Tootfinder

This https://arxiv.org/abs/2307.15819 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Small-time controllability for the nonlinear Schrödinger equation on $\mathbb{R}^N$ via bilinear electromagnetic fields
We address the small-time controllability problem for a nonlinear Schrödinger equation (NLS) on $\mathbb{R}^N$ in the presence of magnetic and electric external fields. We choose a particular framework where the equation becomes $i\partial_t ψ= [-Δ+u_0(t)h_{\vec{0}}+\langle u(t), P\rangle +κ|ψ|^{2p}]ψ$. Here, the control operators are defined by the zeroth Hermite function $h_{\vec{0}}(x)$ and the momentum operator $P=i\nabla$. In detail, we study when it is possible to control …

Direct and Inverse Problems in Baumslag-Solitar Group $BS(1,3)$
Sandeep Singh, Ramandeep Kaur
https://arxiv.org/abs/2402.16128 https://

Direct and Inverse Problems in Baumslag-Solitar Group $BS(1,3)$
For integers $m$ and $n$, the Baumslag-Solitar groups, denoted as $BS(m,n)$, are groups generated by two elements with a single defining relation: $BS(m,n) = \langle a, b | a^mb=ba^n\rangle$. The sum of dilates, denoted as $r \cdot A + s \cdot B$ for integers $r$ and $s$, is defined as $\{ra + sb; a\in A, b\in B\}$. In 2014, Freiman et al. \cite{freiman} derived direct and inverse results for sums of dilates and applied these findings to address specific direct and inverse problems within …

This https://arxiv.org/abs/1805.08606 has been replaced.
link: https://scholar.google.com/scholar?q=a

A set-based reasoner for the description logic $\mathcal{DL}_{\mathbf{D}}^{4,\!\times}$ (Extended Version)
We present a KE-tableau-based implementation of a reasoner for a decidable fragment of (stratified) set theory expressing the description logic $\mathcal{DL}\langle \mathsf{4LQS^{R,\!\times}}\rangle(\mathbf{D})$ ($\mathcal{DL}_{\mathbf{D}}^{4,\!\times}$, for short). Our application solves the main TBox and ABox reasoning problems for $\mathcal{DL}_{\mathbf{D}}^{4,\!\times}$. In particular, it solves the consistency problem for $\mathcal{DL}_{\mathbf{D}}^{4,\!\times}$-knowledge bases represented…

Sources: Social Capital fired two of its partners after they tried to raise ~$2M from outside the firm for AI chipmaker Groq, which rankled Chamath Palihapitiya (Lizette Chapman/Bloomberg)
https://www.bloomberg.com/news/articles/20

Social Capital AI Startup Deal Led Palihapitiya to Fire Partners
Venture capital firm Social Capital suddenly fired two of its partners after they tried to raise outside money for an artificial intelligence startup — an endeavor that provoked the ire of the firm’s leader, high-profile investor Chamath Palihapitiya.

Direct and Inverse Problems in Baumslag-Solitar Group $BS(1,3)$
Sandeep Singh, Ramandeep Kaur
https://arxiv.org/abs/2402.16128 https://

Direct and Inverse Problems in Baumslag-Solitar Group $BS(1,3)$
For integers $m$ and $n$, the Baumslag-Solitar groups, denoted as $BS(m,n)$, are groups generated by two elements with a single defining relation: $BS(m,n) = \langle a, b | a^mb=ba^n\rangle$. The sum of dilates, denoted as $r \cdot A + s \cdot B$ for integers $r$ and $s$, is defined as $\{ra + sb; a\in A, b\in B\}$. In 2014, Freiman et al. \cite{freiman} derived direct and inverse results for sums of dilates and applied these findings to address specific direct and inverse problems within …

This https://arxiv.org/abs/2308.11663 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The direct product of a star and a path is antimagic
A graph $G$ is antimagic if there exists a bijection $f$ from $E(G)$ to $\left\{1,2, \dots,|E(G)|\right\}$ such that the vertex sums for all vertices of $G$ are distinct, where the vertex sum is defined as the sum of the labels of all incident edges. Hartsfield and Ringel conjectured that every connected graph other than $K_2$ admits an antimagic labeling. It is still a challenging problem to address antimagicness in the case of disconnected graphs. In this paper, we study antimagicne…

Schon lustig, daß ich jetzt zwar 25g Gras mit mir rumschleppen dürfte, aber nach wie vor an nix rankomme, während der Fünftklässler da wahrscheinlich weniger Probleme hätte, weil er ja täglich auf dem Marktplatz ist. (Weiß nix konkretes über die Schule aber nehme mal an, daß es noch so läuft wie zu meiner Zeit.)

This https://arxiv.org/abs/1805.08606 has been replaced.
link: https://scholar.google.com/scholar?q=a

A set-based reasoner for the description logic $\mathcal{DL}_{\mathbf{D}}^{4,\!\times}$ (Extended Version)
We present a KE-tableau-based implementation of a reasoner for a decidable fragment of (stratified) set theory expressing the description logic $\mathcal{DL}\langle \mathsf{4LQS^{R,\!\times}}\rangle(\mathbf{D})$ ($\mathcal{DL}_{\mathbf{D}}^{4,\!\times}$, for short). Our application solves the main TBox and ABox reasoning problems for $\mathcal{DL}_{\mathbf{D}}^{4,\!\times}$. In particular, it solves the consistency problem for $\mathcal{DL}_{\mathbf{D}}^{4,\!\times}$-knowledge bases represented…

This https://arxiv.org/abs/2309.10124 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

General Optimal Step-size for ADMM-type Algorithms: Domain Parametrization and Optimal Rates
In this work, we solve a 49-year open problem, the general optimal step-size for ADMM-type algorithms. For a convex program: $\text{min.} \,\, f({x}) + g({z})$, $\text{s.t.}\, {A}{x} - {B}{z} = {c} $, given an arbitrary fixed-point initialization $ ζ^0 $, an optimal step-size choice is given by a root of the following polynomial: \begin{equation*} ρ^4\Vert {A}{x}^\star\Vert^2 - ρ^3\langle {A}{x}^\star, ζ^0\rangle + ρ\langle λ^\star,ζ^0\rangle - \Vertλ^\star\Vert^2 = 0, \end{equation…

This https://arxiv.org/abs/2401.05027 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

An improvement of the lower bound of the number of integers in Littlewood's conjecture
In this paper, we improve the results in the author's previous paper \cite{Usu22}, which deals with the quantitative problem on Littlewood's conjecture. We show that, for any $0<γ<1$, any $(α,β)\in\mathbb{R}^2$ except on a set with Hausdorff dimension about $\sqrtγ$, any small $0<\varepsilon<1$ and any large $N\in\mathbb{N}$, the number of integers $n\in[1,N]$ such that $n\langle nα\rangle\langle nβ\rangle<\varepsilon$ is greater than $γ(\log N)^2/(\log\log N)^2$ up to a universal consta…