Tootfinder

This https://arxiv.org/abs/2202.04452 has been replaced.
link: https://scholar.google.com/scholar?q=a

Sufficient conditions for a problem of Polya
Let $α$ be a non-zero algebraic number. Let $K$ be the Galois closure of $\mathbb{Q}(α)$ with Galois group $G$ and $\bar{\mathbb{Q}}$ be the algebraic closure of $\mathbb{Q}$. In this article, among the other results, we prove the following. If $f\in \bar{\mathbb{Q}}[G]$ is a non-zero element of the group ring $\bar{\mathbb{Q}}[G]$ and $α$ is a given algebraic number such that $f(α^n)$ is a non-zero algebraic integer for infinitely many natural numbers $n$, then $α$ is an algebraic integer…

This https://arxiv.org/abs/2203.03530 has been replaced.
link: https://scholar.google.com/scholar?q=a

A geometric model for blocks of Frobenius kernels
Building on a geometric counterpart of Steinberg's tensor product formula for simple representations of a connected reductive algebraic group $G$ over a field of positive characteristic, and following an idea of Arkhipov--Bezrukavnikov--Braverman--Gaitsgory--Mirković, we define and initiate the study of some categories of perverse sheaves on the affine Grassmannian of the Langlands dual group to $G$ that should provide geometric models for blocks of representations of the Frobenius kernel $G_1…

This https://arxiv.org/abs/2402.03248 has been replaced.
link: https://scholar.google.com/scholar?q=a

On a question of Gary G. Gundersen concerning meromorphic functions sharing three distinct values IM and a fourth value CM
In 1992, Gundersen (Complex Var. Elliptic Equ.20 (1992), no. 1-4, 99-106.) proposed the following famous open question: if two non-constant meromorphic functions share three values IM and share a fourth value CM, then do the functions necessarily share all four values CM? The open question is a long-standing question in the studies of the Nevanlinna$'$s value distribution theory of meromorphic functions, and has not been completely resolved by now. In this paper, we prove that if two distinct n…

This https://arxiv.org/abs/2202.04452 has been replaced.
link: https://scholar.google.com/scholar?q=a

Sufficient conditions for a problem of Polya
Let $α$ be a non-zero algebraic number. Let $K$ be the Galois closure of $\mathbb{Q}(α)$ with Galois group $G$ and $\bar{\mathbb{Q}}$ be the algebraic closure of $\mathbb{Q}$. In this article, among the other results, we prove the following. If $f\in \bar{\mathbb{Q}}[G]$ is a non-zero element of the group ring $\bar{\mathbb{Q}}[G]$ and $α$ is a given algebraic number such that $f(α^n)$ is a non-zero algebraic integer for infinitely many natural numbers $n$, then $α$ is an algebraic integer…

This https://arxiv.org/abs/2310.20408 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_…

Time-varying double-peaked emission lines following the sudden ignition of the dormant galactic nucleus AT2017bcc
We present a pan-chromatic study of AT2017bcc, a nuclear transient that was discovered in 2017 within the skymap of a reported burst-like gravitational wave candidate, G274296. It was initially classified as a superluminous supernova, and then reclassified as a candidate tidal disruption event. Its optical light curve has since shown ongoing variability with a structure function consistent with that of an active galactic nucleus, however earlier data shows no variability for at least 10 years p…

This https://arxiv.org/abs/2212.05697 has been replaced.
link: https://scholar.google.com/scholar?q=a

Aharoni's rainbow cycle conjecture holds up to an additive constant
In 2017, Aharoni proposed the following generalization of the Caccetta-Häggkvist conjecture: if $G$ is a simple $n$-vertex edge-colored graph with $n$ color classes of size at least $r$, then $G$ contains a rainbow cycle of length at most $\lceil n/r \rceil$. In this paper, we prove that, for fixed $r$, Aharoni's conjecture holds up to an additive constant. Specifically, we show that for each fixed $r \geq 1$, there exists a constant $c_r$ such that if $G$ is a simple $n$-vertex edge-colored…

A look at Playtron, which raised a $10M seed to build a Linux-based, platform-agnostic gaming OS to replace Windows or SteamOS, starting with handheld consoles (Sean Hollister/The Verge)
https://www.theverge.com/24090470/playtron-gaming-os-linux-hand…

Playtron: the startup hoping to Steam Deck-ify the world
Exclusive: Playtron tells us about its ambitions to create an operating system specifically for PC gaming handhelds, following in footsteps of Steam Deck, Legion Go, and more.

Understanding the genetic mechanism fueling SARS-CoV-2's ability to generate variants can go a long way in keeping COVID at bay.
In this study published in Nature Microbiology, researchers at Baylor College of Medicine and collaborating institutions developed a new technology called
tARC-seq that revealed a genetic mechanism affecting SARS-CoV-2 divergence
and enabled the team to calculate SARS-CoV-2's mutation rate.
Using tARC-seq, the researchers also capt…

Study discovers hidden mechanism behind rapid COVID variants
The SARS-CoV-2 virus that causes COVID has the unsettling ability of often generating variants of itself. Other viruses also mutate, but as SARS-CoV-2 quickly spread throughout the entire human population during the pandemic, killing millions, the virus' dynamic evolution posed a serious problem: it repeatedly challenged our bodies' immune response fighting the virus and hindered the process of getting updated vaccines ready.

This https://arxiv.org/abs/2207.12531 has been replaced.
link: https://scholar.google.com/scholar?q=a

Distant 2-Colored Components on Embeddings Part I: Connecting Faces
This is the first in a sequence of three papers in which we prove the following generalization of Thomassen's 5-choosability theorem: Let $G$ be a finite graph embedded on a surface of genus $g$. Then $G$ can be $L$-colored, where $L$ is a list-assignment for $G$ in which every vertex has a 5-list except for a collection of pairwise far-apart components, each precolored with an ordinary 2-coloring, as long as the face-width of $G$ is $2^{Ω(g)}$ and the precolored components are of distance $2^…

This https://arxiv.org/abs/2212.11165 has been replaced.
link: https://scholar.google.com/scholar?q=a

Distant 2-Colored Components on Embeddings Part III: The General Case
This is the third in a sequence of three papers in which we prove the following generalization of Thomassen's 5-choosability theorem: Let $G$ be a finite graph embedded on a surface of genus $g$. Then $G$ can be $L$-colored, where $L$ is a list-assignment for $G$ in which every vertex has a 5-list except for a collection of pairwise far-apart components, each precolored with an ordinary 2-coloring, as long as the face-width of $G$ is at least $2^{Ω(g)}$ and the precolored components are of dis…