On the Distribution of Perfect Totients

Model Selection for Mixture Models Using Perfect Sample

We have considered a perfect sample method for model selection of finite mixture models with either known (fixed) or unknown number of components which can be applied in the most general setting with assumptions on the relation between the rival models and the true distribution. It is, both, one or neither to be well-specified or mis-specified, they may be nested or non-nested. We consider mixt...

The Distribution of Totients

This paper is an announcement of many new results concerning the set of totients, i.e. the set of values taken by Euler’s φ-function. The main functions studied are V (x), the number of totients not exceeding x, A(m), the number of solutions of φ(x) = m (the “multiplicity” of m), and Vk(x), the number of m ≤ x with A(m) = k. The first of the main results of the paper is a determination of the t...

Application of perfect mixing model for simulation of vertical roller mills

Vertical roller mills (VRMs) are well-established grinding equipment for various tasks in the coal and cement industry. There are few studies on simulation of VRMs. In this research work, application of perfect mixing model for simulation of a VRM in a cement grinding plant was investigated. Two sampling surveys were carried out on the VRM circuit. The samples and data from the first survey wer...

Evaluation of current distribution induced on perfect electrically conducting scatterers

Investigation of Vibrational Behavior of Perfect and Defective Carbon Nanotubes Using Non–Linear Mass–Spring Model

In the present study, the effects of arrangement and distribution of multifarious types of defects on fundamental frequency of carbon nanotubes are investigated with respect to different chirality and boundary conditions. Interatomic interactions between each pair of carbon atoms are modeled using two types of non–linear spring–like elements. To obtain more information about the influences of d...