hello there the jacobian conjecture is false thanx to my close friend akhil for asking about it and my other close friend fable for working during the world cup final
((1+xy)^3 z + y^2 (1+xy) (4+3xy), y + 3 x (1+xy)^2 z + 3 x y^2 (4+3xy), 2 x - 3 x^2 y - x^3 z): \C^3\to \C^3, has jacobian determinant -2, and sends (0, 0, -1/4), (1, -3/2, 13/2), and (-1, 3/2, 13/2) to (-1/4, 0, 0)
The same way Odysseus used Sinon (this replacement of a man) to trick the Trojans to accept the horse, Nolan used Eliot Page to trick the left to admire a based movie.
Genius
Today we’re launching Medici, our 1st AI assistant for clinic owners w/o CFO & to boost those who have one.
Post mapping paper clinics to one central digital book, entering phase 2: real-time insights.
This gives owners faster feedback loops & advances our commitment towards a simpler, better, faster Healthcare system.
The rise and fall of wokeness: DEI commitments in corporate securities disclosures filed with the SEC. To me this seems a trailing indicator; most other measures of wokeness take off well before 2019 and peak in 2020 or 2021. But the shape! That's what a moral fashion looks like.
Imagine in your 2026 eyes being scandalized that in 1912 US Steel used more power than 1,000,000 homes. Of course it did. Of course it did.
This is what industrialization looks like. We are not outside of history but firmly within it.
Black Hole Can Ring Like a Bell
A Black Hole can vibrate after it is disturbed. Instead of settling instantly, its horizon releases gravitational waves in fading tones called quasinormal modes.
This is commonly known as Ringdown.
Each tone carries information about the black hole’s final mass and spin, which is why physicists call this Black-Hole Spectroscopy. In a way, when Spacetime strikes a Black Hole, the Black Hole answers with its own gravitational sound.
#BlackHole #GeneralRelativity #GravitationalWaves #Spacetime #Einstein #Astrophysics #Physics #Mathematics #Cosmology