Tootfinder

The ordering of hypertrees and unicyclic hypergraphs by the traces of $\mathcal{A}_{\alpha}$-tensor
Jueru Liu, Lizhu Sun, Changjiang Bu
https://arxiv.org/abs/2507.02650

The ordering of hypertrees and unicyclic hypergraphs by the traces of $\mathcal{A}_α$-tensor
For a real number $α\in[0,1]$ and a $k$-uniform hypergraph $\mathcal{H}$, $\mathcal{A}_α(\mathcal{H})=α\mathcal{D}(\mathcal{H})+(1-α)\mathcal{A}(\mathcal{H})$ is called the $\mathcal{A}_α$-tensor of $\mathcal{H}$, where $\mathcal{D}(\mathcal{H})$ and $\mathcal{A}(\mathcal{H})$ are the degree tensor and adjacency tensor of $\mathcal{H}$, respectively. The sum of the $d$-th powers of all eigenvalues of $\mathcal{A}_α(\mathcal{H})$ is called the $d$-th order $\mathcal{A}_α$-spectral moment …

Series D, Episode 04 - Stardrive
AVON: That's one misfortune we don't have to share.
VILA: Fourteen I was when I was first sent to a penal colony. Ship was hit in the main drive by a meteoroid, bang! Y'know what they did to repair it? [Avon and Tarrant begin to look at Vila. As he continues they move in, listening to him.] Activated the force wall and generated an atmosphere inside the force wall so the repair team could work in a vacuum without spacesuits, 'caus…

Ravens RB Keaton Mitchell: I feel like I'm better than before 2023 knee injury https://www.nfl.com/news/ravens-rb-keaton-mitchell-i-feel-like-i-m-better-than-before-2023-knee-injury

This https://arxiv.org/abs/2501.17769 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Colimits of internal categories
We show that for an extensive $1$-category $\mathcal{E}$ with pullbacks and pullback stable coequalisers in which the forgetful functor $\mathcal{U}: \mathbf{Cat}(\mathcal{E})_1 \to \mathbf{Gph}(\mathcal{E})$ has left adjoint, the $2$-category $\mathbf{Cat}(\mathcal{E})$ of internal categories, functors and natural transformations has finite $2$-colimits. In addition, $\mathbf{Cat}(\mathcal{E})$ is extensive, has pullbacks and codescent coequalisers are stable under pullback along discrete Cond…

A generalized Birman-Schwinger principle and applications to one-dimensional Schr\"odinger operators with distributional potentials
Fritz Gesztesy, Roger Nichols
https://arxiv.org/abs/2507.02251

A generalized Birman-Schwinger principle and applications to one-dimensional Schrödinger operators with distributional potentials
Given a self-adjoint operator $H_0$ bounded from below in a complex Hilbert space $\mathcal{H}$, the corresponding scale of spaces $\mathcal{H}_{+1}(H_0) \subset \mathcal{H} \subset \mathcal{H}_{-1}(H_0) = [\mathcal{H}_{+1}(H_0)]^*$, and a fixed $V\in \mathcal{B}(\mathcal{H}_{+1}(H_0),\mathcal{H}_{-1}(H_0))$, we define the operator-valued map $A_V(\,\cdot\,):ρ(H_0)\to \mathcal{B}(\mathcal{H})$ by \[ A_V(z):=-\big(H_0-zI_{\mathcal{H}} \big)^{-1/2}V\big(H_0-zI_{\mathcal{H}} \big)^{-1/2}\in \math…

Suomalainen maitokulttuuri rakennettiin propagandan voimin https://animaliamedia.fi/suomalainen-maitokulttuuri-rakennettiin-propagandan-voimin/

Suomalainen maitokulttuuri rakennettiin propagandan voimin | Animalia-media
Vielä 1900-luvun alussa lehmänmaidolla oli arveluttava maine. Toisen eläimen maidon juonti ei ollut täysin itsestäänselvyys.

Four-dimensional operator systems without the lifting property
Samuel J. Harris
https://arxiv.org/abs/2508.00113 https://arxiv.org/pdf/2508.00113

Four-dimensional operator systems without the lifting property
The purpose of this note is to provide a family of explicit examples of $4$-dimensional operator systems contained in the Calkin algebra $\mathcal{Q}(\mathcal{H})$ on a separable infinite-dimensional Hilbert space $\mathcal{H}$ for which the identity map has no unital completely positive (ucp) lift to $\mathcal{B}(\mathcal{H})$ with respect to the canonical quotient map $π:\mathcal{B}(\mathcal{H}) \to \mathcal{Q}(\mathcal{H})$. More specifically, to each unital $C^*$-algebra $\mathcal{A}$ gene…

US-Geschworenengericht: Tesla trägt Mitschuld an tödlichem Unfall mit Autopilot
Tesla verliert einen Prozess wegen fahrlässiger Tötung durch "Autopilot" und soll Hunderte Millionen US-Dollar Schadenersatz zahlen. Der Autobauer wehrt sich.

Colts WR Adonai Mitchell feeling comfortable in Year 2: 'I knew it would eventually come together' https://www.nfl.com/news/colts-wr-adonai-mitchell-feeling-comfortable-in-year-2-i-knew-it-would-eventually-come-togeth…

Britische Bank Revolut tritt europäischem Bezahlsystem Wero bei
Das europäische Bezahlsystem Wero bekommt einen Schub: Die britische Bank Revolut wird Mitglied und will das System in seine App integrieren.