There is a family of vector bundles over the moduli space stable curves that, while first appearing in theoretical physics, has been an active topic study for algebraic geometers since 1990s. By computing rank exceptional Lie algebra g2 case these three different ways, summation formulas Fibonacci numbers terms golden ratio derived.

Whether the golden ratio is the favorite ratio for people is a controversial research issue until now. The purpose of this study is to investigate whether oriental people in Taiwan have the preference to the western culture originated golden ratio and to find out how the personality affects ratio preference by using the MBTI (Myers-Briggs Type Indicator) test to classify people into different p...

INTRODUCTION The golden proportion has been used in dentistry in an attempt to improve facial function and, possibly, esthetics by simplifying the diagnosis of facial and dental disharmony. The aim of this study is to analyze pre- and postoperative cephalometric tracings of lateral cephalograms of patients with class II and III deformities submitted to orthognathic surgery, and verify if the 13...

We propose two new spectral measures for graphs and networks which characterize the ratios between the width of the ‘‘bulk’’ part of the spectrum and the spectral gap, as well as the ratio between spectral spread and the width of the ‘‘bulk’’ part of the spectrum. Using these definitions we introduce the concept of golden spectral graphs (GSG), which are graphs for which both spectral ratios ar...

Applying the theory of Yang-Lee zeros to nonequilibrium critical phenomena, we investigate the properties of a directed bond percolation process for a complex percolation parameter p. It is shown that for the Golden Ratio p = (1± √ 5)/2 and for p = 2 the survival probability of a cluster can be computed exactly. PACS numbers: 02.50.-r,64.60.Ak,05.50.+q Directed percolation (DP) is an anisotropi...

In this paper, we have presented the golden ratio-Haar wavelet based multimedia steganography. The key features of the proposed method are: 1. New Haar wavelet structure based on the Fibonacci sequence, and Golden Ratio. 2. Parametric transform dependency, as decryption key, on the security of the sensitive data. One of the important differences between the existing transform based data hiding ...