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.
Is a high degree of economic freedom an important part in the development of the economies of developing countries in the last decade of the twentieth century and the beginning of the twentieth century and the atheist. This is because a test subject (deltoid analysis of the relationship between the degree of economic freedom and foreign trade of selected developing countries for the period
( 1990 -2005) to determine the degree of economic freedom in foreign trade promotion in Singapore and Turkey. The research recommends a number of recommendations, the most important is the responsibility of the Ministry of Planning in Iraq that is providing the necessary data for the Fraser Institute, the aim of increasing cooperation
The article critically analyzes traditional translation models. The most influential models of translation in the second half of the 20th century have been mentioned, among which the theory of formal and dynamic equivalence, the theory of regular correspondences, informative, situational-denotative, functional-pragmatic theory of communication levels have been considered. The selected models have been analyzed from the point of view of the universality of their use for different types and types of translation, as well as the ability to comprehend the deep links established between the original and the translation.
Аннотация
The analysis of rigid pavements is a complex mission for many reasons. First, the loading conditions include the repetition of parts of the applied loads (cyclic loads), which produce fatigue in the pavement materials. Additionally, the climatic conditions reveal an important role in the performance of the pavement since the expansion or contraction induced by temperature differences may significantly change the supporting conditions of the pavement. There is an extra difficulty because the pavement structure is made of completely different materials, such as concrete, steel, and soil, with problems related to their interfaces like contact or friction. Because of the problem's difficulty, the finite element simulation is
... Show MoreObjective: The aim of this work was to detect terpenes other than boswellic acid derivatives in olibanum of Boswellia Serrata found in Iraq. Methods: The olibanum of Boswellia Serrata was macerated in methanol for one day, then filtration. Filter at was concentrated till reddish brown syrupy residue was gained, (3%) potassium hydroxide was added till basification. This basic solution was stirred continuously until a uniform emulsion was formed, then extracted with chloroform in a separatory funnel; the chloroform fraction was analyzed by GC /MS spectrometry. Results: GC /MS analysis reveal the presence of terpenes and non-terpenes constituents. Conclusion: Most of the detected terpenes were sesquiterpenes and the least one was di-terpenes.
The performance evaluation process requires a set of criteria and for the purpose of measuring the level of performance achieved by the Unit and the actual level of development of its activities, and in view of the changes and of rapid and continuous variables surrounding the Performance is a reflection of the unit's ability to achieve its objectives, as these units are designed to achieve the objectives of exploiting a range of economic resources available to it, and the performance evaluation process is a form of censorship, focusing on the analysis of the results obtained from the achievement All its activities with a view to determining the extent to which the Unit has achieved its objectives using the resources available to it and h
... Show MoreThe agricultural sector suffers from many risks and natural disasters, such as droughts and heavy rains that cause floods, as well as hail and agricultural pests, etc., that threaten agricultural activity and reduce it, which leads to the failure of farmers and peasants for fear of being subjected to continuous losses. Nevertheless, we notice almost complete reluctance to move towards agricultural insurance, due to the dependence of farmers on the government, which adopts the principle of compensation instead of agricultural insurance when natural disasters happen despite the difficulties and financial hardship as well as the suspicion of corruption that haunt the compensation process and this represents the most important problem for resea
... Show MoreA theoretical analysis of mixing in the secondary combustion chamber of ramjet is presented. Theoretical investigations were initiated to insight into the flow field of the mixing zone of the ramjet combustor and a computer program to calculate axisymmetric, reacting and inert flow was developed. The mathematical model of the mixing zone of ramjet comprises differential equations for: continuity, momentum, stagnation enthalpy, concentration, turbulence energy and its dissipation rate. The simultaneous solution of these equations by means of a finite-difference solution algorithm yields the values of the variable at all internal grid nodes.
The results showed that increasing air mass flow (0.32 to 0.64 kg/s) increases the development o