Tootfinder

'A powerful secondary explosion' — Ukrainian drones destroy Russian ammunition depot in Donetsk Oblast, SBU says: https://benborges.xyz/2025/07/03/a-powerful-secondary-explosion-ukrainian.html

🇺🇦 #NowPlaying on BBCRadio3's #Radio3InConcert
Antonio Vivaldi, Guido Campana, Sara Mingardo, Alena Dantcheva, Monica Piccinini, Lia Serafini, Luca Dordolo, Concerto Italiano & Rinaldo Alessandrini:
🎵 Gloria, RV.588
https://open.spotify.com/track/5Txwlv081K39njx353jh7r

«Je ne comprends pas comment des gens aussi intelligents que des responsables universitaires ne comprennent pas qu’en termes de message et de gestion de leurs entités, il y a quelque chose qui ne va pas.»
https://www.

Dentsu: the video game industry attracts less than 5% of global ad spend despite 3.4B gamers worldwide; 60 game-based productions were in development in 2024 (Jennifer Maas/Variety)
https://variety.com/2025/gaming/news/video-g…

Video Game Industry Draws Less Than 5% of Ad, Marketing Spend
According to a new report from Dentsu Gaming, less than 5% of global media investment goes toward the the video game industry.

Spectral extremal problem for the odd prism
Xinhui Duan, Lu Lu
https://arxiv.org/abs/2507.01266 https://arxiv.org/pdf/2507.01266

Spectral extremal problem for the odd prism
The spectral Turán number $\spex(n, F)$ denotes the maximum spectral radius $ρ(G)$ of an $F$-free graph $G$ of order $n$. This paper determines $\spex\left(n, C_{2k+1}^{\square}\right)$ for all sufficiently large $n$, establishing the unique extremal graph. Here, $C_{2k+1}^{\square}$ is the odd prism -- the Cartesian product $C_{2k+1} \square K_2$ -- where the Cartesian product $G \square F$ has vertex set $V(G) \times V(F)$, and edges between $(u_1,v_1)$ and $(u_2,v_2)$ if either $u_1 = u_2$…

From ⁨⁨⁨⁨⁨#AnnafromUkraine⁩⁩⁩⁩⁩ @AnnafromUkraine@youtube.com
URGENT UPDATE: HUGE EXPLOSION DETONATION AMMO DEPOTS DONETSK Vlog 1093: War in #Ukraine
Just now: strike reported on the huge Russian #ammunition

Recognition by the set of exponents in the prime factorization of the product of element orders
Morteza Baniasad Azad, Mostafa Arabtash
https://arxiv.org/abs/2507.02594

Recognition by the set of exponents in the prime factorization of the product of element orders
Let $G$ be a finite group. Let $ρ(G) = \prod_{g \in G} o(g)={p_1}^{α_1} {p_2}^{α_2} \cdots {p_k}^{α_k}$, where $p_1, p_2, \cdots, p_k$ are distinct prime numbers and $o(g)$ denotes the order of $g \in G$. The set of exponents in the prime factorization of the product of element orders is denoted by $ {\operatorname{Exp}}_ρ(G)$, i.e., $ {\operatorname{Exp}}_ρ(G)=\{α_1,α_2, \cdots,α_k\}$. In this paper, we give a new characterization for some groups by $ {\operatorname{Exp}}_ρ(G)$. We p…

The Almighty Bear isn't giving up
https://bsky.app/profile/thealmightybear.bsky.social/post/3lt36zeu23k2f

🇺🇦 #NowPlaying on BBCRadio3's #Radio3InConcert
Antonio Vivaldi, Guido Campana, Sara Mingardo, Alena Dantcheva, Monica Piccinini, Lia Serafini, Luca Dordolo, Concerto Italiano & Rinaldo Alessandrini:
🎵 Gloria, RV.588
https://open.spotify.com/track/5Txwlv081K39njx353jh7r