Tootfinder

Niedersachsen: CDU fordert pauschales Handyverbot an Schulen, SPD dagegen
In Niedersachsen will die Oppositionspartei CDU ein striktes Handyverbot in Schulen bis zur Oberstufe. Die regierende SPD lehnt die Forderungen ab.

Social-Media- & Handyverbote: "Sehr viel mehr offene Fragen als Antworten"
Der Bitkom hat Eltern befragt, wie sie die Smartphone- und Social-Media-Nutzung ihrer Kinder einschätzen und regeln. Mit den Kindern wachsen die Freiheiten.

From homotopy Rota-Baxter algebras to Pre-Calabi-Yau and homotopy double Poisson algebras
Yufei Qin, Kai Wang
https://arxiv.org/abs/2506.03952 https://

From homotopy Rota-Baxter algebras to Pre-Calabi-Yau and homotopy double Poisson algebras
In this paper, we investigate pre-Calabi-Yau algebras and homotopy double Poisson algebras arising from homotopy Rota-Baxter structures. We introduce the notion of cyclic homotopy Rota-Baxter algebras, a class of homotopy Rota-Baxter algebras endowed with additional cyclic symmetry, and present a construction of such structures via a process called cyclic completion. We further introduce the concept of interactive pairs, consisting of two differential graded algebras-designated as the acting al…

HandOver: Enabling Precise Selection & Manipulation of 3D Objects with Mouse and Hand Tracking
Esen K. T\"ut\"unc\"u, Mar Gonzalez-Franco, Eric J. Gonzalez
https://arxiv.org/abs/2508.00211

HandOver: Enabling Precise Selection & Manipulation of 3D Objects with Mouse and Hand Tracking
We present HandOver, an extended reality (XR) interaction technique designed to unify the precision of traditional mouse input for object selection with the expressiveness of hand-tracking for object manipulation. With HandOver, the mouse is used to drive a depth-aware 3D cursor enabling precise and restful targeting -by hovering their hand over the mouse, the user can then seamlessly transition into direct 3D manipulation of the target object. In a formal user study, we compare HandOver agains…

Homotopy equivalence of digital pictures in $\mathbb{Z}^2$
Dae-Woong Lee, P. Christopher Staecker
https://arxiv.org/abs/2509.03023 https://arxiv.org/pdf/25…

Homotopy equivalence of digital pictures in $\mathbb{Z}^2$
We investigate the properties of digital homotopy in the context of digital pictures $(X,κ,\bar κ)$, where $X\subsetneq \mathbb{Z}^n$ is a finite set, $κ$ is an adjacency relation on $X$, and $\bar κ$ is an adjacency relation on the complement of $X$. In particular we focus on homotopy equivalence between digital pictures in $\mathbb{Z}^2$. We define a numerical homotopy-type invariant for digital pictures in $\mathbb{Z}^2$ called the outer perimeter, which is a basic tool for distinguishin…

The derivator of a dg-category
Francesco Genovese, Chiara Sava, Jan \v{S}\v{t}ov\'i\v{c}ek
https://arxiv.org/abs/2508.02612 https://arxiv.org/pdf/2508.…

The derivator of a dg-category
In this work, we construct the stable derivator associated to a homotopically complete and cocomplete dg-category by explicitly defining homotopy Kan extensions via suitable weighted homotopy limits and colimits in dg-categories. By restricting the domain of the derivator to finite direct categories, we obtain a well-defined derivator even for pretriangulated dg-categories. This definition enables an explicit description of the derivator associated to a weakly idempotent complete Frobenius exac…

Forum Bildung Digitalisierung: Orientierungspapier zur Handyverbotsdebatte
Hat Sloterdijks Drogenvergleich das Fass zum Überlaufen gebracht? Das jetzt erschienene Papier zur Verbotsdebatte will sie auf jeden Fall wieder versachlichen.

A note on the Greek letter elements of the homotopy of the $L_n$-local spheres
Ryo Kato, Katsumi Shimomura, Mao-no-suke Shimomura
https://arxiv.org/abs/2507.02155

A note on the Greek letter elements of the homotopy of the $L_n$-local spheres
Let $BP$ denote the Brown-Peterson spectrum at a prime $p$, whose homotopy groups are isomorphic to the polynomial algebra generated by elements $v_i$'s for $i\ge 1$. We consider the homotopy groups of the $v_n^{-1}BP$-localized sphere spectrum $L_nS^0$ with $n^2\le 2p-1$, and show that the groups contain the $n$-th Greek letter family. For the proof of this, we further show the existence of the $v_n^{-1}BP$-localized Smith-Toda spectrum $W_n$ for the case $n^2\le 2p-1$. If the Smith-Toda spect…

Verbände: 6-GHz-Band muss für WLAN frei sein, um digitale Zukunft zu sichern
In Brüssel zeichnet sich ein handfester Frequenzstreit ab: Mobilfunkanbieter beanspruchen das wertvolle obere 6-GHz-Band für 5G & Co. Das stößt auf Gegenwehr.

A note on the rational homotopy type of the projectivization of the tangent bundle of complex projective spaces
Meshach Ndlovu, Jean Baptiste Gatsinzi
https://arxiv.org/abs/2508.01797

A note on the rational homotopy type of the projectivization of the tangent bundle of complex projective spaces
In this paper, we determine the rational homotopy type of the total space of the projectivization of the complex tangent bundle $τ: \mathbb{C}^n \longrightarrow E \longrightarrow \mathbb{C}P^{n}$. We show that the total space $P(E)$ of the projectivization bundle $P(τ): \mathbb{C}P^{n-1} \longrightarrow P(E) \longrightarrow \mathbb{C}P^{n}$ has the rational homotopy type of $\mathrm{U}(n+1)/\mathrm{U}(1)\times \mathrm{U}(1)\times \mathrm{U}(n-1)$.