Tootfinder

📷🎥 Lights, cameras…on #TNC25!
From thought-provoking keynotes to spontaneous hallway chats, #TNC25 was packed with unforgettable moments—and now you can relive them all.
The official #TNC25 photos and reco…

Vier neue #Elektrobusse ergänzen seit Juni den #Nahverkehr in #Plauen.
Die zwölf Meter langen eCitaro bieten 85 Plätze und erleichtern mit Niederflur und breitem Gang das Einsteigen für Rol…

Elektro-Busse im Plauener Stadtgebiet unterwegs
Oberbürgermeister Steffen Zenner war zusammen mit Landrat Thomas Hennig einer der ersten, der einen Blick in die neuen Elektro-Busse der Plauener Straßenbahn GmbH werfen konnte. Vier batterieelektrisch betriebene Busse sind ab jetzt schrittweise im Streckennetz der PSB unterwegs: Am 4. Juni wurden sie auf dem Betriebshof in der Wiesenstraße durch Oberbürgermeister Steffen Zenner, Landrat Thomas Hennig, dem Geschäftsführer der PSB, Karsten Treiber, sowie Ulrich Piotrowski, Verkaufsleiter b…

Amazon launches its second batch of 27 Kuiper satellites to low Earth orbit via a ULA rocket, taking the total in orbit to 54 of its planned 3,236 constellation (Annie Palmer/CNBC)
https://www.cnbc.com/2025/06/23/amazon-kuiper-satellites-musk-starlink.h…

Amazon launches second batch of Kuiper internet satellites, taking on Elon Musk's Starlink
Amazon has sent more Kuiper craft into space as it looks to deploy a satellite constellation that rivals Starlink, a service operated by Elon Musk's SpaceX.

Planar Tur\'an number of disjoint union of $C_3$ and $C_5$
Luyi Li, Ping Li, Guiying Yan, Qiang Zhou
https://arxiv.org/abs/2507.16351 https://

Planar Turán number of disjoint union of $C_3$ and $C_5$
The planar Turán number of $H$, denoted by $ex_{\mathcal{P}}(n,H)$, is the maximum number of edges in an $n$-vertex $H$-free planar graph. The planar Turán number of $k\geq 3$ vertex-disjoint union of cycles is the trivial value $3n-6$. Let $C_{\ell}$ denote the cycle of length $\ell$ and $C_{\ell}\cup C_t$ denote the union of disjoint cycles $C_{\ell}$ and $C_t$. The planar Turán number $ex_{\mathcal{P}}(n,H)$ is known if $H=C_{\ell}\cup C_k$, where $\ell,k\in \{3,4\}$. In this paper, we de…

Barack Obama Sees Death Threat Surge After Trump's Treason Claims (Kate Plummer/Newsweek)
https://www.newsweek.com/barack-obama-trump-treason-arrest-russia-death-threats-2102949
http://www.memeorandum.com/250724/p110#a250724p110

When both your wife and your girlfriend are busy, you take yourself out! #polyamory #gobraves

International #degrowth conference starts in #Oslo later today, til Friday.
You can watch plenaries on the #livestream. Looks like Gustavo Petro will not now be giving the inaugural address but Irene Vélez…

Ground states of the planar nonlinear Schr\"odinger--Newton system with a point interaction
Gustavo de Paula Ramos
https://arxiv.org/abs/2506.18202 ht…

Ground states of the planar nonlinear Schrödinger--Newton system with a point interaction
We establish sufficient conditions for the existence of ground states of the following normalized nonlinear Schrödinger--Newton system with a point interaction: \[ \begin{cases} - Δ_αu = w u + βu |u|^{p - 2} &\text{on} ~ \mathbb{R}^2; \\ - Δw = 2 π|u|^2 &\text{on} ~ \mathbb{R}^2; \\ \|u\|_{L^2}^2 = c, \end{cases} \] where $p > 2$; $α, β\in \mathbb{R}$ and $- Δ_α$ denotes the Laplacian of point interaction with scattering length $(- 2 πα)^{- 1}$. Additio…

When both your wife and your girlfriend are busy, you take yourself out! #polyamory #gobraves

Planar-Toroidal Decomposition of $K_{12}$
Allan Bickle, Russell Campbell
https://arxiv.org/abs/2507.17084 https://arxiv.org/pdf/2507.…

Planar-Toroidal Decomposition of $K_{12}$
In 1978, Anderson and White asked whether there is a decomposition of $K_{12}$ into two graphs, one planar and one toroidal. Using theoretical arguments and a computer search of all maximal planar graphs of order 12, we show that no such decomposition exists. We further show that if $G$ is planar of order 12 and $H\subseteq\overline{G}$ is toroidal, then $H$ has at least two fewer edges than $\overline{G}$. A computer search found all 123 unique pairs $\left(G,H\right)$ that make this an equali…