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.
In this study, plastic wastes named (PET and PVC) were used to prepare polymer matrix composite (PMC) which can be used in different applications. Composite materials were prepared by mixing unsaturated polyester resin (UP) with plastic wastes, two types of plastic waste were used in this work included polyethylene-terephthalate (PET) and Polyvinyl chloride (PVC) with various weight fractions (0, 5,10,15, 20 and 25%) added as a filler in flakes form. In this work, some of the tests that were carried out included (tensile, bending, and compressive strength) as mechanical tests, in addition to (thermal conductivity and water absorption) as physical tests. The values of tensile, compressive strength and Young's modulus of UP increased after
... Show MoreAntioxidant status imbalance and inflammatory process are cooperative events involved in type 2 diabetes mellitus. This study aimed to investigate superoxide dismutase as a potential biomarkers of antioxidant imbalance, matrix-metaloprotinase-9, and interleukin -18 as biomarkers of inflammation in serum and to estimate the effects of other confounding factors gender, age and finally measuring the relation among the interested biomarkers.
This case - control study included 50 patients, and 45 of healthy subjects matched age –gender were also enrolled in this study as a control group. The focused  
... Show MorePVA:PEG/MnCl2 composites have been prepared by adding (MnCl2) to the mixture of the poly vinyl alcohol (PVA) and poly ethylene glycol (PEG) with different weight percentages (0, 2, 4, 6, 8 and 10) wt.% by using casting method. The type of charge carriers, concentration (nH) and Hall mobility (μH) have been estimated from Hall measurements and show that the films of all concentration have a negative Hall coefficient. In D.C measurement increase temperature leads to decrease the electrical resistance. The D.C conductivity of the composites increases with the increasing of the concentration of additive particles and temperature. The activation energy decreases for all composites with increasing the concentration of the additive particles.
... Show MoreSeveral attempts have been made to modify the quasi-Newton condition in order to obtain rapid convergence with complete properties (symmetric and positive definite) of the inverse of Hessian matrix (second derivative of the objective function). There are many unconstrained optimization methods that do not generate positive definiteness of the inverse of Hessian matrix. One of those methods is the symmetric rank 1( H-version) update (SR1 update), where this update satisfies the quasi-Newton condition and the symmetric property of inverse of Hessian matrix, but does not preserve the positive definite property of the inverse of Hessian matrix where the initial inverse of Hessian matrix is positive definiteness. The positive definite prope
... Show MoreThis study suggests using the recycled plastic waste to prepare the polymer matrix composite (PMCs) to use in different applications. Composite materials were prepared by mixing the polyester resin (UP) with plastic waste, two types of plastic waste were used in this work included polyethylene-terephthalate (PET) and Polyvinyl chloride (PVC) with varies weight fractions (0, 5, 10, 15, 20 and 25 %) added as a filler in flakes form. Charpy impact test was performed on the prepared samples to calculate the values of impact strength (I.S). Flexural and hardness tests were carried out to calculate the values of flexural strength and hardness. Acoustic insulation and optical microscope tests were carried out. In general, it is found that UP/PV
... Show MoreThe Boltzmann transport equation is solved by using two- terms approximation for pure gases . This method of solution is used to calculate the electron energy distribution function and electric transport parameters were evaluated in the range of E/N varying from . 172152110./510.VcmENVcm
From the results we can conclude that the electron energy distribution function of CF4 gas is nearly Maxwellian at (1,2)Td, and when E/N increase the distribution function is non Maxwellian. Behavior of electrons transport parameters is nearly from the experimental results in references. The drift velocity of electron in carbon tetraflouride is large compared with other gases
Three-dimensional nonlinear thermal numerical simulations are conducted for the friction stir welding (FSW) of AA 7020-T53. Three welding cases with tool (rotational and travel) speeds of 900rpm-40mm/min, 1400rpm-16mm/min and 1400rpm-40mm/in are analyzed. The objective is to study the variation of transient temperature in a friction stir welded plate of 5mm workpiece thickness. Based on the experimental records of transient temperature at several specific locations during the friction stir welding process for the AA 7020-T53, thermal numerical simulation is developed. The numerical results show that the temperature field in the FSW process is symmetrically distributed with respect to the welding line, increasing travel speed decreasing tran
... Show MoreThe objective of this research was to estimate the dose distribution delivered by radioactive gold nanoparticles (198 AuNPs or 199 AuNPs) to the tumor inside the human prostate as well as to normal tissues surrounding the tumor using the Monte-Carlo N-Particle code (MCNP-6.1. 1 code). Background Radioactive gold nanoparticles are emerging as promising agents for cancer therapy and are being investigated to treat prostate cancer in animals. In order to use them as a new therapeutic modality to treat human prostate cancer, accurate radiation dosimetry simulations are required to estimate the energy deposition in the tumor and surrounding tissue and to establish the course of therapy for the patient. Materials and methods A simple geometrical
... Show MoreShatt al-Arab is the only navigational artery in Iraq, extending from the city of Qurna to its mouth in the Arabian Gulf at the city of Al-Fao within the governorate of Basrah for a length of approximately 204 km. Its width ranges from 400 m to 2000 m, and its depth ranges from 8 m to 20 m. The southern part of it, 93 km long from Umm al-Rassas Island to Ras al-Bisha, represents the international border between Iraq and Iran, where the Thalweg line represents the border between the two countries, which is the deepest point in the riverbed (according to the 1975 Algiers Agreement). The western bank (the Iraqi side) within the common border of Shatt al-Arab is subject to continuous erosion, which leads to the shifting of t
... Show MoreFreshwater mussels are a guild of stationary, suspended-feeding species; they perform significant ecological functions like nitrogen cycling, bioturbation that gives oxygen and habitat that other creatures need to survive, and increasing water clearance by filtration. Knowledge of the freshwater mussel Unio tigridis Bourguignat, 1852, distribution, and molecular study in Iraq was inadequate. In the current study, this species of freshwater Mussels belonging to the family Unionidae was collected from different locations in the Greater Zab River, from April 2022 to November 2022. The average water temperature of the site was arranged between (17.8 to 36.1 C°). All previous studies in the Kurdistan Region and Iraq were based on morphologic
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