Based on the extension theory of matter element, the matter element of imaginary part of object is discussed.

Inequalities between the eigenvalues of matrices andits real parts as well as its imaginary parts;

The upper bounds and lower bounds of the matrix eigenvalues,and the inequalities of their real parts and imaginary parts are studied; meantime some new upper bounds and lower bounds of the eigenvalues are also given out in this paper.

Under the Thermofield Dynamics, according to the cutting theorem at finite temperature a set of systematic explicit cutting rules to the Feynman diagrams and the relative Feynman rules are proposed, which can be used as an easy approach to calculate the imaginary parts of the thermal Green functions.

Solving the composite structures of different mediums with virtual boundary element method;

The virtual boundary element method for the potential problems;

Based on the fundamental solution of plane piezoelectric problems and the basic thought of the virtual boundary element method for elasticity, this paper presents a virtual boundary element-equivalent collocation method for plane piezoelectric materials.

To process the pumping well as a series of virtual units could simulate the changes between the drawdown and the time in each point of the calculating region,research the law of water movement,solve the pumping of group wells at constant rate under the condition of the random boundary,forecast the phreatic surface,instruct the construction progress and appraise the rationality of the water l.