26 papers
Simple close curve magnetization and application to Bellman's lost in the forest problem
Theophilus Agama
In this paper, we introduce and develop the notion of simple closed-curve magnetization. We provide an application to the Bellman lost in the forest problem by assuming special geo…
On the ErdÅs distance problem
Theophilus Agama
In this paper, using the compression method, we recover the lower bound for the ErdÅs unit distance problem and provide an alternative proof to the distinct distance conjecture. I…
Complex Circles of Partition and the Expansion Principles
Berndt Gensel, Theophilus Agama
In this paper, we further develop the theory of circles of partition by introducing the notion of complex circles of partition. This work generalizes the classical framework, exten…
On the distribution of addition chains
Theophilus Agama
Addition chains are a classical construction for fast exponentiation and related computation problems. In this paper, we study a chain for a fixed integer by decomposing each g…
Studies in Additive Number Theory by Circles of Partition
Theophilus Agama, Berndt Gensel
In this paper, we introduce and develop the circle embedding method. This method hinges essentially on a combinatorial-geometric structure which we choose to call circles of partit…
On the pointwise periodicity of multiplicative and additive functions
Theophilus Agama
We study the problem of estimating the number of points of coincidences of an idealized gap on the set of integers under a given multiplicative function $g:\mathbb{N}\longrightarro…