Journal of Informatics and Mathematical Sciences

Some Results on the Spectral Radius of Banach Algebra

Luma Barghooth — Fri, 30 Dec 2022 00:00:00 +0000

Al-Banach algebra was introduced in 1940 by Russian mathematician I.M. Gelfand and arose from the observation that some Banach spaces exhibit interesting properties when they can be provided with operations and examples. Among the linear functions adopted in Al-Banach commutative algebra and its maxima, as well as with the spectra of its elements in one way or another that leads us towards the central component of the spectra mapping theory and the spectral radius formula. In this paper, we get some results on the spectral radius of Al-Banach algebra.

Effects of Triaxiality of Primaries on Existence and Stability of Collinear Equilibrium Points in Elliptical Restricted Three Body Problem

Shilpi Dewangan, Poonam Duggad, A. Narayan — Fri, 30 Dec 2022 00:00:00 +0000

This paper deals with the motion of oblate infinitesimal mass around the triaxial primaries in the framework of elliptical restricted three body problem. The triaxial primaries are moving around each other in elliptic orbits about the common barycentre and the oblate infinitesimal is moving in the neighbourhood of collinear equilibrium points. It is observed that location and stability of the oblate infinitesimal around the collinear points are affected by the triaxiality of primaries.\ Furthermore, the results shown that the behaviour of infinitesimal mass around the collinear points \(L_1\) and \(L_2\) are unstable, while the behaviour of infinitesimal mass around \(L_3\) is shown stable for some parameters of triaxiality of primaries.

Resonance Stability of Oblate Infinitesimal in the Neighbourhood of Triangular Equilibrium Points for Triaxial Primaries in the Elliptic Restricted Three Body Problem

Shilpi Dewangan, Poonam Duggad, A. Narayan — Fri, 30 Dec 2022 00:00:00 +0000

The present study aims to investigates the existence of resonance and linear stability of oblate infinitesimal in the neighbourhood of triangular equilibrium points of the elliptical restricted three body problem, considering effect of triaxial primaries in circular and elliptical cases. For this the Hamiltonian function, convergent in nature and describing the motion of the infinitesimal body in the neighbourhood of the triangular equilibrium solutions is derived. Also, the Hamiltonian for the system is expanded in powers of the generalized components of momenta. Further, canonical transformation has also been used to study the stability of the triangular equilibrium points. The study primarily focuses on establishing the relation for determining the range of stability at and near the resonance frequency at \(\omega _2 =\frac{1}{2}\). It is observed that the parametric resonance is only possible at the resonance frequency \(\omega _2 =\frac{1}{2}\) in circular and elliptical cases.