Stars are the building blocks of the Universe and, as such, are essential to understanding many aspects of astrophysics. Our understanding of cosmology, galaxies and planetary formation all depend on stellar evolution. To understand how stars evolve we need to investigate stars in different evolutionary stages. So far, individual p-mode frequencies have been identified for a few stars. Asteroseismology, as a tool to use the indirect information contained in stellar oscillations to probe the stellar interiors, is an active field of research presently. That is because the frequencies of these oscillation depend on the sound speed inside the star, which in turn depends on density, temperature, gas motion and other properties of the stellar interior. Therefore, the analysis of the oscillations takes the window to “see”the interior of stars. Using these oscillations, we can study the stellar structure and evolution of low mass stars, construct the stellar model and test the stellar evolution theory. In a word, asteroseismology provides us a chance to study and improve our stellar structure and evolution theory. The goals of the work presented are to investigate the stellar structure and evolution of low-mass main sequence stars and construct the stellar structure and evolution theory including the rotation and magnetic field. The relations between the effects of magnetic fields and rotation and all physical variables are presented. The investigations are extended to the problem of interaction between magnetic fields and convection, the effect of the magnetic fields to the equation of state, and the transport of angular momentum and mixing of the chemical elements owing to the meridional circulation and turbulence. The models of stellar structure and evolution theory including the magnetic fields and rotation are significantly developed. Since asteroseismology has provided a great deal of insight into the stellar interiors, the inclusions of new physical effects in the structure and evolution of solar-like stars greatly improve the comparisons with observations. The magnetic fields and rotation may influence all the outputs of stellar evolution, therefore, the relative importance of the effets is to try to explain observed stellar activities and their special behaviors. In additional, We proposed a new quantity which can be correlated with stellar age and developed a new asteroseismic HR diagram to determine the mass and age of solar-like stars. This asteroseismic technique that will provide the tools to connect data with models using the seismic data.
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