Related papers: Closed Form Expressions for the Potentials and Acc…
In this paper, we consider the motion of a particle on a surface of revolution under the influence of a central force field. We prove that there are at most two analytic central potentials for which all the bounded, nonsingular orbits are…
One of the common approximations in long-term evolution studies of small bodies is the use of circular orbits averaging the actual eccentric ones, facilitating the coupling of processes with very different timescales, such as the orbital…
We show that the general solution of scalar field cosmology in $d$ dimensions with exponential potentials for flat Robertson-Walker metric can be found in a straightforward way by introducing new variables which completely decouple the…
A synthesis of the present knowledge on gamma-ray emission from the magnetosphere of a rapidly rotating neutron star is presented, focusing on the electrodynamics of particle accelerators. The combined curvature, synchrotron, and…
Since physical theories employ mathematical models to describe and predict physical phenomena, our knowledge depends on the models available to that end. To increase their scope we present a particular type of simplified models, serial…
We study the rotational properties of a two-component Bose-Einstein condensed gas of distinguishable atoms which are confined in a ring potential using both the mean-field approximation, as well as the method of diagonalization of the…
The issue of so-called maximal regularity is discussed within a Hilbert space framework for a class of evolutionary equations. Viewing evolutionary equations as a sums of two unbounded operators, showing maximal regularity amounts to…
A theoretical framework is developed to describe the transformation that distributes probability density functions uniformly over space. In one dimension, the cumulative distribution can be used, but does not generalize to higher…
In an effort to better understand the formation and evolution of barred galaxies, we have examined the properties of equatorial orbits in the effective potential of one model of a rapidly rotating, steady-state gas-dynamical bar that has…
General results on equatorial geodesics are exposed in the case of circular spacetimes featuring an equatorial reflection symmetry. The way the geodesic equation equivalently rewrites in terms of an effective potential is explicitly…
We find exact power-law solutions for scalar-tensor theories and clarify the conditions under which they can account for an accelerated expansion of the Universe. These solutions have the property that the signs of both the Hubble rate and…
The structure of globular clusters and elliptical galaxies are described in an unified way through a new class of lowered models inspired on the nonextensive kinetic theory. These power law models are specified by a single parameter q which…
We derive the exact form of effective potential in Kerr geometry from the general relativistic radial momentum equation. The effective potential accurately mimics the general relativistic features, over the entire range of the spin…
We study the elliptic maximal functions defined by averages over ellipses and rotated ellipses which are multi-parametric variants of the circular maximal function. We prove that those maximal functions are bounded on $L^p$ for some $p\neq…
Determining the velocity field of structures such as galaxies, stars, and fluid planets is a relevant topic in astrophysics and astronomy. Depending on the shape of the astrophysical object, the internal velocity field may be obtained by…
We develop the basic theory of geometrically closed rings as a generalisation of algebraically closed fields, on the grounds of notions coming from positive model theory and affine algebraic geometry. For this purpose we consider several…
Quarkonium resonances in the complex-mass scale are studied. Relativistic quark potential model is used to describe the quark-antiquark system. The complex-mass formula is obtained from two exact asymptotic solutions for the QCD motivated…
We introduce a variable radius form of the extended exterior sphere condition of [16], and then, we prove that the complement of a closed set satisfying this new property is nothing but the union of closed balls with lower semicontinous…
Analytical expressions are derived for classical trajectories in repulsive Coulomb plus multi-step attractive potentials. Thereafter the closed form expressions are obtained for classical deflection functions. The expressions are expected…
The convolution of a function with an isotropic Gaussian appears in many contexts such as differential equations, computer vision, signal processing, and numerical optimization. Although this convolution does not always have a closed form…