The renormalization constants present in the lattice evaluation of the topolog-ical susceptibility can be non-perturbatively calculated by using the so-called heating method. We test this method for the O(3) non-linear σ-model in two dimensions. We work in a regime where perturbative calculations are exact and useful to check the values obtained from the heating method. The result of the test i...

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

Based on a geometrical method, the internal relationships between locally parameterized curves and the local parameterized surfaces are analyzed. A necessary and sufficient condition is derived for the local convexity of parameterized surfaces and functional surfaces. A criterion for local convexity (concavity) of parameterized surfaces is found, also, the criterion condition of binary function...

The adaptive perturbation method decomposes a Hamiltonian by the diagonal elements and nondiagonal of Fock state. state are solvable but can contain information about coupling constants. We study harmonic oscillator with interacting potential, [Formula: see text], where text] constants, is position operator. In this study, each perturbed term has an exact solution. demonstrate accurate spectrum...