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Multivariate Analysis - First Edition
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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.

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Publication Date
Sun Jun 01 2014
Journal Name
Journal Of Economics And Administrative Sciences
Design Sampling Plan when Life Time Follows Logistic Distribution
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Design sampling plan was and still one of most importance subjects because it give lowest cost  comparing with others, time live statistical distribution should be known to give best estimators for  parameters of sampling plan and get best sampling plan.

Research dell with design sampling plan when live time distribution follow Logistic distribution with () as location and shape parameters, using these information can help us getting (number of groups, sample size) associated with reject or accept the Lot

Experimental results for simulated data shows the least number of groups and sample size needs to reject or accept the Lot with certain probability of

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Publication Date
Sun Jan 01 2012
Journal Name
Ibn Al- Haitham J. Fo R Pure & Appl. Sci
Multiple Mixing Ratios of Gamma Rays From Reaction Using a2-ratio Method
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The -multiple mixing ratios of γ-transitions from levels of populated in the are calculated in the present work by using the a2-ratio methods. We used the experimental coefficient (a2) for two γ-transitions from the same initial state, the statistical tensor, which is related to the a2-coefficient would be the same for the two transitions. This method was used in a previous work for pure transitions or which can be considered pure. In these cases the multiple mixing ratios for the second transition ( ) equal zero, but in our work we applied this method for mixed γ-transitions and then the multiple mixing ratio ( ) is known for one transition. Then we calculate the ( ) value and versareversa. The weight average of the -values calcu

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Publication Date
Mon Feb 18 2019
Journal Name
Iraqi Journal Of Physics
Relative intensity distribution in the rotational structure for B1Σ+- A1Π and B1Σ+- X1Σ+ electronic systems of BeO molecule
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Theoretical spectroscopic study of  Beryllium Oxide has been carried out, Boltzmann distribution of P, Q and R branches in the range of (0<J<13) at temperature 4200K for (0-0) band for electronic transitions B1Σ+-A1Π and B1Σ-X1Σ. The Boltzmann distribution of these branches has a maximum values at equal J approximately while the values of relative population are different. For the B1Σ+- X1Σ+ transition the branch's lines extend towards lower wavenumber. This is because (Bv'-Bv") value is negative, i.e  Bv'< Bv" For B1Σ+-A1Π

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Publication Date
Mon Apr 23 2018
Journal Name
International Journal Of Quantum Information
Key rate estimation of measurement-device-independent quantum key distribution protocol in satellite-earth and intersatellite links
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In this work, an estimation of the key rate of measurement-device-independent quantum key distribution (MDI-QKD) protocol in free space was performed. The examined free space links included satellite-earth downlink, uplink and intersatellite link. Various attenuation effects were considered such as diffraction, atmosphere, turbulence and the efficiency of the detection system. Two cases were tested: asymptotic case with infinite number of decoy states and one-decoy state case. The estimated key rate showed the possibility of applying MDI-QKD in earth-satellite and intersatellite links, offering longer single link distance to be covered.

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Publication Date
Sat Jun 06 2020
Journal Name
Journal Of The College Of Education For Women
Geographical Distribution of Power Plants in Iraq in 2015 Using Geographic Information Systems
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The study aims to study the geographical distribution of electricpower plants in Iraq, except the governorates of Kurdistan Region (Dohuk, Erbil, Sulaymaniyah) due to lack of data.

In order to reach the goal of the research was based on some mathematical equations and statistical methods to determine how the geographical distribution of these stations (gas, hydropower, steam, diesel) within the provinces and the concentration of them as well as the possibility of the classification of power plants in Iraq to facilitate understanding of distribution in a scientific manner is characterized by objectively.

The most important results of the research are that there are a number of factors that led to the irregular distribution

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Publication Date
Thu Dec 01 2011
Journal Name
Journal Of Economics And Administrative Sciences
On Shrunken Estimation of Generalized Exponential Distribution
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This paper deal with the estimation of the shape parameter (a) of Generalized Exponential (GE) distribution when the scale parameter (l) is known via preliminary test single stage shrinkage estimator (SSSE) when a prior knowledge (a0) a vailable about the shape parameter as initial value due past experiences as well as suitable region (R) for testing this prior knowledge.

The Expression for the Bias, Mean squared error [MSE] and Relative Efficiency [R.Eff(×)] for the proposed estimator are derived. Numerical results about beha

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Publication Date
Sun Sep 06 2015
Journal Name
Baghdad Science Journal
Oscillations of Third Order Half Linear Neutral Differential Equations
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In this paper the oscillation criterion was investigated for all solutions of the third-order half linear neutral differential equations. Some necessary and sufficient conditions are established for every solution of (a(t)[(x(t)±p(t)x(?(t) ) )^'' ]^? )^'+q(t) x^? (?(t) )=0, t?t_0, to be oscillatory. Examples are given to illustrate our main results.

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Publication Date
Sat Jan 01 2022
Journal Name
International Journal Of Nonlinear Analysis And Applications
A general solution of some linear partial differential equations via two integral transforms
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In this paper, a new analytical method is introduced to find the general solution of linear partial differential equations. In this method, each Laplace transform (LT) and Sumudu transform (ST) is used independently along with canonical coordinates. The strength of this method is that it is easy to implement and does not require initial conditions.

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Publication Date
Sat Jan 01 2022
Journal Name
International Journal Of Hydrogen Energy
Optimisation of operating parameters on the performance characteristics of a free piston engine linear generator fuelled by CNG–H2 blends using the response surface methodology (RSM)
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The free piston engine linear generator (FPELG) is a simple engine structure with few components, making it a promising power generation system. However, because the engine works without a crankshaft, the handling of the piston motion control (PMC) is the main challenge influencing the stability and performance of FPELGs. In this article, the optimal operating parameters of FPELG for maximising engine performance and reducing exhaust gas emissions were studied. Moreover, the influence of adding hydrogen (H2) to compressed natural gas (CNG) fuel on FPELG performance was investigated. The influence of operating parameters on in-cylinder pressure was also analysed. The single-piston FPELG fuelled by CNG blended with H2 was used to run the expe

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Publication Date
Sat Apr 03 2021
Journal Name
Lubricants
UV-Visible Spectrophotometer for Distinguishing Oxidation Time of Engine Oil
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Samples of gasoline engine oil (SAE 5W20) that had been exposed to various oxidation times were inspected with a UV-Visible (UV-Vis) spectrophotometer to select the best wavelengths and wavelength ranges for distinguishing oxidation times. Engine oil samples were subjected to different thermal oxidation periods of 0, 24, 48, 72, 96, 120, and 144 hours, resulting in a range of total base number (TBN) levels. Each wavelength (190.5 – 849.5 nm) and selected wavelength ranges were evaluated to determine the wavelength or wavelength ranges that could best distinguish among all oxidation times. The best wavelengths and wavelength ranges were analyzed with linear regression to determine the best wavelength or range to predict oxidation t

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