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"Curvature of differentiable Hilbert modules and Kasparov modules" by Bram Mesland, Adam Rennie et al.

In this paper we introduce the curvature of densely defined universal connections on Hilbert C⁎-modules relative to a spectral triple (or unbounded Kasparov module), obtaining a well-defined curvature operator. Fixing the spectral triple, we find that modulo junk forms, the curvature only depends on the represented form of the universal connection. We refine our definition of curvature to factorizations of unbounded Kasparov modules. Our definition recovers all the curvature data of a Riemannian submersion of compact manifolds, viewed as a KK-factorization. ....

K Theory , Oncommutative Geometry , Iemannian Submersion , Pectral Triples ,

The Famous Fossils Scientists Got Incredibly Wrong

We sort of take for granted the depictions of prehistoric beasties illustrated in the books of our childhood. But piecing together Earth s murky past is a lot harder than it sounds. ....

Waals Gewest , Ghedoghedo Wikimedia Commons , Gideon Mantell , University Of Oregon , Wikimedia Commons , Public Domain ,

KGO ABC World News Tonight With David Muir December 12, 2021 00:19:00

The capsule landing safely back on earth. tj watching on in studio, with amy and me on the ground in west texas. it was great. reporter: just more than ten minutes after liftoff, the capsule landing safely back on earth, met by blue origin founder jeff bezos. and this touching moment. michael sharing a hug with fellow crew member. laura shepard churchley, the daughter of the first american in space, alan shepard. amy catching up with michael after his once-in-lifetime flight. just see the curvature, the atmosphere, blue, the earth, just it was too short. astronaut strahan going to the moon next? if they invite me i m going to the moon, and i m going to walk and talk, moon walk. reporter: independent got to tell you, i ve seen a lot of space launches but there s something very different about seeing your own friend go up ....

Capsule Landing , Tj Watching , West Texas , Laura Shepard Churchley , Michael Strahan , Blue Origin , First American In Space , Alan Shepard , Jeff Bezos , Michael Sharing A , Astronaut Strahan , Moon Walk ,

CNN At This Hour With Kate Bolduan December 9, 2021 16:56:00

Overwhelming sadness up there when i saw the earth and how tiny the earth is. i mean, we say tiny, but when you can see the curvature from where you re standing and, realize one end connects to the other for a very short while, you realize it isn t just tiny, it s insignificant, and we are so insignificant. and the fact that we re my sadness came about by the knowledge of how much harm we re doing our earth and when i am able to think about it more, kate. here s the conclusion i ve arrived at. it s terrible what we re doing to the earth and we need to fix it immediately. that s the general lesson, but it s also how insignificant the earth is, the planet is, compared to space and how incomparably insignificant we are on the planet, so there s ....

Progress Isn T , Kate Bolduan ,

BBCNEWS Click November 25, 2021 03:35:00

Are the sutures the ones that are working still, the growth lines. so, the way we do the surgery is we make a small window in the bone here. the algorithms needed to create these images have been made possible by the harnessing of data from 60 operations over the course of the last seven years. so here, the grey is the head shape as it s now, the green is the predicted head shape, so the first change that you can see is that the back of his head which, at the moment is sloping down, is pushed up a little and there s a more regular curvature to it. this immersive experience allows the parents to see from all angles a truly personalised picture of exactly how archie s head can be reshaped with surgery. would you like us to suggest anything about the head shape that you would like to see done differently? ....

Growth Lines , Sloping Down ,