We give simple and unified proofs of weak holomorhpic Morse inequalities on complete manifolds, $q$-convex pseudoconvex domains, weakly $1$-complete manifolds covering manifolds. This paper is essentially based the asymptotic Bergman kernel functions Bochner-Kodaira-Nakano formulas.

Support Vector Machines (SVM) and kernel techniques have been proven effective on various application domains using attributevalue representation. A number of works have been done to apply SVM on First-Order Logic (FOL) data as well as using SVM with Inductive Logic Programming (ILP). In this paper, we propose kernel functions for FOL data developed from the four-layer distance metric. Since ou...

We derive whole series of new integral inequalities of the Hardy-type, with non-conjugate exponents. First, we prove and discuss two equivalent general inequa-li-ties of such type, as well as their corresponding reverse inequalities. General results are then applied to special Hardy-type kernel and power weights. Also, some estimates of weight functions and constant factors are obtained. ...