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FAUST XXVII: The circumbinary disk and the outflow of the L 1551 IRS 5 binary system
Aurora Dur\'an, Laurent Loinard, Pedro R. Rivera-Ortiz, Geovanni Cort\'es-Rangel, Eleonora Bianchi, Paola Caselli, Cecilia Ceccarelli, Claire J. Chandler, Claudio Codella, Nicol\'as Cuello, Marta De Simone, Tomoyuki Hanawa, Doug Johnstone, Fran\c{c}ois Menard, Maria Jos\'e Maureira, Anna Miotello, Linda Podio, Takeshi Sakai, Giovanni Sabatini, Leonardo Testi, Charlotte Vastel, Ziwei Zha…

FAUST XXVII: The circumbinary disk and the outflow of the L 1551 IRS 5 binary system
Using continuum and $\text{C}^{18}\text{O}\:(2-1)$ line data obtained from the large ALMA program FAUST, we studied the structure of the protostellar binary system L1551 IRS5 at scales between 30 and 3,000 au to constrain its properties, from the circumstellar and circumbinary disks up to the envelope and outflow scales, which exhibits complex and entangled structures at the scales of its inner and outer envelopes, presumably caused by the influence of the central binary. Assuming a dust-to-gas…

Algorithmic methods of finite discrete structures. Topological graph drawing (part III)
Sergey Kurapov, Maxim Davidovsky
https://arxiv.org/abs/2506.10936 h…

Algorithmic methods of finite discrete structures. Topological graph drawing (part III)
The manuscript considers mathematical models for creating a topological drawing of a graph based on the methods of G. Ringel's vertex rotation theory. An algorithm is presented for generating a topological drawing of a flat part of a graph based on the selection of a basis for the cycle subspace C(G) using the Monte Carlo method. A steepest descent method for constructing a topological drawing of a flat subgraph is described in the manuscript. The topological drawing of a graph is constructed u…

This https://arxiv.org/abs/2409.17464 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Computation of $\langle Φ^2\rangle$ and quantum fluxes at the polar interior of a spinning black hole
Renormalization of physical quantities for quantum field theories in curved spacetimes can be achieved via the consistent subtraction of counterterms within a regularization scheme such as a point-splitting method. Pragmatic mode-sum regularization (PMR) is a point-splitting method which is particularly suitable for rotating black hole spacetimes. We extend and tailor the t-splitting variant of PMR specifically for the interior of a Kerr black hole on the axis of rotation, focusing on a minimal…

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On the heat kernel of a Cayley graph of $\operatorname{PSL}_2\mathbb{Z}$
Anders Karlsson, Kamila Kashaeva
https://arxiv.org/abs/2506.02340 https://

On the heat kernel of a Cayley graph of $\operatorname{PSL}_2\mathbb{Z}$
In this paper, we obtain an explicit formula for the heat kernel on the infinite Cayley graph of the modular group $\operatorname{PSL}_2\mathbb{Z}$, given by the presentation $\langle a,b\mid a^2=1, b^3=1\rangle$. Our approach extends the method of Chung--Yau in~\cite{MR1667452} by observing that the Cayley graph strongly and regularly covers a weighted infinite line. We solve the spectral problem on this line to obtain an integral expression for its heat kernel, and then lift this to the Cayle…