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Polarized ferrofluids, lipid monolayers and magnetic bubbles form domains with deformable boundaries. Stability analysis of these domains depends on a family of nontrivial integrals. We present a closed form evaluation of these integrals as…
Within general relativity, we construct sequences of rapidly rotating Dirac stars consisting of a spinor fluid described by an effective equation of state. We find the physically relevant domain of stable configurations and calculate their…
This work proposes a mathematical approach that (re)defines a property of Machine Learning models named stability and determines sufficient conditions to validate it. Machine Learning models are represented as functions, and the…
The stability radius for finitely many interconnected linear exponentially stable well-posed systems with respect to static perturbations is studied. If the output space of each system is finite-dimensional, then a lower bound for the…
We construct magnetized stars composed of a fluid stably stratified by entropy gradients in the framework of general relativity, assuming ideal magnetohydrodynamics and employing a barotropic equation of state. We first revisit basic…
In this paper, we drive and simplify some important equations and relations for an evolving star with spherical symmetry, and then give some simple analysis for their properties and implications. In the light-cone coordinate system, these…
Many exoplanets are discovered in binary star systems in internal or in circumbinary orbits. Whether the planet can be habitable or not depends on the possibility to maintain liquid water on its surface, and therefore on the luminosity of…
In this expository and resources chapter we review selected aspects of the mathematics of dynamical systems, stability, and chaos, within a historical framework that draws together two threads of its early development: celestial mechanics…
We present a stable model for quark stars in Rastall-Rainbow (R-R) gravity. The structure of this configuration is obtained by utilizing an interacting quark matter equation of state. The R-R gravity theory is developed as a combination of…
Magnetic activity is a ubiquitous feature of stars with convective outer layers, with implications from stellar evolution to planetary atmospheres. Investigating the mechanisms responsible for the observed stellar activity signals from days…
Motivated by the possible existence of other universes, with possible variations in the laws of physics, this paper explores the parameter space of fundamental constants that allows for the existence of stars. To make this problem…
We propose the notion of stability on a triangulated category that is a generalization of the T.Bridgeland's stability data. We establish connections between stabilities and t-structures on a category and as application we get the…
Understanding the stability of the magnetic field in radiation zones is of crucial importance for various processes in stellar interior like mixing, circulation and angular momentum transport. The stability properties of a star containing a…
The stability of equilibrium configurations of galaxies or stars are time honored problems in astrophysics. We present mathematical results on these problems which have in recent years been obtained by Yan Guo and the author in the context…
In a Hilbert space setting, we study the stability properties of the regularized continuous Newton method with two potentials, which aims at solving inclusions governed by structured monotone operators. The Levenberg-Marquardt…
This paper is an investigation of the stability of some ideal stars. It is in- tended as a study in General Relativity, with emphasis on the coupling to matter, eventually aimed at a better understanding of very strong gravitational fields…
We study $\varepsilon$-stability in continuous logic. We first consider stability in a model, where we obtain a definability of types result with a better approximation than that in the literature. We also prove forking symmetry for…
We study relativistic stars in the context of scalar tensor theories of gravity that try to account for the observed cosmic acceleration and satisfy the local gravity constraints via the chameleon mechanism. More specifically, we consider…
Stability properties of magnetic-field configurations containing the toroidal and axial field are considered. The stability is treated by making use of linear analysis. It is shown that the conditions required for the onset of instability…
This paper investigates the stability properties of the spectrum of the classical Steklov problem under domain perturbation. We find conditions which guarantee the spectral stability and we show their optimality. We emphasize the fact that…