The famous Asgeirsson mean value theorem makes Cauchy problems in the ultra-hyperbolic equations poor posed.

By using fundamental formula and adaptable estimation of inequality, inverse theorem of mean value theorem is given.

In order to improve the invisibility and the robustness of semi-fragile watermark,this paper brings up characteristic and representation in DWT transform domain based on visual features model,and puts forward the quantized central limit theorem which applies to adjust the coefficients in general transform domain.

Popularization of the different Thial mean value theoreme;

On the converse proposition of higher order differential mean value theorem;

Asymptotic property of median for the mean value theorems;

A note on the teaching of Lagrange theorem of mean;

It also puts forward a united extended theorem of famous Cauchy theorem of mean and Taylor theorem of mean.

In this article,a universal method of constructing the auxiliary function is made from the proof of something relevant to the theorem of mean and the theorem of zeros,which is helpful to the learners to master the skills of constructing the auxiliary function and improve the ability in proofing.

An elementray proof of the mid-value theorem in a non-atomic and σ-finite measure space is given by structuring.

This paper explores the expressing problem of broad-sense F-integ r al and provides several theorems: the expression of theorem of truncated functio n, mid-value theorem and rearrangement-converting theorem.

The mid-value theorem is important in the development of Mothematical analysis.