Some interpolation inequalities with the variable step of discrete functions;

Objective: Study the expression form of the discrete function of gray model.

In the paper, the criterion of the white exponential law of a discrete function is given after discussing the necessary and sufficient conditions of a continuous function being an exponential function.

Application of categorization based on distance function in spam filtering;

The improvement of the fault diagnosis of distance function based on immune syst ems mechanism;

Then it fills color in the correct region,gets the value of cell area,perimeter and form factor,writes the seeds using distance function and split the joint region with watersheds segmentation.

On the basis of the principle of separation function method this paper achieved a kind of design of gear with new typed tooth form and carried out a calculation and finite element strength simulation on the main parameters.