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Multivariate Analysis - Second Edition
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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.

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Publication Date
Fri Mar 01 2019
Journal Name
Al-khwarizmi Engineering Journal
Buckling and Pre Stressed Dynamics Analysis of Laminated Composite Plate with Different Boundary Conditions
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Critical buckling and natural frequencies behavior of laminated composite thin plates subjected to in-plane uniform load is obtained using classical laminated plate theory (CLPT). Analytical investigation is presented using Ritz- method for eigenvalue problems of buckling load solutions for laminated symmetric and anti-symmetric, angle and cross ply composite plate with different elastic supports along its edges. Equation of motion of the plate was derived using principle of virtual work and solved using modified Fourier displacement function that satisfies general edge conditions. Various numerical investigation were studied to exhibit a convergence and accuracy of the present solution for considering some design parameters such as edge

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Publication Date
Tue Dec 05 2023
Journal Name
Engineering, Technology & Applied Science Research
Theoretical Analysis of Composite RC Beams with Pultruded GFRP Beams subjected to Impact Loading
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Glass 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. The in

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Publication Date
Thu Jan 10 2019
Journal Name
Journal Of The College Of Education For Women
Spatial analysis of population growth in the district of Tuz Khurmatu for (1977-2012)
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The study population growth of the most important demographic phenomena upon which planners to meet changes in the size of the population increase is through knowledge of the requirements of population growth can be planned for the future. On this basis, Tuz District was chosen for the study of population growth, which set her period (1977-2012), and compared with the growth of the population of the province and the extent of the variation in population growth, according to the administrative units, has touched search numerical and proportional distribution of the population according to the administrative aspects of the judiciary, as well as environmental distribution.

The elimination of the study population growth dramatically

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Publication Date
Wed Jun 01 2022
Journal Name
Iraqi Journal Of Physics
Statistical Analysis and Forecasting of Rainfall Patterns and Trends in Gombe North-Eastern Nigeria
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Rainfall 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

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Publication Date
Wed Mar 15 2023
Journal Name
Al-academy
Analysis of the harmonic structure in the musical compositions of the artist Khaleel Ismail
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 The researcher was interested in studying a crucial aspect of the systematic world music culture. He highlights the analysis of the harmonic construction in the musical compositions of the artist Khalil Ismail, where harmony is a significant Western musical science, a pillar of the structure of instrumental and vocal music.
It depends on the compositions of vertical sounds performed simultaneously, as tones coincide and are sometimes dissonant to give sound resonance that enriches musical work and attracts recipients. Hence, the researcher has many questions, including: Can the composition of the writings of the artist Khalil Ismail determine in an objective research framework? Is there a study on this subject in some detail? whic

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Publication Date
Tue Jan 01 2019
Journal Name
Spe Europec Featured At 81st Eage Conference And Exhibition
Development of Artificial Neural Networks and Multiple Regression Analysis for Estimating of Formation Permeability
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Publication Date
Fri Mar 01 2019
Journal Name
Al-khwarizmi Engineering Journal
Thermo Elasto-Plastic Analysis of Rotating Axisymmetrical Bodies Using Modified Von-Mises Yield Criterion
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In the present work, the behavior of thick-walled cylinder of elasto-plastic material (polymeric material) has been studied analytically. The study is based on modified Von-Mises yield criterion (for non metallic material). The equations of stress distribution are obtained for the cylinder under general cases of elastic expansion, plastic initiation and elastic-plastic expansion.

        A computer program is developed for evaluating the stress distribution. The solution is carried out for worst boundary conditions when the cylinder is subjected to the combination of pressure load, inertia load, and temperature gradient.

        The results are presente

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Publication Date
Sun Feb 03 2019
Journal Name
Journal Of The College Of Education For Women
Analysis of the clause relations in the presidential presuasion in a war against Iraq
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Publication Date
Sat Dec 31 2011
Journal Name
Al-khwarizmi Engineering Journal
The Estimation of Vibrational Energy of Two Coupled (Welded) Plates Using Statistical Energy Analysis
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This paper deals with a method called Statistical Energy Analysis that can be applied to the mechanical and acoustical systems like buildings, bridges and aircrafts …etc. S.E.A as a tool can be applied to the resonant systems in the circumstances of high frequency or/and complex structure». The parameters of S.E.A such as coupling loss factor, internal loss factor, modal density and input power are clarified in this work ; coupled plate sub-systems and explanations are presented for these parameters. The developed system is assumed to be resonant, conservative, linear and there is an equipartition of energy between all the resonant modes within a given frequency band in a given sub-system. The aim of th

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Publication Date
Thu Oct 31 2013
Journal Name
Al-khwarizmi Engineering Journal
An Investigation Study of Thinning Distribution in Single Point Incremental Forming Using FEM Analysis
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Single Point Incremental Forming (SPIF) is a forming technique of sheet material based on layered manufacturing principles. The sheet part is locally deformed through horizontal slices. The moving locus of forming tool (called as toolpath) in these slices constructed to the finished part was performed by the CNC technology. The toolpath was created directly from CAD model of final product. The forming tool is a Ball-end forming tool, which was moved along the toolpath while the edges of sheet material were clamped rigidly on fixture.

This paper presented an investigation study of thinning distribution of a conical shapes carried out by incremental forming and the validation of finite element method to evaluate the limits of the p

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