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Zakir F. Seidov

Publications and source records attributed to Zakir F. Seidov.

18 recordsLinked to original sources
arXiv2004

The generalized Roche model

Some exact analytical formulas are presented for the generalized Roche model of rotating star. The gravitational field of the central core is described by the model of two equal-mass point centers placed symmetrically at rotation axis with the pure imaginary z coordinates. The all basic parameters of the critical figure of the rotating massless envelope are presented in analytical form. The existence of the concave form of the uniformly rotating liquid is shown for a large enough angular velocity of the rotation.

astro-ph↗
arXiv2004

Lane-Emden Equation: perturbation method

The perturbation method is applied to numerical solution of the Lane-Emden Equation of arbitrary index n, and the global parameters of polytropes are found as function of polytropic index n.

astro-ph↗
arXiv2004

The quasi-incompressible planet: some analytics

Exact and approximate analytical formulas are derived for the internal structure and global parameters of the spherical non-rotating quasi-incompressible planet. The planet is modeled by a polytrope with a small polytropic index n << 1, and solutions of the relevant differential equations are obtained analytically, to the second order of n.

astro-ph↗
arXiv2003

The Roche problem: some analytics

Some exact analytical formulas are derived for the potential and mass ratio as a function of Lagrangian points position, in the classical Roche model of the close binary stars.

astro-ph↗
arXiv2003

On the angular momentum of the neutron star

It is shown that the mass loss due to rotation-driven hydrodynamical instability during the catastrophic collapse of the star is small. Neutron star is formed with a large rotational kinetic energy and the spin-down takes place in the following life of neutron star as a pulsar.

astro-ph↗
arXiv2001

Lane-Emden Equation: Picard vs Pade

The very accurate analytical solutions are found to Lane-Emden equation of arbitrary index, n, using Picard type iteration scheme and rational Pade approximants. For n=2 the dimensionless polytropic "radius" and "mass" are 4.35287459595 and 2.4110450121, with the largest ever accuracy.

astro-ph↗
arXiv2000

One relation for self-gravitating bodies

The relation between the gravitational potential energy, W, the central potential, U, and the mass, M: W/U/M is considered for various homogeneous and inhomogeneous self-gravitating bodies.

astro-ph↗
arXiv1999

"Non-1/r" Newtonian gravitation and stellar structure

Some analytical spherical-symmetric equilibrium solutions are cosidered in the Newtonian theory of gravitation with deviations from 1/r law. Stability of star against a first-order phase-transition is shown to be particularly influenced by the deviations of degree in the power-law potential.

astro-ph↗
arXiv1999

Permutations and primes

The problem of N-digit sets all permutations of which give primes is discussed. Such sets may include only digits 1, 3, 7 and 9, and none of 0, 2, 5, 4, 6, 8. Direct calculations show that such full-permutation digit sets occur at N = 1, 2, 3 and are absent in the 4 - 10 interval of N. On the other hand the formal full permutation at N = 19, 23, 317 and 1031 (as well at N = 2) cases is provided by repunits (integers all digits of which are 1). The existence/nonexistence of other (not repunits) full-permutation digit sets for arbitrary large N is an open question with probable negative answer. The maximal-permutation digit sets with maximal number of primes are given for N = 4 - 10.

math.NT↗
arXiv1998

Planck Scale Mixing and Neutrino Puzzles

It is hypotesized that neutrinos are massles and mixed among three (muon, electron and tau) flavors with a mixing length proportional to (E_nu/E_Planck)^-2. It is suggested that this hypothesis mostly reconciles the standard solar models with the observations of the solar Boron and pp neutrinos, and the atmospheric muon-to-electron neutrinos ratio.

astro-ph↗