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.
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In this investigation, Rayleigh–Ritz method is used to calculate the natural frequencies of rectangular isotropic and laminated symmetric and anti-symmetric cross and angle ply composite plate with general elastic supports along its edges. Each of the admissible functions here is composed of a trigonometric function and an arbitrary continuous function that is introduced to ensure the sufficient smoothness of the so-called residual displacement function at the edges. Perhaps more importantly, this study has developed a general approach for deriving a complete set of admissible functions that can be applied to various boundary conditions. Several numerical examples are studied to demonstrate the accuracy and convergence of the current s
... Show MoreThe present study is concerned with the writer's ideologies towards violence against women. The study focuses on analyzing violence against women in English novel to see the extent the writers are being affected and influenced by their genders. It also focuses on showing to what extent the writer's ideologies are reflected in their works. Gender influences social groups ideologies; therefore, when a writer discusses an issue that concerns the other gender, they will be either subjective or objective depending on the degree of influence, i.e., gender has influenced their thoughts as well as behaviors. A single fact may be presented differently by different writers depending on the range of a
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Abstract The painful history of slavery has profoundly affected the identities and social interactions of Afro-Caribbean migrants, whose descendants continue to contend with prejudice and socio-economic marginalization. Andrea Levy's semi-autobiographical novel, The Long Song (2010), traces the turbulent history of Jamaica in the nineteenth century through the lens of Miss Kitty, a character based on Levy's great-great-great grandmother, who was born a slave on the plantation Amity in Saint Catherine's parish. The narrative blends the historical with the fictional and depicts various environmental contexts, inscribed meanings, and human exchanges, including the prominence of social situations perceived through race and class tensions ironic
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Motives: Baghdad is the capital city and an important political, administrative, social, cultural and economic centre of Iraq. Baghdad’s growth and development has been significantly influenced by efforts to accommodate various needs of its steadily growing population. Uncontrolled population and urban growth have exerted negative effects in numerous dimensions, including environmental sustainability because urban expansion occurred in green spaces within the city and the surrounding areas.Aim: The aim of this study was to examine the planning solutions in Baghdad’s green areas in the past and at present, and to identify the key changes in the city’s green areas, including changes in the ratio of green urban spaces to the tota
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In this paper, a novel flow control strategy which is the inlet throttled pump was used to design an angular velocity control system for rotary actuator. Inlet throttled systems have good performance in addition to their high efficiency compared to traditional valve controlled systems. The flow in the proposed system is adjusted by a valve that is positioned at the pump inlet with the purpose of reducing the energy loses across the valve. This regulated flow is used then to control the actuator angular velocity. The system was modeled and the open loop stability and performance were studied. In order to improve the system performance, Robust-Proportional-Integral-Derivative (RPID) and structured singular value (M@#@) controllers have been d
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