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A non-local and time-dependent theory of convection was briefly described. This theory was used to calculate the structure of solar convection zones, the evolution of massive stars, lithium depletion in the atmosphere of the Sun and late-type dwarfs, and stellar oscillations (in Part Ⅱ). The results show that: 1) the theoretical turbulent velocity and temperature fields in the atmosphere and the thermal structure of the convective envelope of the Sun agree with the observations and inferences from helioseismic inversion very well. 2) The so-called semi-convection contradiction in the evolutionary calculations of massive stars was removed automatically, as predicted by us. The theoretical evolution tracks of massive stars run at higher luminosity and the main sequence band becomes noticeably wider in comparison with those calculated using the local mixing-length theory (MLT). This means that the evolutionary mass for a given luminosity was overestimated and the width of the main sequence band was underestimated by the local MLT, which may be part of the reason for the contradiction between the evolutionary and pulsational masses of Cepheid variables and the contradiction between theoretical and observed distributions of luminous stars in the H-R diagram. 3) The predicted lithium depletion, in general, agrees well with the observation of the Sun and Galactic open clusters of different ages. 4) Our theoretical results for non-adiabatic oscillations are in good agreement with the observed mode instability from classic variables of high-luminosity red giants. Almost all the instability strips of the classical pulsating variables (including the Cepheid,    δ    Scuti,    γ    Doradus, βCephei, and SPB strips) were reproduced (Part Ⅱ).

frontiers in astronomy and space sciences

Convection Theory and Relevant Problems in Stellar Structure, Evolution, and Pulsational Stability I Convection Theory and Structure of Convection Zone and Stellar Evolution