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Normalized solutions to Kirchhoff equation with the Sobolev critical exponent in high dimensional spaces
Ruikang Lu, Qilin Xie, Jianshe Yu
https://arxiv.org/abs/2509.13663 https…

Normalized solutions to Kirchhoff equation with the Sobolev critical exponent in high dimensional spaces
The following well-known Kirchhoff equation with the Sobolev critical exponent has been extensively studied, \begin{equation*} -\Big(a+b\int_{\mathbb R^N} | \nabla u|^2dx\Big) Δu+λu=μ|u|^{q-2}u+|u|^{2^*-2}u \ \ {\rm in}\ \ \mathbb{R}^N, \ \ N\geq4, \end{equation*} having prescribed mass $\int_{\mathbb R^N}|u|^2dx=c$, where $a$, $c$ are two positive constants, $b,μ$ are two parameters, $λ$ appears as a real Lagrange multiplier and $2

China’s CO2 emissions have now been flat or falling for 18 months.
The rapid adoption of electric vehicles (EVs) saw CO2 emissions from transport fuel drop by 5% year-on-year, while there were also declines from cement and steel production.
While emissions from the power sector were flat year-on-year, a big rise in the chemical industry’s CO2 output offset reductions elsewhere.

Analysis: China’s CO2 emissions have now been flat or falling for 18 months - Carbon Brief
China’s carbon dioxide (CO2) emissions were unchanged from a year earlier in the third quarter of 2025, extending a flat or falling trend that started in March 2024.

Detector-based measurement-induced state updates in AdS/CFT
Vijay Balasubramanian, Esko Keski-Vakkuri, Nicola Pranzini
https://arxiv.org/abs/2509.13457 https://

Detector-based measurement-induced state updates in AdS/CFT
Conventional understandings of quantum theory hold that measurements change the state of an observed system following the Lüders update rule. Textbooks describe the application of this idea to non-relativistic systems, but extensions to relativistic and gravitating systems encounter subtleties. One consistent approach is via detector-based measurements. We study the effects of such measurements in a CFT with a holographic dual. We work out the boundary space-time regions associated to a Lüder…

DIPLODOCUS II: Implementation of transport equations and test cases relevant to micro-scale physics of jetted astrophysical sources
Christopher N. Everett, Marc Klinger-Plaisier, Garret Cotter
https://arxiv.org/abs/2510.12505

DIPLODOCUS II: Implementation of transport equations and test cases relevant to micro-scale physics of jetted astrophysical sources
DIPLODOCUS (Distribution-In-PLateaux methODOlogy for the CompUtation of transport equationS) is a novel framework being developed for the general transport of particle distribution functions through the seven dimensions of phase space, including forcing terms and interactions between particles. Following Paper I, which details the background analytic framework, this second paper provides an overview of the numerical implementation in the form of the code package Diplodocus.jl, written in Julia,…

Spatial two-grid compact difference scheme for two-dimensional nonlinear diffusion-wave equations with variable exponent
Hao Zhang, Kexin Li, Wenlin Qiu
https://arxiv.org/abs/2510.12188

Spatial two-grid compact difference scheme for two-dimensional nonlinear diffusion-wave equations with variable exponent
This paper presents a spatial two-grid (STG) compact difference scheme for a two-dimensional (2D) nonlinear diffusion-wave equation with variable exponent, which describes, e.g., the propagation of mechanical diffusive waves in viscoelastic media with varying material properties. Following the idea of the convolution approach, the diffusion-wave model is first transformed into an equivalent formulation. A fully discrete scheme is then developed by applying a compact difference approximation in …

For #Caturday, a reminder that Widget remains available for adoption in the NYC metro area. She would prefer a calm house without kids (we are not a calm house). She's super affectionate! #CatsOfMastodon

Urban Adventure 🏞️
城市探险 🏞️
📷Zeiss Ikon Super Ikonta 533/16
🎞️Ilford HP5, expired 1993
#filmphotography #Photography #blackandwhite

Sunspot Observations in 1684-1702: John Flamsteed and Philippe de La Hire
Nadezhda Zolotova, Mikhail Vokhmyanin
https://arxiv.org/abs/2510.11375 https://ar…

Sunspot Observations in 1684-1702: John Flamsteed and Philippe de La Hire
In this work, we present an extensive review and detailed analysis of sunspot measurements, drawings, and engravings made by John Flamsteed and, mainly, by Philippe de La Hire during the Maunder minimum. All available information and contemporary knowledge about the sunspot nature are shown. The coordinates, areas, and numbers of sunspots and sunspot groups are reconstructed. Based on these observations, La Hire, Jean-Dominique Cassini, and his son Jacques Cassini regularly published results th…

Phase space analysis of an exponential model in $f(Q)$ gravity including linear dark-sector interactions
Ivan R. Vasquez, A. Oliveros
https://arxiv.org/abs/2510.12020 https://…

Phase space analysis of an exponential model in $f(Q)$ gravity including linear dark-sector interactions
We present a cosmological analysis of an exponential $f(Q)$ gravity model, within the dynamical systems formalism. Following the method introduced by Böhmer \textit{et al} [Universe \textbf{9} no.4, 166 (2023)], the modified Friedmann modified equations are successfully reduced to an autonomous system. Given the exponential form of $f(Q)$, the equilibrium conditions result in transcendental equations, which we approximate to identify the critical points. We therefore perform a general stabilit…

Finite element analysis of a nonlinear heat Equation with damping and pumping effects
Rishabh Shukla, Wasim Akram, Manil T. Mohan
https://arxiv.org/abs/2510.10210 https://

Finite element analysis of a nonlinear heat Equation with damping and pumping effects
We study the following nonlinear heat equation with damping and pumping effects (a reaction-diffusion equation) posed on a bounded simply connected convex domain $Ω\subset \mathbb{R}^d$, $d \geq 1$ with Lipschitz boundary $\partialΩ$: $$ \frac{\partial u(t)}{\partial t} - νΔu(t) + α|u(t)|^{p-2}u(t) - \sum_{\ell=1}^M β_{\ell} |u(t)|^{q_{\ell}-2}u(t) = f(t), \quad t>0, $$ subject to homogeneous Dirichlet boundary conditions and the initial condition $u(0)=u_0$, where $2 …