The aim of this paper is to establish new integral inequalities involving functions of two independent variables which is related to Hardy s integral inequality.

Regulative relationship is the genuine relationship of sufficient condition which includes two independences.

The key problem for an equilibrium system is to stipulate its state and define several independent variables.

In the multi-variable system,there generally exist errors in the determination of independent variable number based on covariance matrix eigenvalues because of the nonuniformity in data space.

The shortest path computation with neural network based on independent variables;

Dual Structure, Two Cost-ignoring, Two Variables and Peasant Issue of Ancient China: A Study of the Relationship between State and Peasant in Ancient China;

A study of the relation between characteristic thermodynamic variable and independent variable of one phase equilibrium system;

Based on the defining of independent variables of the state in the equilibrium system, this paper discusses how to select independent variables in different states and the relation between intensive variable and extensive variable when to select independent variables.