Tootfinder

Biggest remaining need for every NFC team: Secondary help for Packers, Cowboys, protection for Baker Mayfield

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

Classification of biharmonic Riemannian submersions from manifolds with constant sectional curvature
Shun Maeta, Miho Shito
https://arxiv.org/abs/2509.05939 https://

Classification of biharmonic Riemannian submersions from manifolds with constant sectional curvature
In 2011, Wang and Ou (Math. Z. 269:917-925, 2011) showed that any biharmonic Riemannian submersion from a 3-dimensional Riemannian manifold with constant sectional curvature to a surface is harmonic. In this paper, we generalize the 3-dimensional setting to arbitrary dimensions. By constructing an adapted orthonormal frame, we simplify the biharmonic equation for Riemannian submersions and analyze the curvature properties of Riemannian manifolds with constant sectional curvature. As a result, w…

Oracle reports Q1 revenue up 12% YoY to $14.93B, vs. $15.04B est., and remaining performance obligations up 359% to $455B; ORCL jumps 19% after hours (Jordan Novet/CNBC)
https://www.cnbc.com/2025/09/09/oracle-orcl-q1-earnings-report-2026.html

Oracle pops 22% on cloud growth projections even as earnings miss estimates
Oracle said total remaining performance obligations jumped 359% from a year earlier, indicating big growth prospects.

A Riemannian conjugate subgradient method for nonconvex and nonsmooth optimization on manifolds
Chunming Tang, Shaohui Liang, Huangyue Chen
https://arxiv.org/abs/2509.05947 http…

A Riemannian conjugate subgradient method for nonconvex and nonsmooth optimization on manifolds
Conjugate gradient (CG) methods are widely acknowledged as efficient for minimizing continuously differentiable functions in Euclidean spaces. In recent years, various CG methods have been extended to Riemannian manifold optimization, but existing Riemannian CG methods are confined to smooth objective functions and cannot handle nonsmooth ones. This paper proposes a Riemannian conjugate subgradient method for a class of nonconvex, nonsmooth optimization problems on manifolds. Specifically, we f…

Properties and examples of Kobayashi hyperbolic Riemannian manifolds
Herv\'e Gaussier, Alexandre Sukhov
https://arxiv.org/abs/2509.06802 https://arxiv.…

Properties and examples of Kobayashi hyperbolic Riemannian manifolds
We prove an analogue of the Brody lemma in the framework of Riemannian manifolds. We also present new examples of Riemannian manifolds that are hyperbolic in the sense of Kobayashi.

Average Nikolskii factors for random diffusion polynomials on closed Riemannian manifolds
Yun Ling, Heping Wang
https://arxiv.org/abs/2507.06505 https://…

Average Nikolskii factors for random diffusion polynomials on closed Riemannian manifolds
For $1\le p,q\le \infty$, the Nikolskii factor for a diffusion polynomial $P_{\bf a}$ of degree at most $n$ is defined by $$N_{p,q}(P_{\bf a})=\frac{\|P_{\bf a}\|_{q}}{\|P_{\bf a}\|_{p}},\ \ P_{\bf a}({\bf x})=\sum_{k:λ_{k}\leq n}a_{k}ϕ_{k}({\bf x}),$$ where ${\bf a}=\{a_k\}_{λ_k\le n}$, and $\{(ϕ_k,-λ_k^2)\}_{k=0}^\infty$ are the eigenpairs of the Laplace-Beltrami operator $Δ_{\mathbb M}$ on a closed smooth Riemannian manifold $\mathbb M$ with normalized Riemannian me…

Decentralized Online Riemannian Optimization Beyond Hadamard Manifolds
Emre Sahinoglu, Shahin Shahrampour
https://arxiv.org/abs/2509.07779 https://arxiv.or…

Decentralized Online Riemannian Optimization Beyond Hadamard Manifolds
We study decentralized online Riemannian optimization over manifolds with possibly positive curvature, going beyond the Hadamard manifold setting. Decentralized optimization techniques rely on a consensus step that is well understood in Euclidean spaces because of their linearity. However, in positively curved Riemannian spaces, a main technical challenge is that geodesic distances may not induce a globally convex structure. In this work, we first analyze a curvature-aware Riemannian consensus …

Biggest remaining need for every AFC team: Jets wide receivers, Bengals edge rushers headline list

https://www.cbssports.com/nfl/news/biggest

Curvature inequalities for anti-invariant submersion from quaternionic space forms
Kirti Gupta, Punam Gupta, R. K. Gangele
https://arxiv.org/abs/2507.06259

Curvature inequalities for anti-invariant submersion from quaternionic space forms
This paper focuses on deriving several curvature inequalities involving the Ricci and scalar curvatures of the horizontal and vertical distributions in anti-invariant Riemannian submersions from quaternionic space forms onto Riemannian manifolds. In addition, a Ricci curvature inequality for anti-invariant Riemannian submersions is established. The equality cases for all derived inequalities are also examined.

Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking
Jun Chen, Lina Liu, Tianyi Zhu, Yong Liu, Guang Dai, Yunliang Jiang, Ivor W. Tsang
https://arxiv.org/abs/2506.07351

Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking
This paper considers the problem of decentralized optimization on compact submanifolds, where a finite sum of smooth (possibly non-convex) local functions is minimized by $n$ agents forming an undirected and connected graph. However, the efficiency of distributed optimization is often hindered by communication bottlenecks. To mitigate this, we propose the Quantized Riemannian Gradient Tracking (Q-RGT) algorithm, where agents update their local variables using quantized gradients. The introducti…