Heat kernel Riemannian Manifold, Harnack Inequality;

The Heat Kernels Construction of Symmetric Spaces of Type Ⅲ;

We review the properties of the heat kernel of strong elliptic operators and subelliptic operators with divergence form.

The possible reasons for the discrepancy between calculation results based on the statistical evaporation model and experimental data of giant dipole resonance of very hot nuclei are discussed.

The experimental studies and achievements recently made at the Heavy Ion ResearchFacility of Lanzhou(HIRFL) are reviewed with an emphasis on the three research fields: the study ofintermediate energy heavy ion collision and properties of hot nuclei, the synthesis and study of nucleifar from stability, and the applications of heavy ions.

Microscopic study of nuclear charge distribution in hot nucleus;

It is indicated that each theoretical representative point located in the temperature plateau (temperature backhanding) of ALADIN caloric curve does not necessarily fall-down into the region of temperature plateau (temperature backhanding) of the caloric curve of corresponding projectile remnant (hot nucleus).

Since the fusion-fragmentation model includes both the dynamical formation and the statistical disassembly of hot nucleus, all the ALADIN data can be reproduced very well if the model parameter concerning excitation energy is somewhat adjusted.