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

The main purpose of this work is to introduce some types of fuzzy convergence sequences of operators defined on a standard fuzzy normed space (SFN-spaces) and investigate some properties and relationships between these concepts. Firstly, the definition of weak fuzzy convergence sequence in terms of fuzzy bounded linear functional is given. Then the notions of weakly and strongly fuzzy convergence sequences of operators  are introduced and essential theorems related to these concepts are proved. In particular, if ( ) is a strongly fuzzy convergent sequence with a limit  where linear operator from complete standard fuzzy normed space  into a standard fuzzy normed space  then  belongs to the set of all fuzzy bounded linear operators

Owing to the energy crisis and pollution problems of today, investigations have concentrated on
decreasing fuel consumption and on lowering the concentration of toxic components in combustion
products by using non-petroleum, renewable, sustainable and non-polluting fuels. While conventional energy sources such as natural gas, oil and coal are non-renewable, alcohol can be coupled to renewable and sustainable energy sources.
In this study, the combustion characteristics of diesel fuel and methanol blends were compared.
The tests were performed at steady state conditions in a four-cylinder DI diesel engine at full load at
1500-rpm engine speed. The experimental results showed that diesel methanol blends provided
12.7% inc

  There are many researches deals with constructing an efficient solutions for real problem having Multi - objective confronted with each others. In this paper we construct a decision for Multi – objectives based on building a mathematical model formulating a unique objective function by combining the confronted objectives functions. Also we are presented some theories concerning this problem. Areal application problem has been presented to show the efficiency of the performance of our model and the method. Finally we obtained some results by randomly generating some problems.

Many of the key stream generators which are used in practice are LFSR-based in the sense that they produce the key stream according to a rule y = C(L(x)), where L(x) denotes an internal linear bit stream, produced by small number of parallel linear feedback shift registers (LFSRs), and C denotes some nonlinear compression function. In this paper we combine between the output sequences from the linear feedback shift registers with the sequences out from non linear key generator to get the final very strong key sequence

      The main problem when dealing with fuzzy data variables is that it cannot be formed by a model that represents the data through the method of Fuzzy Least Squares Estimator (FLSE) which gives false estimates of the invalidity of the method in the case of the existence of the problem of multicollinearity. To overcome this problem, the Fuzzy Bridge Regression Estimator (FBRE) Method was relied upon to estimate a fuzzy linear regression model by triangular fuzzy numbers. Moreover, the detection of the problem of multicollinearity in the fuzzy data can be done by using Variance Inflation Factor when the inputs variable of the model crisp, output variable, and parameters are fuzzed. The results were compared usin

This research studies the effect of adding micro, nano and hybrid by ratio (1:1) of (Al2O3,TiO2) to epoxy resin on thermal conductivity before and after immersion in HCl acid for (14 day) with normality (0.3 N) at weight fraction (0.02, 0.04, 0.06, 0.08) and thickness (6mm). The results of thermal conductivity reveled that epoxy reinforced by (Al2O3) and mixture (TiO2+Al2O3) increases with increasing the weight fraction, but the thermal conductivity (k) a values for micro and Nano (TiO2) decrease with increasing the weight fraction of reinforced, while the immersion in acidic solution (HCl) that the (k) values after immersion more than the value in before immersion.

     Applications of quantitative methods, which had been explicit attention during previous period (the last two centuries) is the method of application sales man or traveling salesman method. According to this interest by the actual need for a lot of the production sectors and companies that distribute their products, whether locally made or the imported for customers or other industry sectors where most of the productive sectors and companies distributed always aspired to (increase profits, imports, the production quantity, quantity of exports. etc. ...) this is the part of the other hand, want to behave during the process of distribution routes that achieve the best or the least or most appropriate.