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.
This paper proposes a novel finite-time generalized proportional integral observer (FTGPIO) based a sliding mode control (SMC) scheme for the tracking control problem of high order uncertain systems subject to fast time-varying disturbances. For this purpose, the construction of the controller consists of two consecutive steps. First, the novel FTGPIO is designed to observe unmeasurable plant dynamics states and disturbance with its higher time derivatives in finite time rather than infinite time as in the standard GPIO. In the FTGPO estimator, the finite time convergence rate of estimations is well achieved, whereas the convergence rate of estimations by classical GPIO is asymptotic and slow. Secondly, on the basis of the finite and fast e
... Show MoreIn this paper, fire resistance and residual capacity tests were carried out on encased pultruded glass fiber-reinforced polymer (GFRP) I-beams with high-strength concrete beams. The specimens were loaded concurrently under 25% of the ultimate load and fire exposure (an increase in temperature of 700 °C) for 70 min. Subsequently, the fire-damaged specimens were allowed to cool and then were loaded statically until failure to explore the residual behaviors. The effects of using shear connectors and web stiffeners on the residual behavior were investigated. Finite Element (FE) analysis was developed to simulate the encased pultruded GFRP I-beams under the effect of fire loading. The thermal analyses were performed using the general-pu
... Show MoreThe large number of failure in electrical power plant leads to the sudden stopping of work. In some cases, the necessary reserve materials are not available for maintenance which leads to interrupt of power generation in the electrical power plant unit. The present study, deals with the determination of availability aspects of generator in unit 5 of Al-Dourra electric power plant. In order to evaluate this generator's availability performance, a wide range of studies have been conducted to gather accurate information at the level of detail considered suitable to achieve the availability analysis aim. The Weibull Distribution is used to perform the reliability analysis via Minitab 17, and Artificial Neural Networks (ANNs) by approaching o
... Show MoreBackground: Both bladder cancer and schistosomiasis are endemic in Egypt. The former has a unique epidemiological pattern, which has been linked to bladder infestation by Schistosoma. The last decades have witnessed a great reduction in the infection rate of schistosomiasis and a decline in the incidence and changes in the patterns of bladder cancer. Whether these changes are linked to each other or a co-incidence is a subject of investigations.
Method: Literature on epidemiological data of bladder cancer and Schistosoma in Egypt was searched for in Medline, Scopus, PubMed, and Google Scholar. Furthermore, a hand search for literature and reports released by the Egyptian government and involved agencies was perfo
... Show MoreThe importance of vibrations in rotating rotors in engineering applications has been examined, as has the best approach to interpreting vibration data. The most extensively used analytical approaches for rotating shaft vibration analysis have been investigated. In this research, a detailed study was made of the Rayleigh and Dunkerley methods due to their importance in the special calculations to find the amplitude of vibrations in the rotation system. The multi-node method was used to calculate both Dunkerley's and Rayleigh's methods. An experimental platform was built to study the vibrations that occur in the rotating shafts, and the results were compared with theoretical calculations and with different distances of the bearings. It pro
... Show MoreIn this work, the occurrence conditions of both local Bifurcation and persistence were studied, Saddle-node bifurcation appears near fourth point, near the first point, the second point and the third point a transcritical bifurcation occurred but no pitchfork bifurcation happened near any of the four equilibrium points. In addition to study conditions for Hopf-bifurcation near positive stable point that is the fourth point. Besides discuss persistence occurrence as globally property of the food chain of three species include prey, first predator and top predator with impact of toxin in all species and harvesting effect on the predator’s only. Numerical results for the set of hypothe
Congenital adrenal hyperplasia is a group of autosomal recessive disorders. The most frequent one is 21-hydroxylase deficiency. Analyzing
The main objective of this research is to find out the effect of deviation in the aggregate gradients of asphalt mixtures from the Job Mix Formula (JMF) on the general mixture performance. Three road layers were worked on (wearing layer, binder layer, and base layer) and statistical analysis was performed for the data of completed projects in Baghdad city, and the sieve that carried the largest number of deviations for each layer was identified. No.8 sieve (2.36mm), No.50 sieve (0.3mm), and 3/8'' sieve (9.5mm) had the largest number of deviations in the wearing layer, the binder layer, and the base layer respectively. After that, a mixture called Mix 1, was made. This mixture was selected from a number of completed mixtures, and it
... Show MoreNowadays, internet security is a critical concern; the One of the most difficult study issues in network security is "intrusion detection". Fight against external threats. Intrusion detection is a novel method of securing computers and data networks that are already in use. To boost the efficacy of intrusion detection systems, machine learning and deep learning are widely deployed. While work on intrusion detection systems is already underway, based on data mining and machine learning is effective, it requires to detect intrusions by training static batch classifiers regardless considering the time-varying features of a regular data stream. Real-world problems, on the other hand, rarely fit into models that have such constraints. Furthermor
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