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. 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. 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 our students.
Most of the Weibull models studied in the literature were appropriate for modelling a continuous random variable which assumes the variable takes on real values over the interval [0,∞]. One of the new studies in statistics is when the variables take on discrete values. The idea was first introduced by Nakagawa and Osaki, as they introduced discrete Weibull distribution with two shape parameters q and β where 0 < q < 1 and b > 0. Weibull models for modelling discrete random variables assume only non-negative integer values. Such models are useful for modelling for example; the number of cycles to failure when components are subjected to cyclical loading. Discrete Weibull models can be obta
... Show MoreAl Huweizah Marsh is considered as the largest marsh at the southern part of Iraq. About one third of the marsh is located within the Iranian territory. Iran began to construct earth dikes along the Iraqi-Iranian international borders to separate the Iranian part of the marsh. The electrical conductivity, EC, value was adopted to be the indicator for the water salinity within the marsh. A steady two-dimensional water quality routing model was implemented by using the RMA2 and RMA4 softwares within the SMS computer package to estimate the distribution of the
EC values within the marsh seasonally during the wet, moderate and dry water years. The EC distribution Patterns were estimated considering the expected two cases of the marsh futu
Quantum key distribution (QKD) provides unconditional security in theory. However, practical QKD systems face challenges in maximizing the secure key rate and extending transmission distances. In this paper, we introduce a comparative study of the BB84 protocol using coincidence detection with two different quantum channels: a free space and underwater quantum channels. A simulated seawater was used as an example for underwater quantum channel. Different single photon detection modules were used on Bob’s side to capture the coincidence counts. Results showed that increasing the mean photon number generally leads to a higher rate of coincidence detection and therefore higher possibility of increasing the secure key rate. The secure key rat
... Show MoreThe capacity factor is the main factor in assessing the efficiency of wind Turbine. This paper presents a procedure to find the optimal wind turbine for five different locations in Iraq based on finding the highest capacity factor of wind turbine for different locations. The wind data for twelve successive years (2009-2020) of five locations in Iraq are collected and analyzed. The longitudes and latitudes of the candidate sites are (44.3661o E, 33.3152o N), (47.7738o E, 30.5258o N), (45.8160o E, 32.5165o N), (44.33265o E, 32.0107o N) and (46.25691o E, 31.0510o N) for Baghdad, Basrah, Al-Kut, Al-Najaf, and Al-Nasiriyah respectively. The average wind velocity, standard deviation, Weibull shape and scale factors, and probability density functi
... Show MoreThe effect of short range correlations on the inelastic Coulomb form factors for excited +2 states (1.982, 3.919, 5.250 and 8.210MeV) and +4 states (3.553, 7.114, 8.960 and 10.310 MeV) in O18 is analyzed. This effect (which depends on the correlation parameterβ) is inserted into the ground state charge density distribution through the Jastrow type correlation function. The single particle harmonic oscillator wave function is used with an oscillator size parameter .b The parameters β and b are adjusted for each excited state separately so as to reproduce the experimental root mean square charge radius of .18O The nucleusO18 is considered as an inert core of C12 with two protons and four neutrons distributed over 212521211sdp−− activ
... Show MoreThe two-neutron halo-nuclei (17B, 11Li, 8He) was investigated using a two-body nucleon density distribution (2BNDD) with two frequency shell model (TFSM). The structure of valence two-neutron of 17B nucleus in a pure (1d5/2) state and in a pure (1p1/2) state for 11L and 8He nuclei. For our tested nucleus, an efficient (2BNDD's) operator for point nucleon system folded with two-body correlation operator's functions was used to investigate nuclear matter density distributions, root-mean square (rms) radii, and elastic electron scattering form factors. In the nucleon-nucleon forces the correlation took account of
... Show MoreThe coefficient of performance of a window type Air-Conditioner system can be improved if a reduction in the work of compressor can be achieved by a suitable technique. The present study investigates the effect of dispersing a low concentration of TiO2 nanoparticles in the mineral oil based lubricant, as well as on the overall performance of a window type Air-Conditioner system using R22 as the working fluid. An enhancement in the COP of the refrigeration system has been observed and the existence of an optimum volume fraction noticed, with low concentrations of nanoparticles suspended in the mineral oil. Results showed that the average compressor work reduced by 13.3%, which ultimately resulted in an increase of 11.99% in the COP due to
... Show MoreMarketing information system (KMIS) is an essential factor of developing business’ performance and getting sustainable success. The main goal of the research is to measure effect of MIS on customer orientation and product innovation. Also, another goal is to analyze the mediation role of product innovation in relationship MIS and customer orientation. This study sought to analyze the marketing information system and measure its effect on the customer orientation and product innovation. The data of the study were collected using questionnaire. The data were analyzed using statistical tools and SPSS programming. The results of the study showed that the KMIS can positively and significantly effect product innovation. Also, t
... Show MoreThis study aims to encapsulate atenolol within floating alginate-ethylcellulose beads as an oral controlled-release delivery system using aqueous colloidal polymer dispersion (ACPD) method.To optimize drug entrapment efficiency and dissolution behavior of the prepared beads, different parameters of drug: polymer ratio, polymer mixture ratio, and gelling agent concentration were involved.The prepared beads were investigated with respect to their buoyancy, encapsulation efficiency, and dissolution behavior in the media: 0.1 N HCl (pH 1.2), acetate buffer (pH 4.6) and phosphate buffer (pH 6.8). The release kinetics and mechanism of the drug from the prepared beads was investigated.All prepared atenolol beads remained f
... Show MoreBackground: Inflammation of the brain parenchyma brought on by a virus is known as viral encephalitis. It coexists frequently with viral meningitis and is the most prevalent kind of encephalitis. Objectives: To throw light on viral encephalitis, its types, epidemiology, symptoms and complications. Results: Although it can affect people of all ages, viral infections are the most prevalent cause of viral encephalitis, which is typically seen in young children and old people. Arboviruses, rhabdoviruses, enteroviruses, herpesviruses, retroviruses, orthomyxoviruses, orthopneumoviruses, and coronaviruses are just a few of the viruses that have been known to cause encephalitis. Conclusion: As new viruses emerge, diagnostic techniques advan
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