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 study aimed to isolate and phenotype lymphocytes in untreated children patients with chronic allergic asthma. To reach such aim the study involved (25) patients from children (17 male and 9 female) whom their ages where between (3-10) years, in addition to (15) apparently healthy children (9 male and 6 female) in the same ages involved as control group. The data demonstrated that there was a significant increase in the mean percentages of T-lymphocytes (CD3+ cells) in the peripheral blood of patients (66.75±0.29)**, in comparison with control group (43.58±0.19), a significant increase in the mean percentages of T-helper lymphocytes (CD4+ cells) in the pe
... Show MoreIn this paper, we will illustrate a gamma regression model assuming that the dependent variable (Y) is a gamma distribution and that it's mean ( ) is related through a linear predictor with link function which is identity link function g(μ) = μ. It also contains the shape parameter which is not constant and depends on the linear predictor and with link function which is the log link and we will estimate the parameters of gamma regression by using two estimation methods which are The Maximum Likelihood and the Bayesian and a comparison between these methods by using the standard comparison of average squares of error (MSE), where the two methods were applied to real da
... Show MoreChaotic features of nuclear energy spectrum in 68Ge nucleus are investigated by nuclear shell model. The energies are calculated through doing shell model calculations employing the OXBASH computer code with effective interaction of F5PVH. The 68Ge nucleus is supposed to have an inert core of 56Ni with 12 nucleons (4 protons and 8 neutrons) move in the f5p-model space ( and ). The nuclear level density of considered classes of states is seen to have a Gaussian form, which is in accord with the prediction of other theoretical studies. The statistical fluctuations of the energy spectrum (the level spacing P(s) and the Dyson-Mehta (or statistics) are well described by the Gaussian orthogonal ens
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In this work, a test room was built in Baghdad city, with (2*1.5*1.5) m3 in dimensions, while the solar chimneys (SC) were designed with aspect ratio (ar) bigger than 12. Test room was supplied by many solar collectors; vertical single side of air pass with ar equals 25, and tilted 45o double side of air passes with ar equals 50 for each pass, both collectors consist of flat thermal energy storage box collector (TESB) that covered by transparent clear acrylic sheet, third type of collector is array of evacuated tubular collectors with thermosyphon in 45o instelled in the bottom of TESB of vertical SC. The TESB was
... Show MoreThe encoding of long low density parity check (LDPC) codes presents a challenge compared to its decoding. The Quasi Cyclic (QC) LDPC codes offer the advantage for reducing the complexity for both encoding and decoding due to its QC structure. Most QC-LDPC codes have rank deficient parity matrix and this introduces extra complexity over the codes with full rank parity matrix. In this paper an encoding scheme of QC-LDPC codes is presented that is suitable for codes with full rank parity matrix and rank deficient parity matrx. The extra effort required by the codes with rank deficient parity matrix over the codes of full rank parity matrix is investigated.
Biomass has been extensively investigated, because of its presence as clean energy source. Tars and particulates formation problems are still the major challenges in development especially in the implementation of gasification technologies into nowadays energy supply systems. Laser Induced Fluorescence spectroscopy (LIF) method is incorporated for determining aromatic and Polycyclic Aromatic Hydrocarbons (PAH) produced at high temperature gasification technology. The effect of tars deposition when the gases are cooled has been highly reduced by introducing a new concept of measurement cell. The samples of PAH components have been prepared with the standard constrictions of measured PAHs by using gas chromatograph (GC). OPO laser with tun
... Show MoreIn this paper, a new third kind Chebyshev wavelets operational matrix of derivative is presented, then the operational matrix of derivative is applied for solving optimal control problems using, third kind Chebyshev wavelets expansions. The proposed method consists of reducing the linear system of optimal control problem into a system of algebraic equations, by expanding the state variables, as a series in terms of third kind Chebyshev wavelets with unknown coefficients. Example to illustrate the effectiveness of the method has been presented.
Symmetric cryptography forms the backbone of secure data communication and storage by relying on the strength and randomness of cryptographic keys. This increases complexity, enhances cryptographic systems' overall robustness, and is immune to various attacks. The present work proposes a hybrid model based on the Latin square matrix (LSM) and subtractive random number generator (SRNG) algorithms for producing random keys. The hybrid model enhances the security of the cipher key against different attacks and increases the degree of diffusion. Different key lengths can also be generated based on the algorithm without compromising security. It comprises two phases. The first phase generates a seed value that depends on producing a rand
... Show MoreThe remediation oil production by matrix acidizing method on the well named "X" (for confidential reasons) is scrutinized in this paper. Initial production of 1150 bpd, production index of 2.8 STB/Psi/d and permeability of 150md, in 2018 two years down the lane this dropped to 450 bpd, production index 0.7 STB/Psi/d. The declined observed on the production index is trouble shouted and after elimination of (no completion damage/perforation damage), the skin is calculated by carrying out a well test (build-up test) whose extrapolation in excel over times gave us a skin of 40.The reservoir heterogeneity, containing >20% of feldspar, carbonates and paraffin’s guided thematrix acidizing design and treatment proposition to remedy thi
... Show MoreIn this study, a different design of passive air Solar Chimney(SC)was tested by installing it in the south wall of insulated test room in Baghdad city. The SC was designed from vertical and inclined parts connected serially together, the vertical SC (first part) has a single pass and Thermal Energy Storage Box Collector (TESB (refined paraffin wax as Phase Change Material(PCM)-Copper Foam Matrix(CFM))), while the inclined SC was designed in single pass, double passes and double pass with TESB (semi refined paraffin wax with copper foam matrix) with selective working angle ((30o, 45o and 60o). A computational model was employed and solved by Finite Volume Method (FVM) to simulate the air i
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