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.
Analysis system of sports players is very important for individuals in weightlifting. Assessment of player and strength is important for the performance of weightlifting. This paper proposes an analytical method for weightlifters with check-by-frame video. This analysis system can compute the major steps of seven positions in both snatch and clean and jerk methods in frame-video weightlifting monitoring of movements. Each user can compute the major steps of the seven positions of Hu moments among two frames in the video during training, and the Euclidian distance can be computed for the Hu moment values and lifting moment values in the snatch and clean and jerk methods during training. The outcome of the proposed system shows on efficien
... Show MoreSewer system plays an indispensable task in urban cities by protecting public health and the environment. The operation, maintenance, and rehabilitation of this network have to be in a sustainable and scientific manner. For this purpose, it is important to support operators, decision makers and municipalities with performance evaluation procedure that is based on operational factors. In this paper, serviceability and performance indicator (PI) principles are employed to propose methodology comprising two enhanced PI curves that can be used to evaluate the individual sewers depending on operational factors such as flowing velocity and wastewater level in the sewers. In order to test this methodology; a case study of al-Ru
... Show MoreThis study investigates the influence of asymmetric involute teeth profiles for helical gears on the bending stress. Theoretically, bending stress has been estimated in spur involute gears which have symmetric teeth profile by based on the Lewis, 1892 equation. Later, this equation is developed by, Abdullah, 2012. to determine the effect of an asymmetric tooth profile for the spur gear on the bending stress. And then these equations are applied with stress concentration factor once for symmetric and once other for asymmetric teeth profile. In this paper, the bending stresses for various types of helical gear with various types of asymmetric teeth profile are calculated numerically for defined the stress concentration fac
... Show MoreThe Dirichlet process is an important fundamental object in nonparametric Bayesian modelling, applied to a wide range of problems in machine learning, statistics, and bioinformatics, among other fields. This flexible stochastic process models rich data structures with unknown or evolving number of clusters. It is a valuable tool for encoding the true complexity of real-world data in computer models. Our results show that the Dirichlet process improves, both in distribution density and in signal-to-noise ratio, with larger sample size; achieves slow decay rate to its base distribution; has improved convergence and stability; and thrives with a Gaussian base distribution, which is much better than the Gamma distribution. The performance depen
... Show MoreABSTRACT This paper has a three-pronged objective: offering a unitary set of semantic distinctive features to the analysis of nominal “hatred synonyms” in the lexicon of both English and Standard Arabic (SA), applying it procedurally to test its scope of functionality crosslinguistically, and singling out the closest noun synonymous equivalents among the membership of the two sets in this particular lexical semantic field in both languages. The componential analysis and the matching procedures carried have been functional in identifying ten totally matching equivalents (i.e. at 55.6%), and eight partially matching ones (i.e. at %44.4%). This result shows that while total matching equivalences do exist in the translation of certain Eng
... Show MoreThe present study focused mainly on the buckling behavior of composite laminated plates subjected to mechanical loads. Mechanical loads are analyzed by experimental analysis, analytical analysis (for laminates without cutouts) and numerical analysis by finite element method (for laminates with and without cutouts) for different type of loads which could be uniform or non-uniform, uniaxial or biaxial. In addition to many design parameters of the laminates such as aspect ratio, thickness ratio, and lamination angle or the parameters of the cutout such as shape, size, position, direction, and radii rounding) which are changed to studytheir effects on the buckling characteristics with various boundary conditions. Levy method of classical lam
... Show MoreIn the present work a theoretical analysis depending on the new higher order . element in shear deformation theory for simply supported cross-ply laminated plate is developed. The new displacement field of the middle surface expanded as a combination of exponential and trigonometric function of thickness coordinate with the transverse displacement taken to be constant through the thickness. The governing equations are derived using Hamilton’s principle and solved using Navier solution method to obtain the deflection and stresses under uniform sinusoidal load. The effect of many design parameters such as number of laminates, aspect ratio and thickness ratio on static behavior of the laminated composite plate has been studied. The
... Show MoreFuzzy logic is used to solve the load flow and contingency analysis problems, so decreasing computing time and its the best selection instead of the traditional methods. The proposed method is very accurate with outstanding computation time, which made the fuzzy load flow (FLF) suitable for real time application for small- as well as large-scale power systems. In addition that, the FLF efficiently able to solve load flow problem of ill-conditioned power systems and contingency analysis. The FLF method using Gaussian membership function requires less number of iterations and less computing time than that required in the FLF method using triangular membership function. Using sparsity technique for the input Ybus sparse matrix data gi
... Show MoreA load flow program is developed using MATLAB and based on the Newton–Raphson method,which shows very fast and efficient rate of convergence as well as computationally the proposed method is very efficient and it requires less computer memory through the use of sparsing method and other methods in programming to accelerate the run speed to be near the real time.
The designed program computes the voltage magnitudes and phase angles at each bus of the network under steady–state operating conditions. It also computes the power flow and power losses for all equipment, including transformers and transmission lines taking into consideration the effects of off–nominal, tap and phase shift transformers, generators, shunt capacitors, sh