An injective map from the vertex set of a graph G—its order may not be finite—to the set of all natural numbers is called an arithmetic (a geometric) labeling of G if the map from the edge set which assigns to each edge the sum (product) of the numbers assigned to its ends by the former map, is injective and the range of the latter map forms an arithmetic (a geometric) progression. A graph is c...

Here, we initiate a program to study relationships between finite groups and arithmetic–geometric invariants in systematic way. To do this, first introduce notion of optimal module for group the setting holomorphic mock Jacobi forms. Then, classify modules cyclic prime order, special case weight 2 index 1, where class numbers imaginary quadratic fields play an important role. Finally, exhibit c...

This paper proposes arithmetic and geometric Paasche quality-adjusted price indexes that combine micro data from the base period with macro data on the averages of asset prices and characteristics at the index period. The suggested index has two types of advantages relative to traditional Paasche indexes: (i) simplification and cost reduction of data acquisition and manipulation; and (ii) poten...

In this paper, we investigate the means of the values of prime counting function $pi(x)$. First, we compute the arithmetic, the geometric, and the harmonic means of the values of this function, and then we study the limit value of the ratio of them.