Two arithmetic theorems

Arithmetic and the Incompleteness Theorems

Arithmetic Duality Theorems Second Edition

Addendum/Erratum for Arithmetic Duality Theorems

Then H need not be divisible, i.e., we need not have pH D H . We only know H is contained in pG. Moreover, for x in H , there need not exist an infinite sequence y1;y2;y3:::: such that py2 D y1, py3 D y2; ::. We only know that there exist arbitrarily long finite such sequences. There does exist a unique maximal divisible subgroup D of M , and D is a subgroup of H . Moreover, M DD ̊N where N is a...

Two Types of Geometric–Arithmetic Index of V–phenylenic Nanotube

The concept of geometric-arithmetic indices was introduced in the chemical graph theory. These indices are defined by the following general formula:     ( ) 2 ( ) uv E G u v u v Q Q Q Q GA G , where Qu is some quantity that in a unique manner can be associated with the vertex u of graph G. In this paper the exact formula for two types of geometric-arithmetic index of Vphenylenic nanotube ar...

Two Pebbling Theorems