Related papers: Rational approximation to the Thomas--Fermi equati…
Exact and simple calculation of Thomas rotation and Thomas precessions along a circular world line is presented in an absolute (coordinate-free) formulation of special relativity. Besides the simplicity of calculations the absolute…
In this paper, we present an improved continued fraction approximation of the Wallis ratio. This approximation is fast in comparison with the recently discovered asymptotic series. We also establish the double-side inequality related to…
We give explicit and asymptotic lower bounds for the quantity $|e^{s/t}-M/N|$ by studying a generalized continued fraction expansion of $e^{s/t}$. In cases $|s|\geq 3$ we improve existing results by extracting a large common factor from the…
A very simple but useful almost sure convergence theorem of probability is given.
In this work, an efficient approximation scheme has been proposed for getting accurate approximate solution of nonlinear partial differential equations with constant or variable coefficients satisfying initial conditions in a series of…
For the stationary Gross-Pitaevskii equation with harmonic real and linear imaginary potentials in the space of one dimension, we study the ground state in the limit of large densities (large chemical potentials), where the solution…
We give a simple direct proof of Fermat's two squares theorem. Our argument uses no intricate notions or ideas; one might say that it is a proof by careful bookkeeping. As such, the proof may be particularly easy to comprehend by students…
The Schwinger quantum correction to the classic Thomas-Fermi atom is directly derived by solving for the latter without recourse to a modeling after the harmonic oscillator potential and without solving for the particle density.
Instantaneous derivation of the Thomas precession.
A reasonably complete theory of the approximation of an irrational by rational fractions whose numerators and denominators lie in prescribed arithmetic progressions is developed in this paper. Results are both, on the one hand, from a…
The method of self-similar factor approximants is shown to be very convenient for solving different evolution equations and boundary-value problems typical of physical applications. The method is general and simple, being a straightforward…
We consider the problem of approaching real numbers with rational numbers with prime denominator and with a single numerator allowed for each denominator. We obtain basic results, both probabilistic and deterministic, draw connections to…
Stirling's formula is a powerful asymptotic approximation of the factorial function. Many well-known proofs of this formula are grounded in integral calculus. In this paper, we present an alternative proof of Stirling's formula using only…
An effective field approximation, similar to the atomic Thomas-Fermi approach, is proposed for studying non-Abelian gauge theories which includes finite-volume effects. As applications of the formalism the equation of state for an SU(2)…
Based on M. Hall's theorem we prove a simple result dealing with real numbers which admit exact approximations by rationals.
We briefly review the Thomas-Fermi statistical model of atoms in the classical non-relativistic formulation and in the generalised finite-nucleus relativistic formulation. We then discuss the classical generalisation of the model to finite…
We give a reciprocity formula for a two-variable sum where the variables satisfy a linear congruence condition. We also prove that such sum is a measure of how well a rational is approximable from below and show that the reciprocity formula…
This paper studies a method, which has been proposed in the Physics literature by [8, 7, 10], for estimating the quasi-stationary distribution. In contrast to existing methods in eigenvector estimation, the method eliminates the need for…
This article provides a simple proof of the quadratic formula, which also produces an efficient and natural method for solving general quadratic equations. The derivation is computationally light and conceptually natural, and has the…
In this paper we describe an algorithm for implicitizing rational hypersurfaces in case there exists at most a finite number of base points. It is based on a technique exposed in math.AG/0210096, where implicit equations are obtained as…