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

A new procedure of depth estimation to the apex of dyke-like sources from
magnetic data has been achieved through the application of a derived equation. The
procedure consists of applying a simple filtering technique to the total magnetic
intensity data profiles resulting from dyke-like bodies, having various depths, widths
and inclination angles. A background trending line is drawn for the filtered profile
and the output profile is considered for further calculations.
Two straight lines are drawn along the maximum slopes of the filtered profile
flanks. Then, the horizontal distances between the two lines at various amplitude
levels are measured and plotted against the amplitudes and the resulted relation is a

Maximum values of one particle radial electronic density distribution has been calculated by using Hartree-Fock (HF)wave function with data published by[A. Sarsa et al. Atomic Data and Nuclear Data Tables 88 (2004) 163–202] for K and L shells for some Be-like ions. The Results confirm that there is a linear behavior restricted the increasing of maximum points of one particle radial electronic density distribution for K and L shells throughout some Be-like ions. This linear behavior can be described by using the nth term formula of arithmetic sequence, that can be used to calculate the maximum radial electronic density distribution for any ion within Be like ions for Z<20.

The presence and prevalence of V. cholerae were investigated in forty five water samples collected from different locations of Tiger River/ Baghdad city. Twenty one isolates were isolated by adopting a simple isolation techniques. The final identification revealed that only three isolates were confirmed as V. cholerae. They were named 1J, 1R and Dial 131 which are all serogrouped as non-O1. Toxin Coregulated Pili (TCP) and heat labile enterotoxin (LT) were determined in only the environmental isolate 1J while non of the isolates produced heat stabile toxin (ST). The purification scheme was improved, few steps were adopted to include back extraction of ammonium sulfate, saturation between 80-20%, desalting through Sephadex G25, and gel filt

The effected of the long transmission line (TL) between the actuator and the hydraulic control valve sometimes essentials. The study is concerned with modeling the TL which carries the oil from the electro-hydraulic servovalve to the actuator. The pressure value inside the TL has been controlled by the electro-hydraulic servovalve as a voltage supplied to the servovalve amplifier. The flow rate through the TL has been simulated by using the lumped π element electrical analogy method for laminar flow. The control voltage supplied to servovalve can be achieved by the direct using of the voltage function generator or indirect C⁺⁺ program connected to the DAP-view program built in the DAP-card data acqu

The principal aim of this research is to use the definition of fuzzy normed space
to define fuzzy bounded operator as an introduction to define the fuzzy norm of a
fuzzy bounded linear operator then we proved that the fuzzy normed space FB(X,Y)
consisting of all fuzzy bounded linear operators from a fuzzy norm space X into a
fuzzy norm space Y is fuzzy complete if Y is fuzzy complete. Also we introduce
different types of fuzzy convergence of operators.

Shell-and-double concentric tube heat exchanger is one of the new designs that enhance the heat transfer process. Entransy dissipation is a recent development that incorporates thermodynamics in the design and optimization of heat exchangers. In this paper the concept of entransy dissipation is related to the shell-and-double concentric tube heat exchanger for the first time, where the experiments were conducted using hot oil with temperature of 80, 100 and 120°C, flow rate of cold water was 0.667, 1, and 1.334 kg/m³ respectively and the temperature of inlet cold water was 20°C. The entransy dissipation rate due to heat transfer and to fluid friction or pressure drop was studied.

      In this paper, we define a new subclass of multivalent functions defined by the generalized integral operator with negative coefficients in the open unit disk U. We also give and study some interesting properties such as coefficient estimates, subordination theorems and integral means inequalities by using the famous Littlewood's subordination theorem. Finally, we conclude a type of inequalities that is upper bound and lower bound for topology multivalent functions of all analytic functions.  

          The aim of this paper is to translate the basic properties of the classical complete normed algebra to the complete fuzzy normed algebra at this end a proof of multiplication fuzzy continuous is given. Also a proof of every fuzzy normed algebra  without identity can be embedded into fuzzy normed algebra  with identity  and  is an ideal in  is given. Moreover the proof of the resolvent set of a non zero element in complete fuzzy normed space is equal to the set of complex numbers is given. Finally basic properties of the resolvent space of a complete fuzzy normed algebra is given.

The aim of this paper is to study the effects of magnetohydrodynamic (MHD) on
flow of field of Oldroyd-B fluid between two side walls parallel to the plate .
The continuity and motion equations, for the problem under consideration are
obtained. It is found that the motion equation contains fraction derivative of
different order and the magnetohydrodynamic (MHD) parameter M .The effect of M
upon the velocity field is analyzed ,many types of fractional models are also
considered through taken different values of the fraction derivative order . This has
been done through plotting the velocity field by using Mathemitca package .
Close form for the stress tensor was obtained in many cases, which have been
studied be