unit vectors $x_1,\ldots,x_n \in \mathbb{R}^d$, we study the continuous ReLU derivative Gram matrix $H$, whose entries are obtained by averaging pairwise gated inner products over a standard Gaussian direction.
By Zhao Song