Related papers: Uniformly Rotating Homogeneous Rings in Newtonian …
We propose a new treatment for the quantum three-body problem. It is based on an expansion of the wave function on harmonic oscillator functions with different sizes in the Jacobi coordinates. The matrix elements of the Hamiltonian can be…
We study the dynamics of a class of Hamiltonian systems with dissipation, coupled to noise, in a singular (small mass) limit. We derive the homogenized equation for the position degrees of freedom in the limit, including the presence of a…
It is shown that the sum of stress-energy tensors of the electromagnetic and gravitational fields, the acceleration field and the pressure field inside a stationary uniform spherical body within the framework of relativistic uniform model…
We apply the modified acceleration law obtained from Einstein gravity coupled explaining galaxy rotation curves without exotic dark matter. Our sample of galaxies includes low surface brightness (LSB) and high surface brightness (HSB)…
In this review article, we present the main results from our most recent research concerning the oscillations of fast rotating neutron stars. We derive a set of time evolution equations for the investigation of non-axisymmetric oscillations…
Higgs algebras are used to construct rotational Hamiltonians. The correspondence between the spectrum of a triaxial rotor and the spectrum of a cubic Higgs algebra is demonstrated. It is shown that a suitable choice of the parameters of the…
The paper analyzes the rotation averaging problem as a minimization problem for a potential function of the corresponding gradient system. This dynamical system is one generalization of the famous Kuramoto model on special orthogonal group…
``Rubber'' coated rolling bodies satisfy a no-twist in addition to the no slip satisfied by ``marble'' coated bodies. Rubber rolling has an interesting differential geometric appeal because the geodesic curvatures of the curves on the…
We examine the rotation of the plane of polarization for linearly polarized light rays by the weak gravitational field of an isolated physical system. Based on the rotation of inertial frames, we review the general integral expression for…
We consider QM with non-Hermitian quasi-diagonalizable Hamiltonians, i.e. the Hamiltonians having a number of Jordan cells in particular biorthogonal bases. The "self-orthogonality" phenomenon is clarified in terms of a correct spectral…
Recently, in a series of papers, we established the existence and found a general solution for the simultaneously rotating and twisting locally rotationally symmetric spacetimes in general relativity, which can model inhomogeneous and…
We propose a new approach to the numerical solution of ergodic problems arising in the homogenization of Hamilton-Jacobi (HJ) equations. It is based on a Newton-like method for solving inconsistent systems of nonlinear equations, coming…
We prove a differential version of the Artin-Rees lemma with the use of Noetherian differential operators. As a consequence, we obtain several uniformity results for nonreduced rings.
The Hartree-Fock-Rothaan equations are solved for He-like ions using the iterative self-consistent method. New complete and orthonormal sets of exponential-type orbitals are employed as the basis. These orbitals satisfy the orthonormality…
The values of the homogeneous weight are determined for finite Frobenius rings that are a direct product of local Frobenius rings. This is used to investigate the partition induced by this weight and its dual partition under…
We introduce orthogonal ring patterns in the 2-sphere and in the hyperbolic plane, consisting of pairs of concentric circles, which generalize circle patterns. We show that their radii are described by a discrete integrable system. This is…
We study Einstein's equations with an isotropic but inhomogeneous metric in the cosmic rest frame. The equations are solved perturbatively in the late Universe. The leading plus next-to-leading order results agree with observations without…
A rotating metric solution in Einstein-Gauss-Bonnet gravity with a negative cosmological constant was recently found in the Chern-Simons point. We construct a rotating thin shell gluing two spacetimes in Einstein-Gauss-Bonnet gravity, using…
This work proposes and investigates a new model of the rotating rigid body based on the non-twisting frame. Such a frame consists of three mutually orthogonal unit vectors whose rotation rate around one of the three axis remains zero at all…
Here, we derive the metric for the spacetime around rotating object for the gravity action having nonlocal correction of $R\Box^{-2} R $ to the Einstein-Hilbert action. Starting with the generic stationary, axisymmetric metric, we solve the…