Abstract:
According to different topological configurations, we suggest that there are two kinds of extreme black holes in the nature. We find that the Euler characteristic plays an essential role to classify these two kinds of extreme black holes. For the first kind of extreme black holes, Euler characteristic is zero, and for the second kind, Euler characteristic is two or one provided they are four dimensional holes or two dimensional holes respectively.

Abstract:
Through direct thermodynamic calculations we have shown that different classical entropies of two-dimensional extreme black holes appear due to two different treatments, namely Hawking's treatment and Zaslavskii's treatment. Geometrical and topological properties corresponding to these different treatments are investigated. Quantum entropies of the scalar fields on the backgrounds of these black holes concerning different treatments are also exhibited. Different results of entropy and geometry lead us to argue that there are two kinds of extreme black holes in the nature. Explanation of black hole phase transition has also been given from the quantum point of view.

Abstract:
Using the quark mass density- and temperature-dependent model, we have studied the properties of the dibaryon systems. The binding energy, radius and mean lifetime of Omega-Omega and Omega-Xi are given. We find the dibaryons Omega-Omega, Omega-Xi are metastable at zero temperature, but the strong decay channel for Omega-Omega opens when temperature arrives at 129.3MeV. It is shown that our results are in good agreement with those given by the chiral S(3) quark model.

Abstract:
A new improved quark mass density-dependent model including u, d quarks, $\sigma$ mesons, $\omega$ mesons and $\rho$ mesons is presented. Employing this model, the properties of nuclear matter, neutron matter and neutron star are studied. We find that it can describe above properties successfully. The results given by the new improved quark mass density- dependent model and by the quark meson coupling model are compared.

Abstract:
By using the finite temperature quantum field theory, we calculate the finite temperature effective potential and extend the improved quark mass density-dependent model to finite temperature. It is shown that this model can not only describe the saturation properties of nuclear matter, but also explain the quark deconfinement phase transition successfully. The critical temperature is given and the effect of $\omega$- meson is addressed.

Abstract:
The ambiguities and inconsistencies in previous thermodynamic treatments for the quark mass density-dependent model are addressed. A new treatment is suggested to obtain the self-consistent results. A new independent variable of effective mass is introduced to make the traditional thermodynamic calculation with partial derivative still practicable. The contribution from physical vacuum has been discussed. We find that the properties of strange quark matter given by quark mass density-dependent model are nearly the same as those obtained by MIT bag model after considering the contribution of the physical vacuum.

Abstract:
The thermodynamic consistency of quasiparticle boson system with effective mass $m^*$ and zero chemical potential is studied. We take the quasiparticle gluon plasma model as a toy model. The failure of previous treatments based on traditional partial derivative is addressed. We show that a consistent thermodynamic treatment can be applied to such boson system provided that a new degree of freedom $m^*$ is introduced in the partial derivative calculation. A pressure modification term different from the vacuum contribution is derived based on the new independent variable $m^*$. A complete and self-consistent thermodynamic treatment for quasiparticle system, which can be widely applied to effective mass models, has been constructed.

Abstract:
Using the quark mass density- and temperature dependent model, we have studied the thermodynamical properties and the stability of strangelet at finite temperature. The temperature, charge and strangeness dependences on the stability of strangelet are investigated. We find that the stable strangelets are only occured in the high strangeness and high negative charge region.

Abstract:
A Wronskian determinant approach is suggested to study the energy and the wave function for one-dimensional Schrodinger equation. An integral equation and the corresponding Green's function are constructed. As an example, we employed this approach to study the problem of double-well potential with strong coupling. A series expansion of ground state energy up to the second order approximation of iterative procedure is given.

Abstract:
The thermodynamics with medium effects expressed by the dispersion relation of the temperature and density dependent particle mass is studied. Many previous treatments have been reviewed. A new thermodynamical treatment based on the equilibrium state is suggested. Employing the quark mass density- and temperature-dependent model, the discrepancies between our treatment and others are addressed.