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.
In this work, the total linear attenuation coefficients µ(cm
-1
) were calculated and studied
for particulate reinforced polymer-based composites. Unsaturated polyester (UP) resin was
used as a matrix filled with different concentrations of Al, Fe, and Pb metal powders as
reinforcements. The effect of the metal powders addition at different weight percentages in
the range of (10,20,30,40,50)wt % and gamma energy on attenuation coefficients was studied.
The results show, as the metallic particulates content increase, the attenuation coefficients will
increase too, while it, were exhibited a decrease in their values when the gamma energy
increase.The total linear attenuation coefficients of gamma ray fo
This paper demonstrates the construction of a modern generalized Exponential Rayleigh distribution by merging two distributions with a single parameter. The "New generalized Exponential-Rayleigh distribution" specifies joining the Reliability function of exponential pdf with the Reliability function of Rayleigh pdf, and then adding a shape parameter for this distribution. Finally, the mathematical and statistical characteristics of such a distribution are accomplished
Gypsum is one of the important construction materials in Iraq in plastering surfaces and gypsum board , the ability of gypsum to give a comfortable an aesthetic ambiance as a construction material increase the need of gypsum , The particle size , total surface area and particle size distribution were factors affecting plaster properties used for construction properties . In this study gypsum paste was used with different mixing ratios of particle size and studied the physical properties of these types of pastes named (standard consistency ,setting time ,density) and compressive strength . The results showed that the water to gypsum ratio increased with increasing the fineness of the gypsum to (0.75%) and the setting time to the maxi
... Show MoreThe substantial key to initiate an explicit statistical formula for a physically specified continua is to consider a derivative expression, in order to identify the definitive configuration of the continua itself. Moreover, this statistical formula is to reflect the whole distribution of the formula of which the considered continua is the most likely to be dependent. However, a somewhat mathematically and physically tedious path to arrive at the required statistical formula is needed. The procedure in the present research is to establish, modify, and implement an optimized amalgamation between Airy stress function for elastically-deformed media and the multi-canonical joint probability density functions for multivariate distribution complet
... Show MoreAbstract:
In light of the development in the banking environment and the increasing reliance on electronic systems in providing banking services and due to the intense competition witnessed by the banking sector, the need has emerged to apply the comprehensive electronic banking system, which works on the Internet in providing new and diverse banking services regardless of time and place by linking all branches to one central database, and despite the advantages achieved from the application of the comprehensive system, there is a set of risks that accompany the use of that system, What requires the auditors to develop the audit method in line with the size of the development in the
... Show MoreIn a resource-limited world, there is an urgent need to develop new economic models, from the traditional unsustainable industrial model of product consumption and disposal, to a new model based on the concepts of sustainability in its comprehensive sense, the so-called circular economy, using fewer resources in manufacturing processes and changing practices in product disposal to waste, by removing its use, recycling and manufacturing to start another manufacturing process. In an era of intense competition in domestic and global markets, the importance of the circular economy is highlighted in its ability to strengthen the competitiveness of enterprises in those markets, by reducing the cost and increasing the quality of the pro
... Show MoreThe research aims to develop the general performance and improve the level of activity of private insurance companies in line with the current progress of the country. Besides, Evaluating financial performance to diagnose weaknesses and strengths in sample research companies and then developing appropriate solutions. The deviation in the financial performance of the research sample was revealed by measuring the various accounts of the company. The research sample included five companies in the private insurance sector listed in the Iraqi Stock Exchange Market, which represent the private insurance sector. The research concluded that the added economic value is a broad concept that goes beyond the traditional performance evaluation process a
... Show More This paper studies the existence of positive solutions for the following boundary value problem :-
y(b) 0 α y(a) - β y(a) 0 bta f(y) g(t) λy    ï‚¢ï€
The solution procedure follows using the Fixed point theorem and obtains that this problem has at least one positive solution .Also,it determines ( ï¬ ) Eigenvalue which would be needed to find the positive solution .
The aim of this paper is to present a new methodology to find the private key of RSA. A new initial value which is generated from a new equation is selected to speed up the process. In fact, after this value is found, brute force attack is chosen to discover the private key. In addition, for a proposed equation, the multiplier of Euler totient function to find both of the public key and the private key is assigned as 1. Then, it implies that an equation that estimates a new initial value is suitable for the small multiplier. The experimental results show that if all prime factors of the modulus are assigned larger than 3 and the multiplier is 1, the distance between an initial value and the private key
... Show MoreIn this paper, we have generalized the concept of one dimensional Emad - Falih integral transform into two dimensional, namely, a double Emad - Falih integral transform. Further, some main properties and theorems related to the double Emad - Falih transform are established. To show the proposed transform's efficiency, high accuracy, and applicability, we have implemented the new integral transform for solving partial differential equations. Many researchers have used double integral transformations in solving partial differential equations and their applications. One of the most important uses of double integral transformations is how to solve partial differential equations and turning them into simple algebraic ones. The most important
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