Tootfinder

I've finished this week's New European, my dose of comforting confirmatory bias that leaves me angry, almost satisfied and a feeling of intellectual and cultural superiority to 'them'.
This may not be a Good Thing.
But realising it is at least sane.
#NewEuropean #StillAngry

Im using case_when() quite a lot, case_match() is new to me: #rstats

A problem with the Stack Exchange Data Dump is that it's an unwieldy pile of XML files.
I wrote a script to process it down into SQLite databases with basic indexes to make it more usable out of the box. Just finished uploading it to the Internet Archive
https://archive.org/details/SEqlite<…

SEqlite : Stack Exchange Community : Free Download, Borrow, and Streaming : Internet Archive
A SQLite version of the Stack Exchange Data Dump. 100% Unendorsed by Stack Exchange. Terms same as the original.The following is reproduced from the original...

Local Fourier uniformity of higher divisor functions on average
Mengdi Wang
https://arxiv.org/abs/2402.18342 https://arxiv.org/pdf/24…

Local Fourier uniformity of higher divisor functions on average
Let $τ_k$ be the $k$-fold divisor function. By constructing an approximant of $τ_k$, denoted as $τ_k^*$, which is a normalized truncation of the $k$-fold divisor function, we prove that when $\exp\left(C\log^{1/2}X(\log\log X)^{1/2}\right)\leq H\leq X$ and $C>0$ is sufficiently large, the following estimate holds for almost all $x\in[X,2X]$: \[ \Big|\sum_{x

Laut Beschreibung ist dies eine ehemalige "Mietskasernen" und das Gerichtsgebäude in der sehenswerten Stadt #Bamberg. #Reise

This https://arxiv.org/abs/2404.10616 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLO_…

One is all you need: Second-order Unification without First-order Variables
We consider the fragment of Second-Order unification with the following properties: (i) only one second-order variable allowed, (ii) first-order variables do not occur. We show that Hilbert's 10$^{th}$ problem is reducible to this fragment if the signature contains a binary function symbol and two constants. This generalizes known undecidability results. Furthermore, We show that adding the following restriction: (i) the second-order variable has arity 1, (ii) the signature is finite, and (iii)…

Im using case_when() quite a lot, case_match() is new to me: #rstats

Graphics Processing Unit/Artificial Neural Network-accelerated large-eddy simulation of turbulent combustion: Application to swirling premixed flames
Min Zhang, Runze Mao, Han Li, Zhenhua An, Zhi X. Chen
https://arxiv.org/abs/2402.18858

Graphics Processing Unit/Artificial Neural Network-accelerated large-eddy simulation of turbulent combustion: Application to swirling premixed flames
Within the scope of reacting flow simulations, the real-time direct integration (DI) of stiff ordinary differential equations (ODE) for the computation of chemical kinetics stands as the primary demand on computational resources. Meanwhile, as the number of transport equations that need to be solved increases, the computational cost grows more substantially, particularly for those combustion models involving direct coupling of chemistry and flow such as the transported probability density funct…

Multiplicity results for fully nonlinear elliptic equations with natural gradient growth
Mohan Mallick, Ram Baran Verma
https://arxiv.org/abs/2404.19042 https://arxiv.org/pdf/2404.19042
arXiv:2404.19042v1 Announce Type: new
Abstract: In this paper, we prove a theorem concerning the existence of three solutions for the following boundary value problem: \begin{equation*} -\mathcal{M}_{\lambda,\Lambda}^ (D^2u)-\Gamma|Du|^2=f(u)~~~\text{in}\ \Omega, u=0~~~\text{on}\ \partial\Omega, \end{equation*} where $f:[0,\infty]\to[0,\infty]$ is a $C^{\alpha}$ function and $\Omega$ denotes a bounded, smooth domain in $\mathbb{R}^N$. By constructing two ordered pairs of sub and supersolutions for a specific class of $f$ exhibiting sublinear growth, we further establish the existence of three positive solutions to the aforementioned boundary value problem.

Sixth-order parabolic equation on an interval: Eigenfunction expansion, Green's function, and intermediate asymptotics for a finite thin film with elastic resistance
Nectarios C. Papanicolaou, Ivan C. Christov
https://arxiv.org/abs/2402.18740

Sixth-order parabolic equation on an interval: Eigenfunction expansion, Green's function, and intermediate asymptotics for a finite thin film with elastic resistance
A linear sixth-order partial differential equation (PDE) of ``parabolic'' type describes the dynamics of thin liquid films beneath surfaces with elastic bending resistance when deflections from the equilibrium film height are small. On a finite domain, the associated sixth-order Sturm--Liouville eigenvalue value problem is self-adjoint for the boundary conditions corresponding to a thin film in a closed trough, and the eigenfunctions form a complete orthonormal set. Using these eigenfunctions, …