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 (as done in the first edition 2019). 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. While the revised new chapters have been added (as the curr

This paper is concerned with pre-test single and double stage shrunken estimators for the mean (?) of normal distribution when a prior estimate (?0) of the actule value (?) is available, using specifying shrinkage weight factors ?(?) as well as pre-test region (R). Expressions for the Bias [B(?)], mean squared error [MSE(?)], Efficiency [EFF(?)] and Expected sample size [E(n/?)] of proposed estimators are derived. Numerical results and conclusions are drawn about selection different constants included in these expressions. Comparisons between suggested estimators, with respect to classical estimators in the sense of Bias and Relative Efficiency, are given. Furthermore, comparisons with the earlier existing works are drawn.

         Values ​​are penetrating or interfering in the lives of individuals and groups and are connected to them in the sense of life itself, because they are closely linked to the motives of behavior, hopes and goals, and can be said that values ​​are everything. The concept of values ​​is one of the concepts that have received the attention of researchers from different disciplines. This has resulted in a kind of confusion and variation in use from one specialization to the other, and uses multiple uses within one specialization. Therefore, there is no uniform definition of values ​​because they relate to individuals. Individuals differ in many things, such as perception,

This study reports the fabrication of tin oxide (SnO₂) thin films using pulsed laser deposition (PLD). The effect of ⁶⁰Co (300, 900, and 1200 Gy) gamma radiation on the structural, morphological, and optical features is systematically demonstrated using X-ray diffraction (XRD), field emission scanning electron microscopy (FE-SEM), atomic force microscopy (AFM), and ultraviolet-visible light analysis (UV-Vis), respectively In XRD tests, the size of the crystallites decreased from 45.5 to 40.8 nm for the control samples and from 1200 Gy to 60Co for the irradiated samples. Using FESEM analysis, the particle diameter revealed a similar trend to that attained using XRD; in particular, the average diameters were 93.8 and

 The aim of this work  is to evaluate concentrations of  natural and artificial radionuclide  in nine different samples of condiments from local markets.     The concentrations of 238 U , 232 Th ,40k  and 137Cs  were measured by using gamma spectroscopy with a high- purity germanium detector. The concentrations of 238 U, 232 Th ,40k  and 137Cs   were found to be in a range of  (21.4 - 91.13), (15.7 - 88.11) , (285.56 – 1100) and (5.1 - 27.5) Bq.kg-1  respectively. These concentrations are not hazardous to public health and the activities are within the allowed  levels

Activities associated with mining of uranium have generated significant quantities of waste materials containing uranium and other toxic metals. A qualitative and quantitative study was performed to assess the situation of nuclear pollution resulting from waste of drilling and exploration left on the surface layer of soil surrounding the abandoned uranium mine hole located in the southern of Najaf province in Iraq state. To measure the specific activity, twenty five surface soil samples were collected, prepared and analyzed by using gamma- ray spectrometer based on high counting efficiency NaI(Tl) scintillation detector. The results showed that the specific activities in Bq/kg are 37.31 to 1112.47 with mean of 268.16, 0.28 to 18.57 with

     In this study, gamma ray transmission method have been used to determine the total porosity in four samples: pure Alumina  ( Al₂O₃   ),  Al₂O₃ + (0.2wt%)MgO ,  Al₂O₃ + (0.6wt% )Y₂O₃  and Al₂O₃+ (8wt% ) ZrO₂ .

      The experimental setup for the gamma ray transmission consist of ¹³⁷Cs gamma source ( 662 KeV  ), a  NaI (Tl) scintillation detector measured the attenuation of strongly collimated  gamma beam through alumina samples.

The porosity obtained by the gamma ray transmission method were compare

In the present work the Buildup factor for gamma rays were studied in shields from epoxy reinforced by lead powder and by aluminum powder, for NaI(Tl) scintillation detector size ( ×? ), using two radioactive sources (Co-60 and Cs-137). The shields which are used (epoxy reinforced by lead powder with concentration (10-60)% and epoxy reinforced by aluminum powder with concentration (10-50)% by thick (6mm) and epoxy reinforced by lead powder with concentration (50%) with thick (2,4,6,8,10)mm. The experimental results show that: The linear absorption factor and Buildup factor increase with increase the concentration for the powders which used in reinforcement and high for aluminum powder than the lead powder and decrease with inc

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