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.
Buckling analysis of a laminated composite thin plate with different boundary conditions subjected to in-plane uniform load are studied depending on classical laminated plate theory; analytically using (Rayleigh-Ritz method). Equation of motion of the plates was derived using the principle of virtual work and solved using modified Fourier displacement function that satisfies general edge conditions. The eigenvalue problem generated by using Ritz method, the set of linear algebraic equations can be solved using MATLAB for symmetric and anti-symmetric, cross and angle-ply laminated plate considering some design parameters such as aspect ratios, number of layers, lamination type and orthotropic ratio. The results obtained g
... Show MoreManipulation is a discursive concept which plays a key role in political discourse by which politicians can impose some impact on their recipients through using linguistic features, most prominent of which are personal pronouns (Van Dijk, 1995). The aim of this study is to investigate how politicians utilize the personal pronouns, namely; We and I and their possessive forms as a tool of manipulating the audience's mind based on Van Dijk's "ideological square" which shows positive-self representation and negative-other representation (Van Dijk,1998:p.69). To this end, American President Donald Trump's 2020 State of the Union speech was chosen to be the data of analysis. Only (8)
... Show MoreThe general trend in Iraqi banks is focused towards the application of international financial reporting standards, especially the international financial reporting standard IFRS 9 “Financial Instruments”, in addition to the directives issued on the Central Bank of Iraq’s instructions for the year 2018 regarding the development of expected credit losses models, and not to adhere to a specific method for calculating these losses and authorizing the banks’ departments to adopt the method of calculating losses that suits the nature of the bank’s activity and to be consistent in its use from time to time. The research problem revolves around the different methodologies for calculatin
... Show MoreAn 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
... Show MoreRainfall in Nigeria is highly dynamic and variable on a temporal and spatial scale. This has taken a more pronounced dimension due to climate change. In this study, Standard Precipitation Index (SPI) and Mann-Kendall test statistical tools were employed to analyze rainfall trends and patterns in Gombe metropolis between 1990 and 2020 and the ARIMA model was used for making the forecast for ten (10) years. Daily rainfall data of 31 years obtained from Nigerian Meteorological Agency, (NIMET) was used for the study. The daily rainfall data was subjected to several analyses. Standard precipitation index showed that alternation of wet and dry period conditions had been witnessed in the study area. The result obtained showed that there is an u
... Show MoreGlass Fiber Reinforced Polymer (GFRP) beams have gained attention due to their promising mechanical properties and potential for structural applications. Combining GFRP core and encasing materials creates a composite beam with superior mechanical properties. This paper describes the testing encased GFRP beams as composite Reinforced Concrete (RC) beams under low-velocity impact load. Theoretical analysis was used with practical results to simulate the tested beams' behavior and predict the generated energies during the impact loading. The impact response was investigated using repeated drops of 42.5 kg falling mass from various heights. An analysis was performed using accelerometer readings to calculate the generalized inertial load
... Show MoreThis paper discusses using H2 and H∞ robust control approaches for designing control systems. These approaches are applied to elementary control system designs, and their respective implementation and pros and cons are introduced. The H∞ control synthesis mainly enforces closed-loop stability, covering some physical constraints and limitations. While noise rejection and disturbance attenuation are more naturally expressed in performance optimization, which can represent the H2 control synthesis problem. The paper also applies these two methodologies to multi-plant systems to study the stability and performance of the designed controllers. Simulation results show that the H2 controller tracks a desirable cl
... Show MoreThis paper aims at studying the illocutionary speech acts: direct and indirect to show the most dominant ones in a presidential speech delivered by the USA president. The speech is about the most critical health issue in the world, COVID-19 outbreak. A descriptive qualitative study was conducted by observing the first speech delivered by president Trump concerning coronavirus outbreak and surveying the illocutionary acts: directive, declarative, commissive, expressive, and representative. Searle's (1985) classification of illocutionary speech acts is adopted in the analysis.
What are the main types of the illocutionary speech acts performed by Trump in his speech?; Why does
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