In this project new theoretical methods were developed to investigate the properties of impurity electronic systems strongly correlated. We were discuss Generalized Wick Theorem (GWT) proposed in 1990 by one of our authors and published in TMF. It contains new element as Kubo cumulants, irreducible Green's functions and correlation functions. Analogous generalization has been proposed by Metzner one year late in PRB. By using this new conception the main theoretical models as Hubbard, Anderson and Holstein have been investigated and in next period of time this study will be continued. We were formulated the main equations of the non-equilibrium of the Anderson model. The simplest irreducible Green's function was used and its properties determined.

We were formulate and investigate the new model of Anderson with two strongly correlated impurity centers and analyze the mechanism of exchange the fluctuations between them.

The diagrammatic technique for strongly correlated systems was be formulated by using GWT and irreducible diagrams used for different positions of time evolution contours. The corresponding matrix Green's functions were introduced.

The improved Hubbard model was used which describe the quasi-bi-dimensional systems with two bands taking into account deviation of the electrons from half filling of bands and also take in consideration the presence of the Cooper pairs and anisotropy of energy spectrum.

The theory of the phase transitions was elaborated inclusive for the transition dielectric-semimetal which is connected with the umklapp processes of scattering.The parameters which together with the deformation of the Fermi surface result in mixed state of spin density wave and superconductivity, to the maximal value of the transition temperature in the superconducting state and determine the dependence of physical quantities of the temperature and impurity concentration were determined.

The string model of quark gluon which was elaborated for study of the nuclear reactions with hadrons and heavy ions at intermediate and relativist energies were developed.
The program of calculations was generalized to take into account new effect of nuclear matter produced by collision of heavy ions at density and temperature extremal. When the conditions of phase transition are Plasmon quark-gluon effect hydrodynamics of the vorticity and helicity kind appear. The obtained results were compared with experimental data.