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.
Markov chains are an application of stochastic models in operation research, helping the analysis and optimization of processes with random events and transitions. The method that will be deployed to obtain the transient solution to a Markov chain problem is an important part of this process. The present paper introduces a novel Ordinary Differential Equation (ODE) approach to solve the Markov chain problem. The probability distribution of a continuous-time Markov chain with an infinitesimal generator at a given time is considered, which is a resulting solution of the Chapman-Kolmogorov differential equation. This study presents a one-step second-derivative method with better accuracy in solving the first-order Initial Value Problem
... Show MoreThe bony pelvis has a major role in weight transmission to the lower limbs. The complexities of its geometric form, material properties, and loading conditions render it an open subject to biomechanical analysis.
The present study deals with area measurement, and three-dimensional finite element analysis of the hip bone to investigate magnitudes, load direction, and stress distribution under physiological loading conditions.
The surface areas of the auricular surface, lunate surface, and symphysis pubis were measured in (35) adult hip bones. A solid model was translated into ANSYS parametric design language to be analyzed by finite element analysis method under different loading conditions.
The surface
... Show MoreReading is one of the essential components of the English language. Countries that use English as a second language (ESL) sometimes have difficulties in reading and comprehension. According to many researches, mother tongue has proved some interferences with learning a second language. This study investigated the results of reading difficulties of young second language learners in terms of accuracy, comprehension, and rate using the Neale Analysis of Reading Ability test. The study was carried out in one of the High Schools for Boys in Hyderabad, India and included Grade five, aged 10-12 years. In order to understand the reading difficulties of English as a second language, a qualitative approach was employed. Interview, reading tes
... Show MoreA New Spectrophotometric Methods are improved for determination Metronidazole (MTZ) and Metronidazolebenzoate (MTZB) depending on1STand 2nd derivative spectrum of the two drugs by using ethanol as a solvent. Many techniques were proportionated with concentration (peak high to base line, peak to peak and peak area). The linearity of the methodsranged between(1-25µg.ml-1) is obtained. The results were precise and accurate throw RSD% were between (0.041-0.751%) and (0.0331-0.452%), Rec% values between (97.78, 101.87%) and (98.033-102.39%) while the LOD between (0.051-0.231 µg.ml-1) and (0.074-1.04 µg.ml-1) and LOQ between (0.170-0.770µg.ml-1) and (0.074-0.313 µg.ml-1) of (MTZ) and of (MTZB) respectively. These Methods were successfully ap
... Show MoreIn this paper, a new technique is offered for solving three types of linear integral equations of the 2nd kind including Volterra-Fredholm integral equations (LVFIE) (as a general case), Volterra integral equations (LVIE) and Fredholm integral equations (LFIE) (as special cases). The new technique depends on approximating the solution to a polynomial of degree and therefore reducing the problem to a linear programming problem(LPP), which will be solved to find the approximate solution of LVFIE. Moreover, quadrature methods including trapezoidal rule (TR), Simpson 1/3 rule (SR), Boole rule (BR), and Romberg integration formula (RI) are used to approximate the integrals that exist in LVFIE. Also, a comparison between those
... Show MoreIn this paper, a new technique is offered for solving three types of linear integral equations of the 2nd kind including Volterra-Fredholm integral equations (LVFIE) (as a general case), Volterra integral equations (LVIE) and Fredholm integral equations (LFIE) (as special cases). The new technique depends on approximating the solution to a polynomial of degree and therefore reducing the problem to a linear programming problem(LPP), which will be solved to find the approximate solution of LVFIE. Moreover, quadrature methods including trapezoidal rule (TR), Simpson 1/3 rule (SR), Boole rule (BR), and Romberg integration formula (RI) are used to approximate the integrals that exist in LVFIE. Also, a comparison between those methods i
... Show MoreAutorías: Jehan Faris Yousif, Read Idrees Mahmood. Localización: Utopía y praxis latinoamericana: revista internacional de filosofía iberoamericana y teoría social. Nº. 1, 2020. Artículo de Revista en Dialnet.
The exchanges in various fields,like economics, science, culture, etc., have been enhanced unceasingly among different countries around the world in the twenty-first century, thus, the university graduate who masters one foreign language does not meet the need of the labor market in most countries.So, many universities began to develop new programs to cultivate students who can use more foreign languages to serve the intercultural communication. At the same time, there is more scientific research emerged which is related to the relationship between the second and third languages. This humble research seeks to explain the relevant concepts and analyze the real data collected from Shanghai International Studies University in China, to expl
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