Tootfinder

Shepherding Miorita and its flock: A group of near-Earth asteroids driven by apsidal and von Zeipel-Lidov-Kozai secular resonances. A source of low-perihelion asteroids
R. de la Fuente Marcos, C. de la Fuente Marcos, O. V\u{a}duvescu
https://arxiv.org/abs/2507.21251

Shepherding Miorita and its flock: A group of near-Earth asteroids driven by apsidal and von Zeipel-Lidov-Kozai secular resonances. A source of low-perihelion asteroids
Context. Secular resonances can control the dynamical evolution of near-Earth asteroids (NEAs) and, in some cases, lead to increased orbital stability. Asteroid 622577 Miorita (2014 LU14 ) was the first NEA found by the Isaac Newton Telescope (INT) and exhibits unusual dynamical traits although it approaches Venus, Earth, and Mars at relatively close range. Aims. Here, we investigate the orbital context of Miorita and search for possible dynamical analogs within the NEA population. Methods.…

The orbital period and inclination of the neutron star X-ray transient MAXI J1807 132
E. A. Saavedra, T. Mu\~noz-Darias, M. A. P. Torres, I. V. Yanes-Rizo, M. Armas Padilla, A. \'Alvarez-Hern\'andez, J. Casares, D. Mata S\'anchez, S. K. Rout, S. Navarro
https://arxiv.org/abs/2508.20178 …

The orbital period and inclination of the neutron star X-ray transient MAXI J1807+132
The neutron star X-ray transient MAXI J1807+132 has undergone outbursts in 2017, 2019, and 2023. We conducted an $R$-band time series photometry campaign using the Isaac Newton Telescope during the 2022 quiescent state. We detected a periodic variation in the light curve, consistent with ellipsoidal modulation, which allowed us to determine an orbital period of $P_{\rm orb} = 4.258 \pm 0.008$ hr. By modelling the light curve, we obtained a binary inclination of $ i = 72\pm5 \, °$ and a mass ra…

Combinatorial and Gaussian Foundations of Rational Nth Root Approximations: Theorems and Conjectures
Isaac Wolford
https://arxiv.org/abs/2508.14095 https://

Combinatorial and Gaussian Foundations of Rational Nth Root Approximations: Theorems and Conjectures
We present an approach (the biroot method) for nth root approximation that yields closed-form rational functions with coefficients derived from binomial structures, Gaussian functions, or qualifying DAG structures. The method emerges from an analysis of Newton's method applied to root extraction, revealing that successive iterations generate coefficients following rows of Pascal's triangle in an alternating numerator-denominator pattern. After further exploration of these patterns, we formulate…