Tootfinder

Non-radial solutions for the critical quasi-linear H\'{e}non equation involving $p$-Laplacian in $\R^N$
Wei Dai, Lixiu Duan, Changfeng Gui, Yuan Li
https://arxiv.org/abs/2508.13539

Non-radial solutions for the critical quasi-linear Hénon equation involving $p$-Laplacian in $\R^N$
In this paper, we investigate the following $D^{1,p}$-critical quasi-linear Hénon equation involving $p$-Laplacian \begin{equation*}\label{00} \left\{ \begin{aligned} &-Δ_p u=|x|^αu^{p_\al^*-1}, & x\in \R^N, \\ &u>0, & x\in \R^N, \end{aligned} \right. \end{equation*} where $N\geq2$, $10$. By carefully studying the linearized problem and applying the approximation method and bifurcation theory, we prove that, when the parameter $\al$ ta…

At least he understood the location and extent of our problem. Not great on the solution side, but we will be workshopping that... https://bird.makeup/users/macfarlanenews/statuses/1969117630578540785

Scott MacFarlane
ALERT: Justice Dept will seek minimum 30-year prison term for Nicholas Roske, the California man who pleaded guilty in attempt to assassinate Justice Brett Kavanugh Feds argue Roske was targeting UP TO THREE justices for assassination COURT FILING: https://storage.courtlistener.com/recap/gov.uscourts.mdd.514255/gov.uscourts.mdd.514255.98.0.pdf

I'm dispositionally sceptical of falling sky prophesies and what Mr Schneier calls "movie plot threats".
But.
I can't deny I'm a bit nervous that all this noisy dancing up to the edge of disaster and back might be a deliberate scheme, intended to get European militaries locked up on the Eastern front from Finland to Romania, before China finally have a crack at Taiwan.
"Estonia seeks Nato consultation after Russian jets violate airspace"

Nato intercepts Russian warplanes violating Estonian airspace
Estonia says three Russian MiG-31 fighter jets remained in Estonian airspace for 12 minutes.

The Milky Way is a less massive galaxy--new estimates of the Milky Way's local and global stellar masses
Jianhui Lian (Yunnan Uni.), Tao Wang (Yunnan Uni.), Qikang Feng (Peking Uni.), Yang Huang (U of Chinese Academy of Sciences), Helong Guo (Yunnan Uni.)
https://arxiv.org/abs/2508.13665

The Milky Way is a less massive galaxy--new estimates of the Milky Way's local and global stellar masses
Stellar mass is the most fundamental property of a galaxy. While it has been robustly measured for millions of external galaxies, it remains poorly constrained for the Milky Way because of the strong selection effect from our inside perspective. In this work, we reconstruct the intrinsic vertical mass density profile in the solar neighborhood and the radial mass density profile across the entire Galaxy using data from the Gaia and APOGEE surveys, following careful correction for the selection f…

“This is not a hoax, and it’s not going away,”
said Epstein survivor Marina Lacerda.
Trump’s struggles reveal the limits of his usual tactics.
His strategy
—harnessing the anger caused by inequality to deflect blame
—has faltered here.
To understand why, we must look beyond Epstein as a predator to examine the system that protected him.
Documents recently released from Epstein’s estate expose the extent of his aristocratic immunity.
In a 2008 plea …

The real reason Donald Trump can’t escape the Epstein scandal
Donald Trump’s usual tactics to deflect blame are failing as victims of Jeffrey Epstein expose the deep inequalities that protected the predator, and now implicate Trump himself.

Biharmonic nonlinear vector field equations in $\mathbb{R}^4$
Ioannis Arkoudis, Panayotis Smyrnelis
https://arxiv.org/abs/2508.14640 https://arxiv.org/pdf/…

Biharmonic nonlinear vector field equations in $\mathbb{R}^4$
Following the approach of Brezis and Lieb, we prove the existence of a ground state solution for the biharmonic nonlinear vector field equations in the limiting case of space dimension $4$. Our results complete those obtained by Mederski and Siemianowski for dimensions $d\geq 5$. We also extend the biharmonic logarithmic Sobolev inequality to dimension $4$.

HBAR entropy in causal diamond geometry: A near-horizon perspective
Nada Eissa, Carlos R. Ord\'o\~nez, Gustavo Valdivia-Mera
https://arxiv.org/abs/2508.13493 https://…

HBAR entropy in causal diamond geometry: A near-horizon perspective
In this article we extend the Horizon Brightened Acceleration Radiation (HBAR) framework to the causal diamond (CD) spacetime. We study a cloud of two-level atoms, injected at random times in the asymptotic past of the CD, freely falling toward its causal horizon and emitting scalar radiation via a weak dipole coupling to a quantum field. In the near-horizon region, an emergent conformal symmetry-captured by conformal quantum mechanics (CQM)-governs the field dynamics and allows analytic contro…

Apparent Resonance Splitting in Self-Coupled Excitonic Systems
Avishek Sarbajna, Qitong Li, Dorte Rub{\ae}k Danielsen, Skyler Peitso Selvin, Duc Hieu Nguyen, Manh-Ha Doan, Peter B{\o}ggild, Mark L. Brongersma, S{\o}ren Raza
https://arxiv.org/abs/2508.11370

Apparent Resonance Splitting in Self-Coupled Excitonic Systems
Thin films of high-refractive-index excitonic materials enable self-coupling by simultaneously supporting intrinsic excitonic transitions and optical resonances. These optical resonances take the form of Fabry-Perot resonances in thick films and absorption resonances in ultrathin films placed on metallic substrates. Here, we investigate whether these optical resonances lead to true exciton-photon hybridization. Using far-field reflectance and spectrally resolved photocurrent measurements, we st…

Having a meeting going over a "IT Resource Provisioning Guidelines" document.
Feeling a very strong urge to play a gummy game. Or scream. The extent of bikeshedding is painful.
It's especially annoying how the bullet points which came from somewhere generic really do not work for a team of our scale with the sorts of systems we manage. e.g. on most systems the only network-login-capable accounts are sysadmins, most of whom rarely log in but all of whom need work…

Normalized solution for Kirchhoff equation with upper critical exponent and mixed Choquard type nonlinearities
Jinyuan Shang, Wenting Zhao, Xianjiu Huang
https://arxiv.org/abs/2509.14681

Normalized solution for Kirchhoff equation with upper critical exponent and mixed Choquard type nonlinearities
In this paper, we consider the existence of normalized solution to the following Kirchhoff equation with mixed Choquard type nonlinearities: \begin{equation*} \begin{cases} -\left(a + b \int_{\mathbb{R}^3} |\nabla u|^2 \, dx\right) Δu - λu = μ|u|^{q-2} u + (I_α* |u|^{α+ 3}) |u|^{α+1} u, \quad x \in \mathbb{R}^3, \\ \int_{\mathbb{R}^3} u^2 \, dx = ρ^2, \end{cases} \end{equation*} where $a,b,ρ>0$, $α\in \left(0, 3\right)$, $\frac{14}{3} < q < 6$ an…