Tootfinder

Shemar Stewart remains unsigned as Bengals rookies report for training camp https://www.nfl.com/news/shemar-stewart-remains-unsigned-as-bengals-rookies-report-for-training-camp

Las Vegas Raiders predicted to have shocking 53-man roster upsets at running back https://www.sportingnews.com/us/nfl/las-vegas-raiders/news/las-vegas-raiders-predicted-53-man-roster-upsets-running-ba…

🛌 Wissen fürs Kopfkissen: 📖
Kann #Geoengineering gegen die #Erderwärmung helfen?
Wenn technische #Klimalösungen zur Beeinflussung des

Geoengineering: Rettung vor der Erderwärmung oder gefährliches Spiel mit dem Klima?
Geoengineering als Klimaretter? Warum Experten vor Risiken warnen und was wirklich gegen die Erderwärmung hilft.

Deutschland fängt sich einen Tadel von der UNO ein, weil wir einen Innenminister Dobrindt haben, der sich einen Dreck um geltendes Recht schert.
Zeit, an die #Remonstrationspflicht zu erinnern! Die besagt, dass Beamt:innen die Pflicht haben, sich rechtswidrigen Anordnungen zu widersetzen.
Der UN-Hochkommissar für F…

RUSSIA HAS CROSSED THE LINE! Missiles and 344 drones are raining down on Ukraine: https://benborges.xyz/2025/07/19/russia-has-crossed-the-line.html

Cassini-Catalan Determinants via Ramanujan's Theta Identity
Nagananda K G, Jong Sung Kim
https://arxiv.org/abs/2508.11877 https://arxiv.org/pdf/2508.11…

Cassini-Catalan Determinants via Ramanujan's Theta Identity
In this paper, we show that the classical Cassini and Catalan identities for Fibonacci numbers arise naturally from a single quadratic theta-function identity of Ramanujan. Expanding the identity $ψ(q)ψ(q^{3})=ψ(q^{4})φ(q^{6})+q\,φ(q^{2})ψ(q^{12})$ via the Jacobi triple product and equating coefficients yields the unified $q$-determinant $F_{n+r}(q)F_{n-r}(q)-F_{n}(q)^{2}=(-q)^{\,n-r}F_{r}(q)^{2}$, $n\ge r\ge 1$, where $ψ(q)$ and $φ(q)$ are Ramanujan's theta functions with $q$ a complex…

Europe’s Leaders Avoided A Giveaway to Putin, but Emerged Without a Clear Path
The leaders dropped everything to travel to Washington
to ensure President Trump didn’t force a bad deal on Ukraine.
A road map for peace remains elusive.
The seven European leaders put forward a show of support for Mr. Zelensky and unity with each other.
They won a potentially vital, if vague, expression of support from Trump for postwar security guarantees for Ukraine
and sid…

Europe’s Leaders Headed Off Giveaway to Putin, but Emerged Without a Clear Path
The leaders dropped everything to travel to Washington to ensure President Trump didn’t force a bad deal on Ukraine. A road map for peace remains elusive.

Pick Six: Pete Carroll, Chip Kelly running into old friends as team takes on Commanders https://www.raiders.com/news/pick-six-pete-carroll-chip-kelly-running-into-old-friends-as-team-takes-on-commanders

Randy Villegas is an educator, activist, and proud son of immigrants. Born and raised in Kern, California, in a working-class family, Randy knows firsthand the challenges that many Central Valley families face.
His journey - from earning a PhD to teaching and organizing for change - has been rooted in one core belief: that government should work for everyone, not just the powerful few.
With deep ties to our community and a lifelong commitment to justice and equity, Randy is running…

Pick Six: Pete Carroll, Chip Kelly running into old friends as team takes on Commanders https://www.raiders.com/news/pick-six-pete-carroll-chip-kelly-running-into-old-friends-as-team-takes-on-commanders