Tootfinder

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

As Cyber Threats Escalate, the National Vulnerability Database Is Falling Behind
The National Institute of Standards and Technology (NIST) is struggling.
It faces a growing backlog to process data in its vulnerability repository, which publicly shares information assessing and detailing mitigation solutions against new cyber exploits.
With nearly 1,800 new reported vulnerabilities sitting in a queue for analysis this year, delays in processing leave the United States increa…

Skyrmion-Antiskyrmion Lattice: A Net-Zero Topological Phase in Low-Symmetry Frustrated Chiral Magnets
Sayan Banik, Ashis K. Nandy
https://arxiv.org/abs/2509.14207 https://

Skyrmion-Antiskyrmion Lattice: A Net-Zero Topological Phase in Low-Symmetry Frustrated Chiral Magnets
We report the discovery of a thermodynamically stable skyrmion-antiskyrmion lattice in two-dimensional heterostructures, a novel state exhibiting a net-zero global topological charge owing to an equal population of skyrmions and antiskyrmions. This surprising coexistence of oppositely charged solitons remarkably circumvents their anticipated annihilation. We demonstrate the formation and evolution of this phase in Fe films on C1v -symmetric (110) surfaces of GaAs and CdTe semiconductors. Specif…

Subnormal transcendental meromorphic solutions of difference equations with Schwarzian derivative
M. T. Xia, J. R. Long, X. X. Xiang
https://arxiv.org/abs/2510.10626 https://

Subnormal transcendental meromorphic solutions of difference equations with Schwarzian derivative
The existence of subnormal solutions of following three difference equations with Schwarzian derivative $$ω(z+1)-ω(z-1)+a(z)(S(ω,z))^n=R(z,ω(z)),$$ $$ω(z+1)ω(z-1)+a(z)S(ω,z)=R(z,ω(z)),$$ and $$(ω(z)ω(z+1)-1)(ω(z)ω(z-1)-1)+a(z)S(ω,z)=R(z,ω(z))$$ are studied by using Nevanlinna theory, where $n\ge 1$ is an integer, $a(z)$ is small with respect to $ω$, $S(ω,z)$ is Schwarzian derivative, $R(z,ω)$ is rational in $ω$ with small meromorphic coefficients with respect to $ω$. The nece…

Regular Lagrangians in Lefschetz fibrations
Joseph Breen, Agniva Roy, Luya Wang
https://arxiv.org/abs/2510.12170 https://arxiv.org/pdf/2510.12170

Regular Lagrangians in Lefschetz fibrations
We characterize regularity of Lagrangian submanifolds in Weinstein Lefschetz fibrations, establishing a conjecture of Giroux and Pardon. Our main result is the Weinstein analogue of a closed symplectic Lefschetz pencil result of Auroux, Muñoz, and Presas. As an application, given a Legendrian link in tight $S^3$ and an exact filling which is part of an arboreal skeleton for the $4$-ball, we build a Lefschetz fibration such that the image of the filling and all of its mutations are arcs in the …

After almost two centuries,
Baker & Taylor,
a nationwide library book distributor,
will reportedly shut down operations in January.
Baker & Taylor CEO Aman Kochar told employees Monday that following a recent failed acquisition deal with ReaderLink, the Charlotte-based company has no viable path forward, though he had hoped to find another solution

Baker & Taylor Prepares Plan to Shut Down
At a town hall yesterday, B&T owner and CEO Aman Kochar announced that following the termination of the ReaderLink acquisition deal, he does not see a path to keep the library wholesaler in business.

Lässt euch das Urteil des Landgerichts München (Aktenzeichen 42 O 14139/24) auch grad so Atemlos?
Bin ja eher selten ein Fan von GEMA oder Helene Fischer, aber... 🥳⚖️
https://www.heise.de/news/GEMA-vs-OpenAI-Niederlage-fuer-ChatGPT-v…

GEMA vs. OpenAI: Niederlage für ChatGPT vor Münchner Gericht
Das Landgericht München hat gegen OpenAI entschieden. Geklagt hatte die GEMA – es geht um Liedtexte von Helene Fischer und mehr.

If you're using #ForgeJo and are experiencing the error
`fatal: the remote end hung up unexpectedly` when doing "git push", the problem is the client buffer size for HTTP pushes. In my case I have just fixed it by doing the following:
`$ git config http.postBuffer 157286400`
I've found the solution here:

Exact BPS double-kinks in generalized $\phi^4$, $\phi^6$ and sine-Gordon models
R. Casana, E. da Hora, F. C. Simas
https://arxiv.org/abs/2510.09856 https://

Exact BPS double-kinks in generalized $ϕ^4$, $ϕ^6$ and sine-Gordon models
We consider a $(1+1)$-dimensional theory with a single real scalar field $ϕ$ whose kinematics is modified by a generalizing function $f(ϕ)$. After briefly reviewing its Bogomol'nyi-Prasad-Sommerfield (BPS) structure, we focus on a particular $f(ϕ)$ to obtain analytic BPS double-kink solutions in three different models governed by the $ϕ^4$, $ϕ^6$, and sine-Gordon superpotentials. In all cases, the resulting double-kinks approach the boundaries by following an exponential decay, with the ge…

Multiple sign-changing solutions for semilinear subelliptic Dirichlet problem
Hua Chen, Hong-Ge Chen, Jin-Ning Li, Xin Liao
https://arxiv.org/abs/2510.10120 https://

Multiple sign-changing solutions for semilinear subelliptic Dirichlet problem
We study the following perturbation from symmetry problem for the semilinear subelliptic equation \[ \left\{ \begin{array}{cc} -\triangle_{X} u=f(x,u)+g(x,u) & \mbox{in}~Ω, \\[2mm] u\in H_{X,0}^{1}(Ω),\hfill \end{array} \right. \] where $\triangle_{X}=-\sum_{i=1}^{m}X_{i}^{*}X_{i}$ is the self-adjoint sub-elliptic operator associated with Hörmander vector fields $X=(X_{1},X_{2},\ldots,X_{m})$, $Ω$ is an open bounded subset in $\mathbb{R}^n$, and $H_{X,0}^{1}(Ω)$ denotes the weigh…