This paper will explain the relation between golden ratio Phi and Zeta function SUM. First, we introduce why used its functional properties then go through some of Properties in a complex plane. Finally, use this Golden formula, to find sum Prime numbers infinite series with ration Phi, pi.

We determine the maximal set of moves for 2-pile take-away games with prescribed P -positions (bαnc, bβnc) for n ∈ Z≥1 where α ∈ (1, 2) is irrational, 1/α+1/β = 1. This was done in [3] for the special case α = golden ratio. We generalize the infinite Fibonacci word to an infinite wordW with alphabet Σ = {a, b}, in which α replaces the golden ratio, and we analyze the set {s ∈ Z≥0 : W(s) = b, W(...

An observation was made in this research regarding the fact that the signatures of isotropic charge distributions in silicon nanowire transistors (NWT) displayed identical characteristics to the golden ratio (Phi). In turn, a simulation was conducted regarding ultra-scaled n-type Si (NWT) with respect to the 5-nm complementary metal-oxide-semiconductor (CMOS) application. The results reveal tha...

We propose a new declustering scheme for allocating uniform multidimensional data among parallel disks. The scheme, aimed at reducing disk access time for range queries, is based on Golden Ratio Sequences for two dimensions and Kronecker Sequences for higher dimensions. Using exhaustive simulation, we show that, in two dimensions, the worst-case (additive) deviation of the scheme from the optim...

Fragment-based drug discovery (FBDD) is complementary to high-throughput screening. The approach has two key stages: identifying the starting fragment hit to be developed and generating the lead compound from the starting fragment hit. Here, we provide an overview of FBDD and introduce two indices originally developed at Astellas Pharma. The first is related to the size ratio of fragment hits t...