The article starts with Bridgman distribution, discusses something about Maxwell distribution of relativity particles, and then transfers to non-relativity and extreme relativity particles.

Problems investigated in the thesis consist of two parts: one part is the numerical study of dispersion relations in relativistic plasma with Maxwell distribution; another part is the analytical and numerical studies of dispersion relations in relativistic plasma with Fermi distribution.

Application of non-Maxwellian distribution for the ion velocity in calculation of incoherent scattering spectra in high-latitude ionosphere;

This distribution laws takes the Maxwell distribution law as the limiting case when the number of particles N aproaches infinity.

The have proved that Maxwell distribution might give up distribution of turn and vibration in without regular motion,Eigen funtion ( m,v ) is only change by ( I,ω ) or (α,x ).

Based on Maxwellian distribution and De Broglie relation and the relation between the classical law and quantum law ,this paper analyses the relation between characteristic frequency and three-characteristic speed of gaseous molecule in equilibrium states and discusses the applications of division frequency and division temperature as well as the relation between them.