Definition 1. An (archimedean) absolute value on a field k is a real valued function ‖ · ‖ : k → [0,∞) with the following three properties: (1) ‖x‖ = 0 if and only if x = 0. (2) ‖xy‖ = ‖x‖ · ‖y‖. (3) ‖x+ y‖ ≤ ‖x‖+ ‖y‖. A nonarchimedean absolute value satisfies the extra condition that (3’) ‖x+ y‖ ≤ max{‖x‖, ‖y‖}. If k is a field, we denote Mk the set of absolute values on k. As an abuse of nota...

To highlight certain similarities in graphical representations of several well known two-dimensional models statistical mechanics, we introduce and study a new family which specializes to these cases after proper tuning the parameters. be precise, our model consists two independent standard Potts models, with possibly different numbers spins coupling constants (the four parameters model), defin...

This is the Part II of our paper “Height functions for motives”. We consider more general period domains and height on sets motives. also corresponding Hodge theoretic variant Nevanlinna theory.

So it is in the American economy. Just to retain its relative position, a business firm must go through continuous growth and change. To improve its position, it must grow and change at least "twice as fast as that." According to a recent survey of the ioo largest United States corporations from 1909 to 1948, few companies that have stuck to their traditional products and methods have grown in ...