This Book is intended to be textbook studied for undergraduate course in multivariate analysis. This book is designed to be used in semester system. In order to achieve the goals of the book, it is divided into the following chapters (as done in the first edition 2019). Chapter One introduces matrix algebra. Chapter Two devotes to Linear Equation System Solution with quadratic forms, Characteristic roots & vectors. Chapter Three discusses Partitioned Matrices and how to get Inverse, Jacobi and Hessian matrices. Chapter Four deals with Multivariate Normal Distribution (MVN). Chapter Five concern with Joint, Marginal and Conditional Normal Distribution, independency and correlations. While the revised new chapters have been added (as the current second edition 2024). Chapter six introduces mean vector estimation and covariance matrix estimation. Chapter seven devotes to testing concerning mean: one sample mean, and two sample mean. Chapter eight discusses special case of factorial analysis which is principal components analysis. Chapter nine deals with discriminant analysis. While chapter ten deals with cluster analysis. Many solved examples are intended in this book, in addition to a variety of unsolved relied problems at the end of each chapter to enrich the statistical knowledge of the readers.
Comparative Analysis of Economic Policy Stability between Monarchical and Republican Systems: A Theoretical Fundamental Research
Background: Dental implants provide a unique treatment modality for the replacement of a lost dentition .This is accomplished by the insertion of relatively an inert material (a biomaterial) into the soft and hard tissue of the jaws, there by providing support and retention for dental prostheses. Low level laser therapy (LLLT) is an effective tool used to prompt bone repair and remodeling, this has referred to the biostimulation effect of LLLT. The Aim of this study was to evaluate the effects of inflammatory cells on osseointegration of CpTi implant irradiated by low level laser. Materials and Methods: thirty two adult New Zealand white rabbits, received titanium implants were inserted in the tibia. The right side is considered as experime
... Show MoreA Raman spectroscopy method was optimised to examine the chemical changes of aspirin tablets after interaction with helium temperatures. Several aspirin tablets were exposed to plasma-assisted desorption ionisation flame for different times (10, 30, 50, 60, 180 and 300s) and then analysed by Raman spectroscopy using optimal conditions. The changes in chemistry between exposed and fresh (without exposure to plasma) tablets were compared. The vibrational peaks of the aspirin molecule in the Raman spectrum were identified by checking the peak position. The results showed clear spectra with increases in intensity of vibrational peaks until 30s, whereas no spectra were measured for the exposed tablets to plasma flame after 50s. It can, the
... Show MoreAmong all the common mechanical transmission elements, gears still playing the most dominant role especially in the heavy duty works offering extraordinary performance under extreme conditions and that the cause behind the extensive researches concentrating on the enhancement of its durability to do its job as well as possible. Contact stress distribution within the teeth domain is considered as one of the most effective parameters characterizing gear life, performance, efficiency, and application so that it has been well sought for formal gear profiles and paid a lot of attention for moderate tooth shapes. The aim of this work is to investigate the effect of pressure angle, speed ratio, and correction factor on the maxi
... Show MoreThe earth-air heat exchanger (EHX) has a promising potential to passively save the energy consumption of traditional air conditioning systems while maintaining a high degree of indoor comfort. The use of EHX systems for air conditioning in commercial and industrial settings offers several environmental benefits and is capable of operating in both standalone and hybrid modes. This study tests the performance and effectiveness of an EHX design in a sandy soil area in Baghdad, Iraq. The area has a climate of the subtropical semi-humid type. Ambient air temperatures and soil temperatures were recorded throughout the months of 2021. During the months of January and June, the temperatures of the inlet and outflow air at varying air veloci
... Show MoreHypocrisy is found in various aspects of life, whether in religion, politics, or social parts. Hence, some of the church's hypocrisy is an outcome of different ups and downs in life. Starting with the problem in the novel, some of the hypocritical pastors engaged in an immense role in affecting the folk's lives because they persuaded people that God ordered them to do so. To accomplish their personal interests, the abusive monks disguise their verbal speech, smiles, and fine clothes like mild sheep to delusional followers, leaving them with guilt, shame, and spiritual scars. The present study aims to examine the hypocrisy and heresy of the church as portrayed in Okezie Nwoka's novel entitled God of Mercy. It reflects the source of
... Show MoreThis study introduces a highly sensitive trapezium-shaped PCF based on an SPR refractometric sensor with unique design features. The structure of a sensor was designed and analyzed using COMSOL Multiphysics v5.6 based on Finite Element Method (FEM) with a focus on investigating the influence of various geometric parameters on its performance. The two channels were coated with a metallic gold layer to provide chemical stability, and a thin layer of TiO₂ improved the gold's adhesion to the fiber. The findings indicate that the proposed sensor achieves maximum amplitude and wavelength sensitivities of 1,779 RIU⁻¹ and 30,500 nm/RIU, respectively, with corresponding resolutions of 3.2
This paper presents a numerical analysis of the piled-raft foundation (PRF) based on the actual behavior of supporting piles. The raft was modeled as a thin plate, while the piles were modeled as springs in different ways. This research also aims to propose an analytical model of piles based on actual behavior at fieldwork. The results proved that the structural behavior of raft member can be improved through utilizing the actual behavior of supporting piles. When the piles were modeled as non-linear stiffness springs, settlements and bending stresses of raft foundation were reduce marginally as compared with those obtained from piles with linear stiffness springs.
Purpose: aims the study to show How to be can to enhance measurement management by incorporating a risk-based approach and the six sigma method into a more thorough assessment of metrological performance. Theoretical framework: Recent literature has recorded good results in analyzing the impact of Six Sigma and risk management on the energy sector (Barrera García et al., 2022) (D'Emilia et al. 2015). However, this research came to validate and emphasize the most comprehensive assessment of metrological performance by integrating Risk management based approach and Six Sigma analysis. Design/methodology/approach: This study was conducted in Iraqi petroleum refining companies. System quality is measured in terms of sigmas, and t
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