Tootfinder

While awaiting the restoration of digitised manuscripts to the British Library website, I appreciate the image chosen for the latest update: https://blogs.bl.uk/living-knowledge/2024/03/helping-your-research.html
May the staff receive all the hel…

This https://arxiv.org/abs/2303.08413 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On matrix invertible extensions over commutative rings
We introduce the class E2 (resp. SE2) of commutative rings R with the property that each unimodular 2 x 2 matrix with entries in R extends to an invertible 3 x 3 matrix (resp. invertible 3 x 3 matrix whose (3, 3) entry is 0). Among noetherian domains of dimension 1, polynomial rings over Z or Hermite rings, only EDRs belong to the class. Using this, stable ranges, and units and projective modules interpretations, we reobtain (often refine) criteria due to Kaplansky, McGovern, Roitman, Shchedryk…

This https://arxiv.org/abs/2303.08413 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On matrix invertible extensions over commutative rings
We introduce the class E2 (resp. SE2) of commutative rings R with the property that each unimodular 2 x 2 matrix with entries in R extends to an invertible 3 x 3 matrix (resp. invertible 3 x 3 matrix whose (3, 3) entry is 0). Among noetherian domains of dimension 1, polynomial rings over Z or Hermite rings, only EDRs belong to the class. Using this, stable ranges, and units and projective modules interpretations, we reobtain (often refine) criteria due to Kaplansky, McGovern, Roitman, Shchedryk…

Stellar Variability and Distance Indicators in the Near-infrared in Nearby Galaxies. I. RR Lyrae and Anomalous Cepheids in Draco dwarf spheroidal
Anupam Bhardwaj, Marina Rejkuba, Chow-Choong Ngeow, Marcella Marconi, Vincenzo Ripepi, Abhinna Sundar Samantaray, Harinder P. Singh
https://arxiv.org/abs/2404.01394

Stellar Variability and Distance Indicators in the Near-infrared in Nearby Galaxies. I. RR Lyrae and Anomalous Cepheids in Draco dwarf spheroidal
Draco dwarf Spheroidal galaxy (dSph) is one of the nearest and the most dark matter dominated satellites of the Milky Way. We obtained multi-epoch near-infrared (NIR, $JHK_s$) observations of the central region of Draco dSph covering a sky area of $\sim 21'\times21'$ using the WIRCam instrument at the 3.6-m Canada-France-Hawaii Telescope. Homogeneous $JHK_s$ time-series photometry for 212 RR Lyrae (173 fundamental-mode, 24 first-overtone, and 15 mixed-mode variables) and 5 Anomalous Cepheids in…

On the integral representation and the Ra\c{s}a, Jensen and Hermite-Hadamard inequalities for box-$(n_1,\ldots, n_d)$-convex functions
Andrzej Komisarski, Teresa Rajba
https://arxiv.org/abs/2404.13723

On the integral representation and the Raşa, Jensen and Hermite-Hadamard inequalities for box-$(n_1,\ldots, n_d)$-convex functions
We give the integral representation of box-$(n_1,\ldots, n_d)$-convex fun\-ctions, which are a generalization of Popoviciu's $n$-convex and box-$(m,n)$-convex functions. Based on this integral representation, we obtain the Raşa, Jensen and Hermite-Hadamard inequalities for these functions. We extend the results obtained by S. G. Gal, C. P. Niculescu, B. Gavrea, I. Gavrea, A. Komisarski, T. Rajba and T. Popoviciu.

Exceptional points of any order in a generalized Hatano-Nelson model
Julius T. Gohsrich, Jacob Fauman, Flore K. Kunst
https://arxiv.org/abs/2403.12018 http…

Exceptional points of any order in a generalized Hatano-Nelson model
Exceptional points (EPs) are truly non-Hermitian (NH) degeneracies where matrices become defective. The order of such an EP is given by the number of coalescing eigenvectors. On the one hand, most work focusses on studying $N$th-order EPs in $N\leq4$-dimensional NH Bloch Hamiltonians. On the other hand, some works have remarked on the existence of EPs of orders scaling with systems size in models exhibiting the NH skin effect. In this letter, we introduce a new type of EP and provide a recipe o…