We introduce the volume function for C-hermitian invertible sheaves on an arithmetic variety as an analogue of the geometric volume function. The main result of this paper is the continuity of the arithmetic volume function. As a consequence, we have the arithmetic Hilbert-Samuel formula for a nef C-hermitian invertible sheaf. We also give another applications, for example, a generalized Hodge ...

In this note, we present sharp inequalities relating hypergeometric analogues of the arithmetic-geometric mean discussed in [5] and the power mean. The main result generalizes the corresponding sharp inequality for the arithmetic-geometric mean established in [10].

Phenol formaldehyde (phenolic resin) has a wide range of moldings. However, it immense consumption in manufacturing electrical equipment due to its insulating property. Phenolic resin retains properties at the freezing point, and also age cannot be determined. Due insulator property, use equipment. In this article, degree-based topological indices phenol are determined with help M-polynomial. W...