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.
An atomic force microscope (AFM) technique is utilized to investigate the polystyrene (PS) impact upon the morphological properties of the outer as well as inner surface of poly vinyl chloride (PVC) porous fibers. Noticeable a new shape of the nodules at the outer and inner surfaces, namely "Crater nodules", has been observed. The fibers surface images have seen to be regular nodular texture at the skin of the inner and outer surfaces at low PS content. At PS content of 6 wt.%, the nodules structure was varied from Crater shape to stripe. While with increasing of PS content, the pore density reduces as a result of increasing the size of the pore at the fiber surface. Moreover, the test of 3D-AFM images shows that the roughness of both su
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This paper aims at discovering the real implication of deduction in the Arabic culture
with concentration on its applications in Arabic grammar, logic, and fundamentals of Islamic
legislations. Some light has been shed on deduction in the Arabic culture but most of recent
works did not analyze deduction according to the pragmatic analysis. This paper will answer
the following questions:
to what extent deduction in Arabic grammar could comprehend with deduction l logic and
fundamentals of thinking in Islamic thought?
how can we find the deduction thinking in the Qur’anic surah if Ghafir?
Can we find parts of deduction in the surah?
The methodology in this paper is descriptive analytical. This metho
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Background: It has been well known that the success of mandibular implant- retained overdenture heavily depends on initial stability, retention and long term osseointegration this is might be due to optimal stresses distribution in surrounding bones. Types of mandibular implant- retained overdenture anchorage system and number of dental implants play an important role in stresses distribution at the implant-bone interface. It is necessary to keep the stresses below the physiologic tolerance level of the bone .since. And it is difficult to measure these stresses around bone in vivo. In the present study, finite element analysis used to study the stresses distribution around dental implant supporting Mandible implant retained overdenture Mate
... Show MoreA partial temporary immunity SIR epidemic model involv nonlinear treatment rate is proposed and studied. The basic reproduction number is determined. The local and global stability of all equilibria of the model are analyzed. The conditions for occurrence of local bifurcation in the proposed epidemic model are established. Finally, numerical simulation is used to confirm our obtained analytical results and specify the control set of parameters that affect the dynamics of the model.
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This study explores the barriers to adopting green environmental criteria in Supplier Selection (SS) within the Iraqi food industry. It aims to enhance the understanding of sustainable supply chain management in developing nations, with a particular focus on the Iraqi context. A case study approach was utilized to identify eleven key green environmental criteria and 54 sub-criteria, alongside seven major barriers to their adoption. The Best–Worst Method (BWM) was employed to rank the criteria, and Fuzzy Stepwise Weight Assessment Ratio Analysis (SWARA) was used to prioritize the barriers. The analysis revealed that Environmental Management Systems are the most critical criterion for SS. On the other hand, legislation and policies emerged
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An experiment was conducted in a greenhouse - research station B - College of Agricultural Engineering Sciences, University of Baghdad, during the fall season of 2018 with the aim of propagating and initially studying the field performance of 18 and 20 potential potato lines derived from Rivera and Arizona cv. after in vitro exposure of nodal segments to different dosages of gamma rays (0, 10, 20, and 30 Gray) and EMS (0, 10, 20, and 30 mM). Each control cultivar and their derived lines were independently cultured in plastic bags according to the RCBD, with three replications. The results showed that the highest plant height and number of leaves were obtained from Arizona derived lines which gave 60.11 cm and 25.30 leaves.plant-1 in
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