The continuity and differentiability properties of quasi convex functions are discussed,and the specific properties of one real variable of the functions are also given.

The continuity and differentiability for composite function are the important content in advanced mathematics.

Then the paper further gives the definition of the differentiability and its proof when n≥3,the function Z= f(x_1,x_2,……,x_n)is at M.

Another Two Forms of Necessary and Sufficient Condition of Differentiable Complex Function;

The paper introduces a kind of differentiable fractal interpolation function,discusses its generating mechanismas well as the sufficient condition that generates its IFS.

This paper studied a class of multiobjective programing problems involving differentiable n-set functions,and obtained sufficient optimality conditions for weak efficient solutions under generalized convexity conditions.

in this paper, the author proves some equivalent forms of convex function definition, summarizes continuous and differential properties of convex function, obtains some useful results in mathematical programming, and verifies proposition 3.

Furthermore,we obtain a sufficient and necessary condition about continuity of functional series and integral with parameter,and show the sufficient condition about differential.

This paper discusses the existence of partial derivative of x(or y) about a point (X_0, y_0) and analyzes conditions of continuance of X_0(or y_0) about function of y_1(or X_1)--f(x, y,) (or f(x, y) ), and puts forward a conditioned theorem, by which differential sufficient condition of a binary function can be demonstrated.

Mass transfer kinetics of PVP across oil-water interface by using micro visualization technique;