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...

In this paper, new conditions for the stability of V -geometrically ergodic Markov chains are introduced. The results are based on an extension of the standard perturbation theory formulated by Keller and Liverani. The continuity and higher regularity properties are investigated. As an illustration, an asymptotic expansion of the invariant probability measure for an autoregressive model with i....

The adaptive perturbation chooses a non-standard decomposition. Hamiltonian becomes sum of solvable and parts. We calculate the spectrum using method at leading-order to compare numerical solutions. maximum deviation is around 5% for different coupling regions. A study relies on whether choice suitable. Our result with parameters should show that provides appropriate saddle points all In end, w...

There are many mathematical, time-dependent models of hepatitis type C virus (HCV) infection found in the literature. Although the evolution of the level of infection is complex, there are many successful models explaining a variety of in-vivo and in-vitro observations. These models are playing a pivotal role in the pharmaceutical industry by helping researchers and clinicians analyze the perfo...

this paper presents the high order frequency-amplitude relationship for nonlinear transversely vibrating beams with odd and even nonlinearities using homotopy perturbation method with an auxiliary term (hpmat). the governing equations of vibrating buckled beam, beam carrying an intermediate lumped mass and quintic nonlinear beam are investigated to exhibit the reliability and ability of the pro...