The Bertrand-Darboux integrability condition for a certain class of perturbed harmonic oscillators is studied from the viewpoint of the Birkhoff-Gustavson(BG)-normalization: By solving an inverse problem of the BG-normalization on computer algebra, it is shown that if the perturbed harmonic oscillator with a homogeneous cubic-polynomial potential and the perturbed harmonic oscillator with a hom...

This paper focuses on the role that production subsidies play in a Bertrand mixed duopoly. The paper examines four regimes: mixed and private duopoly, each with and without subsidies. The results of this study are compared with the findings of the existing Cournot mixed market literature. As a result, the paper shows that that the introduction of production subsidies into the analyses of Bertra...

the markedly high prevalence of obesity contributes to the increased incidence of chronic diseases, such as diabetes, hypertension, sleep apnea, and heart disease. because of high prevalence of obesity in almost all countries, it has been the focus of many researches throughout the world during the recent decades. along with increasing researches, new concepts and controversies have been emerge...