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.Comment: 32 pp, LATE

Gravitational potential energy of simple bodies: the method of negative density

The method of negative density is presented which allows to obtain the analytical solutions for potential energy of new kinds of homogeneous and ihhomogeneous self-gravitating bodies. The homogeneous bispherical concavo-convex lens is considered in particular.Comment: 4 pages, 3 figure

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.Comment: 3 page

Rotation, mass loss and pulsations of the star: an analytical model

The characteristics of the star with the "prescribed" density distribution $\rho=\rho_c[1-(r/R)^\alpha]$ are analytically studied.Comment: 8 pages, 6 figure

Isotope Separation and Solar Neutrino Experiments

The isotope composition of target chemical elements in the Solar Neutrino Experiments is discussed and the possibility of improving this isotope composition is speculated.Comment: 2 pages, no figures; replaced by revtex file with 1 reference added and minor text changes mad

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.Comment: 25 pages, 5 figure

Gravitational potential energy of simple bodies: the homogeneous bispherical concavo-convex lens

Gravitational potential energy of the homogeneous bispherical concavo-convex lens, with the equal absolute values of radii of curvature of both surfaces is studied.Comment: 3 pages, 3 figure

Surprises of phase transition astrophysics

Highly personalysed and subjective review of studies of the equilibrium, pulsations and stability of stars with the first-order phase transition.Comment: 4 pages, 1 fig, revtex. Essays on Gravitation-99, Gravity Research Foundation, US

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.Comment: 5 pp, revtex, 2 figures; Table II replaced, 1 reference added, minor text changed in sec. V, and other minor typos correcte

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.Comment: 6 pp, Mathematica notebook source include