Tootfinder

Langlands branching rule for type B snake modules
Jingmin Guo, Jian-Rong Li, Keyu Wang
https://arxiv.org/abs/2507.06570 https://arxiv…

Langlands branching rule for type B snake modules
We prove that each snake module of the quantum Kac-Moody algebra of type $B_n^{(1)}$ admits a Langlands dual representation, as conjectured by Frenkel and Hernandez (\textit{Lett. Math. Phys.} (2011) 96:217-261). Furthermore, we establish an explicit formula, called the Langlands branching rule, which gives the multiplicities in the decomposition of the character of a snake module of the quantum Kac-Moody algebra of type $B_n^{(1)}$ into a sum of characters of irreducible representations of its…

On orbit sets generated by semigroups of one-dimensional affine functions
Karim F. Shamazov, Alexey L. Talambutsa
https://arxiv.org/abs/2507.06875 https://…

On orbit sets generated by semigroups of one-dimensional affine functions
The one-dimensional orbit set $\langle F : s \rangle$ is formed by the images of a number $s$ under the action of a semigroup generated by the integer affine functions $f_i=a_i x+b_i$ taken from the set $F=\{f_1,\ldots,f_n\}$. P.Erdös established an upper bound $O(x^{σ+ε})$ for the growth function $|\langle F : s \rangle\cap[0,x]|$, where $1/a_1^σ+1/a_2^σ+\ldots + 1/a_n^σ=1$ and $\varepsilon>0$, which was extended to orbit multisets and real affine functions by J.Lagarias. We co…

Certain Upper Bounds on the $A$-Numerical Radius of Operators in Semi-Hilbertian Spaces and Their Applications
M. H. M. Rashid
https://arxiv.org/abs/2507.05398

Certain Upper Bounds on the $A$-Numerical Radius of Operators in Semi-Hilbertian Spaces and Their Applications
Consider a complex Hilbert space $\left(\mathcal{H}, \langle \cdot, \cdot \rangle\right)$ equipped with a positive bounded linear operator $A$ on $\mathcal{H}$. This induces a semi-norm $\|\cdot\|_A$ through the semi-inner product $\langle x, y \rangle_A = \langle Ax, y \rangle$ for $x, y \in \mathcal{H}$. In this semi-Hilbertian space setting, we investigate the $A$-numerical radius $w_A(T)$ and $A$-operator semi-norm $\|T\|_A$ of bounded operators $T$. This paper presents …

🇺🇦 #NowPlaying on BBCRadio3's #Breakfast
Francis Poulenc:
🎵 Mélancolie, FP 105
#FrancisPoulenc
https://open.spotify.com/track/5F5nZis3VQ5QZoeOWWG5lF

New report details global drought impacts #environment

New report details global drought impacts
The University of Nebraska–Lincoln's National Drought Mitigation Center and the United Nations' Convention to Combat Desertification have released a report outlining the impacts of drought around the world since 2023.

🇺🇦 #NowPlaying on KEXP's #SundaySoul
Ed Lincoln:
🎵 Assim Nao Da
#EdLincoln

Expediting data extraction using a large language model (LLM) and scoping review protocol: a methodological study within a complex scoping review
James Stewart-Evans, Emma Wilson, Tessa Langley, Andrew Prayle, Angela Hands, Karen Exley, Jo Leonardi-Bee
https://arxiv.org/abs/2507.06623

Expediting data extraction using a large language model (LLM) and scoping review protocol: a methodological study within a complex scoping review
The data extraction stages of reviews are resource-intensive, and researchers may seek to expediate data extraction using online (large language models) LLMs and review protocols. Claude 3.5 Sonnet was used to trial two approaches that used a review protocol to prompt data extraction from 10 evidence sources included in a case study scoping review. A protocol-based approach was also used to review extracted data. Limited performance evaluation was undertaken which found high accuracy for the tw…

Spectra of high-dimensional sparse random geometric graphs
Yifan Cao, Yizhe Zhu
https://arxiv.org/abs/2507.06556 https://arxiv.org/pd…

Spectra of high-dimensional sparse random geometric graphs
We analyze the spectral properties of the high-dimensional random geometric graph $ G(n, d, p)$, formed by sampling $n$ i.i.d vectors $\{v_i\}_{i=1}^{n}$ uniformly on a $d$-dimensional unit sphere and connecting each pair $\{i,j\}$ whenever $\langle v_i, v_j \rangle \geq τ$ so that $p=\mathbb P(\langle v_i,v_j\rangle \geq τ)$. This model defines a nonlinear random matrix ensemble with dependent entries. We show that if $d =ω( np\log^{2}(1/p))$ and $np\to\infty$, the limiting spectral distrib…

Depth Preservation and Close-Field Transfer in the Local Langlands Correspondence
Manish Mishra
https://arxiv.org/abs/2509.04997 https://arxiv.org/pdf/2509…

Depth Preservation and Close-Field Transfer in the Local Langlands Correspondence
We introduce a revised notion of depth for Langlands parameters for a connected reductive $G$ defined over a nonarchimedean local field $F$ that restores depth preservation under the local Langlands correspondence (LLC) -- in particular for all tori. We leverage that preservation to derive structural results that, taken together, yield a canonical transfer of broad harmonic-analytic results from characteristic $0$ to characteristic $p$. When $F$ has suitably large positive characteristic, we pr…