Assume that G is a finite group and X is a subset of G. The commuting graph is denoted by С(G,X) and has a set of vertices X with two distinct vertices x, y Î X, being connected together on the condition of xy = yx. In this paper, we investigate the structure of Ϲ(G,X) when G is a particular type of Leech lattice groups, namely Higman–Sims group HS and Janko group J₂, along with  X as a G-conjugacy class of elements of order 3. We will pay particular attention to analyze the discs’ structure and determinate the diameters, girths, and clique number for these graphs.

The present study aims to study the content and spatial distribution of lead (Pb) contamination in the soils of some Baghdad cities (Middle of Iraq). Twenty soil samples were randomly collected from different land-use in the studied area at a depth between 5 to 30 cm. Ten samples are collected from Al-Rissafa side areas (Adhamiya, Al-Wazeeria (Battery Manufacturer), Shikh Omer, Ziyouna, Karada, Shaab, Sadr city, Al-Za’franiya, Al-Dora expressway, and Alselikh ) and other ten samples are collected from Al-Krakh side areas Al-Dora, Al-Masafi junction, Al-Dora, Sayidia, Al-Salam university college, Al-Bayaa (Industrial District), Jehad, Amirya, Abu Ghraib, Al-hurriya, and Kadhimiya. The soil samples have been analyzed for the lead (P

Background: The anterior loop of mental nerve is commonly described as that part of the neurovascular bundle that transverses anterior and inferior to the mental foramen only to loop back to exit the mental foramen. The aim of the study is to evaluate the incidence and extension of anterior loop of mental nerve by using digital panoramic imaging system to avoid nerve damage during different surgical procedures in dentistry. Materials and Method: Panoramic image was taken for all 400 patients and stored in the computer. Then Horizontal and Vertical for the anterior loop extension when exist was measured and recorded in a special case sheet prepared for each subject. Results: Results indicated that out of 400 patients there were only 25 pat

Using a mathematical model to simulate the interaction between prey and predator was suggested and researched. It was believed that the model would entail predator cannibalism and constant refuge in the predator population, while the prey population would experience predation fear and need for a predator-dependent refuge. This study aimed to examine the proposed model's long-term behavior and explore the effects of the model's key parameters. The model's solution was demonstrated to be limited and positive. All potential equilibrium points' existence and stability were tested. When possible, the appropriate Lyapunov function was utilized to demonstrate the equilibrium points' overall stability. The system's persistence requirements were spe

The health of Roadway pavement surface is considered as one of the major issues for safe driving. Pavement surface condition is usually referred to micro and macro textures which enhances the friction between the pavement surface and vehicular tires, while it provides a proper drainage for heavy rainfall water. Measurement of the surface texture is not yet standardized, and many different techniques are implemented by various road agencies around the world based on the availability of equipment’s, skilled technicians’ and funds. An attempt has been made in this investigation to model the surface macro texture measured from sand patch method (SPM), and the surface micro texture measured from out flow time (OFT) and British pendul

This paper proposes a new structure of the hybrid neural controller based on the identification model for nonlinear systems. The goal of this work is to employ the structure of the Modified Elman Neural Network (MENN) model into the NARMA-L2 structure instead of Multi-Layer Perceptron (MLP) model in order to construct a new hybrid neural structure that can be used as an identifier model and a nonlinear controller for the SISO linear or nonlinear systems. Weight parameters of the hybrid neural structure with its serial-parallel configuration are adapted by using the Back propagation learning algorithm. The ability of the proposed hybrid neural structure for nonlinear system has achieved a fast learning with minimum number

Background: Several reports show that hypertension is a leading cause of maternal and fetal morbidity; also ABO blood group may be blamed in susceptibility to human diseases as blood-group antigens which influence the bioavailability of E-selectin, TNF-alpha and intra cellular adhesion molecule-1 (ICAM1) factors that implicated in the pathogenesis of preeclampsia.

Objective: To evaluate the possible