Trump’s tendency to point fingers at others is increasingly in the spotlight
As November’s midterm elections approach Republicans are trying to retain control of Congress
But Trump's unwillingness to accept blame sometimes leads him to deny that there are problems at all,
and could leave GOP leaders in tight races with little reassurance for voters that their concerns are being addressed.
"How water companies could charge you more during drought"
#UK #UnitedKingdom #Drought #Water
Sonnet 074 - LXXIV
But be contented when that fell arrest
Without all bail shall carry me away,
My life hath in this line some interest,
Which for memorial still with thee shall stay.
When thou reviewest this, thou dost review
The very part was consecrate to thee:
The earth can have but earth, which is his due;
My spirit is thine, the better part of me:
So then thou hast but lost the dregs of life,
The prey of worms, my body being d…
@… yes, so they are being consistent:
https://www.eff.org/document/amicus-brief-eff-et-al-thomson-reuters-…
The upper semi-Fredholm radius, extensions of restrictions, and subprojectivity
Abdelhalim Azzouz
https://arxiv.org/abs/2610.03835 https://arxiv.org/pdf/2610.03835 https://arxiv.org/html/2610.03835
arXiv:2610.03835v1 Announce Type: new
Abstract: For a bounded operator $T$ between Banach spaces, let $d_ (T)$ be its distance to the operators that are not upper semi-Fredholm, and let $\inn(T)$ be Schechter's quantity $\inf\|T|_M\|$ over infinite-dimensional subspaces $M$. One always has $\inn(T)\le d_ (T)$, and Gonz\'alez and Martin\'on showed that the two quantities are not equivalent in general. We prove that $d_ (T)$ is the infimum of the norms of operators on the whole space that extend a restriction of $T$ to some infinite-dimensional subspace. The gap between $\inn$ and $d_ $ thus becomes an extension problem, and projection constants enter naturally.
If the domain is uniformly subprojective with constant $\lambda$, then $d_ \le\lambda\,\inn$. In the other direction we prove a quantitative obstruction: a complemented Hilbertian subspace all of whose infinite-dimensional subspaces have projection constant at least $\Lambda$ produces operators with $d_ /\inn\ge\Lambda/2$. Consequently, on the subprojective but not uniformly subprojective space $(\bigoplus_nL_{p_n})_{\ell_2}$ with $p_n\to\infty$, there is no uniform comparison between $\inn$ and $d_ $. We conjecture that uniform comparison is equivalent to uniform subprojectivity.
Finally, we compute $\inn$ for inverses and for shears in terms of the quantity $\tau(T)=\sup_M j(T|_M)$, and we use the arbitrary distortability of Hilbert space to show that a rectangular diagonal operator $\operatorname{diag}(A,B)$ built from two isomorphisms with $\inn(A)=\inn(B)=1$ can have arbitrarily small $\inn$. In contrast, every operator $T$ on a complex Banach space satisfies $\inn(T)\le\tau(T)$, so every automorphism satisfies $\inn(T)\,\inn(T^{-1})\le1$ and the same mechanism cannot work for endomorphisms.
toXiv_bot_toot
The Trump administration is deliberately
targeting children who came to the US unaccompanied by a parent or guardian
as it pushes to quickly return them to the countries they fled
– amid “drastic policy changes” in immigration courts,
according to allegations in a federal lawsuit shared with the Guardian.
The plaintiffs in the lawsuit are trying to prevent imminent deportation to the places from where they escaped danger or harm.
The complaint, filed befor…
Get Rich Slow Club
This isn't a get rich quick scheme, instead it's all about being consistent, and focusing on long-term growth...
Great Australian Pods Podcast Directory: https://www.greataustralianpods.com/get-rich-slow-club/
Crosslisted article(s) found for astro-ph.CO. https://arxiv.org/list/astro-ph.CO/new
[1/1]:
- Consistent Thermal Resummation and Phase Transitions with 2PI Methods
Amitayus Banik, Kimmo Kainulainen
https://arxiv.org/abs/2608.04102 https://mastoxiv.page/@arXiv_hepph_bot/117047502693663591
- Amnesia in the Axion Misalignment Landscape
Kierthika Chathirathas, Cem Er\"oncel, Mathieu Kaltschmidt, Javier Redondo, Kenichi Saikawa
https://arxiv.org/abs/2608.04139 https://mastoxiv.page/@arXiv_hepph_bot/117047523928429238
- Corrections to Hawking radiation from asteroid-mass primordial black holes: analytic and numerica...
Gabriel Vasquez, Bowen Chen, Cara Nel, Emily Koivu, Makana Silva, Christopher M. Hirata
https://arxiv.org/abs/2608.04346 https://mastoxiv.page/@arXiv_grqc_bot/117047445284689579
- Relativistic Signatures of Dark Matter Equations of State in Static Spherically Symmetric Spacetimes
Akash Yadav, Sudhava Yadav, K. K. Venkataratnam
https://arxiv.org/abs/2608.04470 https://mastoxiv.page/@arXiv_grqc_bot/117047473794282581
- Inflow-driven galaxy evolution - I. Revealing the physics of the fundamental metallicity relation
Kai Wang, et al.
https://arxiv.org/abs/2608.04784 https://mastoxiv.page/@arXiv_astrophGA_bot/117047534350606403
- Evolution of matter perturbations in the context of cosmic slowing down
D. Koh Cuende, G. Panotopoulos
https://arxiv.org/abs/2608.04922 https://mastoxiv.page/@arXiv_grqc_bot/117047514099918452
- Post-Inflationary Constraints on Nonminimally Coupled Quintessential Inflation
Min Gi Park, Seong Chan Park, Tomo Takahashi, Jos\'e Jaime Terente D\'iaz
https://arxiv.org/abs/2608.05079 https://mastoxiv.page/@arXiv_grqc_bot/117047542803232910
- CCAT: Design and Characterization of the 350 GHz Instrument Module
Ben Keller, et al.
https://arxiv.org/abs/2608.05121 https://mastoxiv.page/@arXiv_astrophIM_bot/117047574262723419
toXiv_bot_toot
They tell me that Open AI have solved four hundred previously open maths problems this week.
The news media, and even the mathematicians, seem quite credulous about it.
No way to know how many of those will really stand up in the end. Lots of proofs turn out not to be really proofs coz they have a mistake, and AI is quite good at discovering mistakes as well as now apparently discovering maths.
Some of them are counter-examples that prove the conjecture is false and those are gonna be good at last. Machines can check it.
Some have other types of mechanical machine-checkable proof, which is interesting in that we can all believe the checker-machine: coz it's deterministic and understandable.
We can't trust the machine that isn't deterministic or understandable as much though.
GPT says these things are true. Now maths people have to check, because OpenAI staff aren't expert mathematicians either, mostly.
Some of the 400 proofs will fall, I'm sure.
How many tokens will be spent before machines find the flaws that are surely still there? How many tokens until you decide to stop?
But if a machine can prove a thing to itself, but not explain it to any person, is it really doing maths? Even if it's correct more often than people are? Or is doing maths more about making meat understand a thing?
🤔
I'm sure I can't tell if the proofs are true or not. No point me reading them. Mostly won't even understand the question. The boundary of my meager meat-mind's maths-understanding was around barely-degree level.
Can the academic discipline continue as one which is devoted mostly to trying to understand the output of a machine writing about maths, which is mostly right but nobody can really tell without an entire academic discipline trying to check.
In other words, mathematicians now also face a spam problem familiar to many github project leads.
#ai #maths
It’s been four years since the Supreme Court’s decision in Dobbs v. Jackson Women’s Health Organization overturned Roe v. Wade,
ending the federal constitutional right to abortion.
In the immediate aftermath of the decision, national attention centered on implementation of state bans and a rapidly shifting legal landscape.
But four years later, one of the most impactful developments has been less visible:
👉 a significant, sustained and politically consequential shif…