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 pro

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 pro

In this paper we generalize Jacobsons results by proving that any integer  in   is a square-free integer), belong to . All units of  are generated by the fundamental unit  having the forms

our generalization build on using the conditions

This leads us to classify the real quadratic fields  into the sets  Jacobsons results shows that  and Sliwa confirm that  and  are the only real quadratic fields in .

In this paper we generalize Jacobsons results by proving that any integer  in   is a square-free integer), belong to . All units of  are generated by the fundamental unit  having the forms

Our generalization build on using the conditions

This leads us to classify the real quadratic fields  into the sets  Jacobsons results shows that  and Sliwa confirm that  and  are the only real quadratic fields in .

Background: As photochemical reaction that can stiffen the cornea, CXL is the only promising method of preventing progression of keratectasia such as KC and secondary ectasia following refractive surgery. The aim of CXL is to stabilize the underlying condition with a small chance of visual improvement. Objective: To show the sequences of changes in visual acuity and topographic outcomes during 1 year post CXL for patients with progressive Keratoconus.Type of the study: Cross sectional studyMethods: CXL procedure was done for 45 eyes with progressive KC. The following parameters had been monitored pre operatively, 1, 3, 6 and 12 months postoperatively: K apex, K2, corneal thickness at thinnest location, anterior and posterior elevation po

According to the measuring the relationship between organizational loyalty and job satisfaction among staff members at one college in the higher education ministry in Iraq by using exploratory factor analysis methods to extraction the components which have the major effects on the variables related to organizational loyalty and job satisfaction .

The research contains four basic topics، the first section related to methodology and regarding the conceptual framework it is discussed in the second section، and the third section concentrated at the presentation and the analysis Scientific results and practical results are section presented in the fourth.

Multi-carrier direct sequence code division multiple access (MC-DS-CDMA) has emerged recently as a promising candidate for the next generation broadband mobile networks. Multipath fading channels have a severe effect on the performance of wireless communication systems even those systems that exhibit efficient bandwidth, like orthogonal frequency division multiplexing (OFDM) and MC-DS-CDMA; there is always a need for developments in the realisation of these systems as well as efficient channel estimation and equalisation methods to enable these systems to reach their maximum performance. A novel MC-DS-CDMA transceiver based on the Radon-based OFDM, which was recently proposed as a new technique in the realisation of OFDM systems, will be us

Several authors have used ranking function for solving linear programming problem. In This paper is proposed two ranking function for solving fuzzy linear programming and compare these two approach with trapezoidal fuzzy number .The proposed approach is very easy to understand and it can applicable, also the data were chosen from general company distribution of dairy (Canon company) was proposed test approach and compare; This paper prove that the second proposed approach is better to give the results and satisfy the minimal cost using Q.M. Software

     The aim of this investigation is to present the idea of  SAH – ideal , closed SAH – ideal and closed SAH – ideal with respect to an element ,  and s-  of BH – algebra .

We detail and show  theorems which regulate the relationship between these ideas and provide some examples in BH – algebra .