Two new equivalent conditions of extensively subexponential densities;

Some equivalent conditions of one class of heavy-tailed distributions;

Equivalent condition of minimal square solution in Hilbert space and its application;

quasi_invex vector function, Ⅰ_strictly quasi_invex vector function and KT _Ⅰ_strictly quasi_invex vector function are defined, and then the equivalent conditions that every stationary point or Kuhn_Tucker point is an efficient point are obtained for multiobjective programming.

The present paper deals with the conditions of two-parameter σ-fields in the two-parameter martingales theory, and presents some equivalent conditions of (F5)-condition and G(F4′)-condition and their verification.

The topple old idols and carrying out the appreciation of building geological environment are suggested, and ten appreciation conditions building geological environment are put forward.