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.
Physical and chemical adsorption analyses were carried out by nitrogen gas using ASTM apparatus at 77 K and hydrogen gas using volumetric apparatus at room temperature respectively. These analyses were used for determination the effect of coke deposition and poisoning metal on surface area, pore size distribution and metal surface area of fresh and spent hydrodesulphurization catalyst Co-MoAl2O3 .Samples of catalyst (fresh and spent) used in this study are taken from AL-Dura refinery. The results of physical adsorption shows that surface area of spent catalyst reduced to third compare with fresh catalyst and these catalysts exhibit behavior of type four according to BET classification ,so, the pores of these samples are cylindrical, and the
... Show MoreThis Research Tries To Investigate The Problem Of Estimating The Reliability Of Two Parameter Weibull Distribution,By Using Maximum Likelihood Method, And White Method. The Comparison Is done Through Simulation Process Depending On Three Choices Of Models (?=0.8 , ß=0.9) , (?=1.2 , ß=1.5) and (?=2.5 , ß=2). And Sample Size n=10 , 70, 150 We Use the Statistical Criterion Based On the Mean Square Error (MSE) For Comparison Amongst The Methods.
Physical and chemical adsorption analyses were carried out by nitrogen gas using ASTM apparatus at 77 K
and hydrogen gas using volumetric apparatus at room temperature respectively. These analyses were used for
determination the effect of coke deposition and poisoning metal on surface area, pore size distribution and
metal surface area of fresh and spent hydrodesulphurization catalyst Co-Mo\Al2O3 .
Samples of catalyst (fresh and spent) used in this study are taken from AL-Dura refinery.
The results of physical adsorption shows that surface area of spent catalyst reduced to third compare with
fresh catalyst and these catalysts exhibit behavior of type four according to BET classification ,so, the pores
of these sample
Vitamin K-dependent protein (VKDP) contributes to the development of lung cancer. The purpose of this research was to better understanding of the role of blood matrix Gla protein (MGP), VKDPs, Malondialdehyde (MDA), Superoxide dismutase (SOD) and Vitamin K (Vit K) in Iraqi patients with lung cancer before and after the first cycle of chemotherapy. Blood samples were collected from Al amal National Hospital for cancer treatment from October 2021 to May 2022, and a total of 80 samples were collected, divided into two groups (40 patient before taking a chemotherapy and 40 patients after taking chemotherapy), ranging in age from 20 to 45 years old. The results showed that although there were highly statistically significant differences in MD
... Show More... Show MoreThe present article studies the specific cultural features contained in phraseological units. The problem is approached through three different levels:
- The modern linguistic meaning.
- Lexical components of phraseological units.
- The first variables of linguistic units.
The paper emphasizes the gradual process of the cultural charge in the semantic structure of phraseological units.
Наша Статья посвящена вопросам анализа национ-ально - культурной сп
In this work, the calculation of matter density distributions, elastic charge form factors and size radii for halo 11Be, 19C and 11Li nuclei are calculated. Each nuclide under study are divided into two parts; one for core part and the second for halo part. The core part are studied using harmonic-oscillator radial wave functions, while the halo part are studied using the radial wave functions of Woods-Saxon potential. A very good agreement are obtained with experimental data for matter density distributions and available size radii. Besides, the quadrupole moment for 11Li are generated.
This study was established to investigate the correlation between the expression of matrix metalloproteinases (MMP-1) and the pathogenesis of osteoarthritis (OA). Blood samples were collected from 55 female patients with inflammatory OA and controls for estimation of serum (MMP-1) levels. In the current study, there is significant increase (p<0.001) in the mean of serum MMP-1 levels in osteoarthritis females (4027.73 ± 1345.28 pg/ml) than that in control females (798.76 ± 136.79 pg/ml). It was concluded that MMP-1 may be associated with the pathogenesis of osteoarthritis.
The present work investigates the effect of; superficial air velocities of: 1, 3, and 6 cm/s for two types of perforated distributor on hydrodynamic characteristic in a gas-liquid dispersion column of; air-water, and airaqueous-n-propanol solution. Bubble distribution, gas holdup, and power consumption are parameters take in consideration. Experimental work was carried out in perspex column of 8.5 cm inside diameter and 1.5 m height. Two types of bubble generator (perforated plate) were fixed at the bottom of the column; plate A (99 holes of 0.5 mm diameter and free area of 0.34%), plate B (20 holes of 1.5 mm diameter and free area of 0.62%). Photographic technique was used to measure the bubble parameters. The experimental results were
... Show MoreThis paper is interested in certain subclasses of univalent and bi-univalent functions concerning to shell- like curves connected with k-Fibonacci numbers involving modified Sigmoid activation function θ(t)=2/(1+e^(-t) ) ,t ≥0 in unit disk |z|<1 . For estimating of the initial coefficients |c_2 | , |c_3 |, Fekete-Szego ̈ inequality and the second Hankel determinant have been investigated for the functions in our classes.
The ground state proton, neutron and matter densities of exotic 11Be and 15C nuclei are studied by means of the TFSM and BCM. In TFSM, the calculations are based on using different model spaces for the core and the valence (halo) neutron. Besides single particle harmonic oscillator wave functions are employed with two different size parameters Bc and Bv. In BCM, the halo nucleus is considered as a composite projectile consisting of core and valence clusters bounded in a state of relative motion. The internal densities of the clusters are described by single particle Gaussian wave functions.
Elastic electron scattering proton f
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