Tootfinder

On the chain of commuting operators on Banach spaces and Lomonosov's invariant subspace theorem
Tomasz Szczepanski
https://arxiv.org/abs/2507.14297 htt…

On the chain of commuting operators on Banach spaces and Lomonosov's invariant subspace theorem
An operator $T$ on a Banach space is said to be of chain $N$ if there exist non-scalar operators $S_1,...,S_{N-1}$ and a non-zero compact $K$ such that $$T \leftrightarrow S_1 \leftrightarrow S_2 \leftrightarrow ...\leftrightarrow S_{N-1} \leftrightarrow K,$$ where $A\leftrightarrow B$ means $AB=BA$. A connection of this theory to the Lomonosov's Invariant Subspace Theorem is highlighted. It is shown that for every weighted shift $T$ it is of chain $3$. In particular, every non-Lomonosov operat…

MARTA: The connection between chemical enrichment, feedback, and dust in a Wolf-Rayet galaxy at z${\sim}$2
Mirko Curti, Elisa Cataldi, Francesco Belfiore, Bianca Moreschini, Magda Arnaboldi, Martyna Chru\'sli\'nska, Filippo Mannucci, Alessandro Marconi, Quirino D'Amato, Stefano Carniani, William M. Baker, Annalisa De Cia, Nimisha Kumari, Amirnezam Amiri, Giovanni Cresci, Chiaki Kobayashi, Fergus Cullen, Anna Feltre, Roberto Maiolino

MARTA: The connection between chemical enrichment, feedback, and dust in a Wolf-Rayet galaxy at z${\sim}$2
We present the analysis of the stellar and interstellar medium (ISM) properties of MARTA-4327, a star-forming galaxy at z=2.224 observed by means of deep JWST/NIRSpec spectroscopy in both medium- and high-resolution gratings as part of the "Measuring Abundances at high Redshift with the Te Approach" (MARTA) programme. We report one of the highest-redshift detections of the Wolf-Rayet (WR) blue and red bumps in a non-lensed system. The broad He ii$λ$4686 feature is consistent with a young (${\s…

Computing $c$- and $a$-functions from entanglement
Konstantinos Boutivas, Dimitrios Katsinis, Georgios Pastras, Nikolaos Tetradis
https://arxiv.org/abs/2509.03259 https://

Computing $c$- and $a$-functions from entanglement
We confirm the direct connection between entanglement entropy and the notion of irreversibility in the renormalization-group flow in the context of a simple theory for which a calculation from first principles is feasible. The change of the entanglement entropy for a spherical entangling surface as its radius grows from zero to infinity corresponds to the flow from the UV to the IR. Through analytical and numerical means, we compute the entanglement entropy for a free massive scalar theory, mak…

Here We Goooo: Can Dak Prescott, Jake Ferguson re-establish connection? https://www.dallascowboys.com/news/here-we-goooo-can-dak-prescott-jake-ferguson-re-establish-connection

Semantically Reflected Programs
Eduard Kamburjan, Vidar Norstein Klungre, Yuanwei Qu, Rudolf Schlatte, Egor V. Kostylev, Martin Giese, Einar Broch Johnsen
https://arxiv.org/abs/2509.03318

Semantically Reflected Programs
This paper addresses the dichotomy between the formalization of structural and the formalization of behavioral knowledge by means of semantically lifted programs, which explore an intuitive connection between programs and knowledge graphs. While knowledge graphs and ontologies are eminently useful to represent formal knowledge about a system's individuals and universals, programming languages are designed to describe the system's evolution. To address this dichotomy, we introduce a semantic lif…

Here We Goooo: Can Dak Prescott, Jake Ferguson re-establish connection? https://www.dallascowboys.com/news/here-we-goooo-can-dak-prescott-jake-ferguson-re-establish-connection

Prediction of Maximum Temperature record in Spain 1960-2023 by the means of ERA5 atmospheric geopotentials
Elsa Barrio-Torres, Jes\'us Abaurrea, Jes\'us As\'in, Jorge Castillo-Mateo, Ana Carmen Cebri\'an, Zeus Gracia
https://arxiv.org/abs/2509.03459

Prediction of Maximum Temperature record in Spain 1960-2023 by the means of ERA5 atmospheric geopotentials
The increasing frequency of extreme temperature events, such as daily maximum temperature ($T_x$) records, underscores the need for robust tools to understand their drivers and predict their occurrence. Previous studies have identified increasing and non-stationary trends in $T_x$ records across the Iberian Peninsula, particularly during summer, the literature directly exploring their connection with upper-level atmospheric covariates remains limited. This work develops and applies an innovativ…