Due to the constantly growing number of information sources, intelligent information retrieval becomes a more and more important task. We model information sources by description logic (DL) terminologies. The commonalities of user-speci ed examples can be computed by the least common subsumer (LCS) operator. However, in some cases this operator delivers too general results. In this article we s...

There are two parts for this paper. In the first part, we extend some results in a recent paper by Du, Guth, Li and Zhang to more general class of phase functions. The main methods Bourgain-Demeter's $l^2$ decoupling theorem induction on scales. second prove positive maximal extension operator hypersurfaces with principal curvatures. sharp $L^2$ estimates Du Zhang, bilinear method Wolff Tao.

It has a wide application in the problem of physics, chemistry, biology, engineering and applied sciences. The theory Bessel functions is intimately connected with certain types differential equations. A detail account applications are given book Watson [26]. In this present paper, we establish generalized extension k-Bessel-Maitland function involving pathway integral operator. obtain composit...